Pumpprobe experiments in atoms involving laser and synchrotron radiation: an overview
Identifieur interne : 002137 ( Istex/Corpus ); précédent : 002136; suivant : 002138Pumpprobe experiments in atoms involving laser and synchrotron radiation: an overview
Auteurs : F J Wuilleumier ; M. MeyerSource :
- Journal of Physics B: Atomic, Molecular and Optical Physics [ 0953-4075 ] ; 2006.
Abstract
The combined use of laser and synchrotron radiations for atomic photoionization studies started in the early 1980s. The strong potential of these pumpprobe experiments to gain information on excited atomic states is illustrated through some exemplary studies. The first series of experiments carried out with the early synchrotron sources, from 1960 to about 1995, are reviewed, including photoionization of unpolarized and polarized excited atoms, and time-resolved lasersynchrotron studies. With the most advanced generation of synchrotron sources, a whole new class of pumpprobe experiments benefiting from the high brightness of the new synchrotron beams has been developed since 1996. A detailed review of these studies as well as possible future applications of pumpprobe experiments using third generation synchrotron sources and free electron lasers is presented.
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DOI: 10.1088/0953-4075/39/23/R01
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Pumpprobe experiments in atoms involving laser and synchrotron radiation: an overview</title><author><name sortKey="Wuilleumier, F J" sort="Wuilleumier, F J" uniqKey="Wuilleumier F" first="F J" last="Wuilleumier">F J Wuilleumier</name><affiliation><mods:affiliation>Laboratoire d'Interaction du Rayonnement X avec la Matire (LIXAM), Unit Mixte de Recherche no 8624, Centre Universitaire Paris-Sud, Btiment 350, F-91405 Orsay Cedex, France</mods:affiliation></affiliation></author><author><name sortKey="Meyer, M" sort="Meyer, M" uniqKey="Meyer M" first="M" last="Meyer">M. 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The strong potential of these pumpprobe experiments to gain information on excited atomic states is illustrated through some exemplary studies. The first series of experiments carried out with the early synchrotron sources, from 1960 to about 1995, are reviewed, including photoionization of unpolarized and polarized excited atoms, and time-resolved lasersynchrotron studies. With the most advanced generation of synchrotron sources, a whole new class of pumpprobe experiments benefiting from the high brightness of the new synchrotron beams has been developed since 1996. A detailed review of these studies as well as possible future applications of pumpprobe experiments using third generation synchrotron sources and free electron lasers is presented.</div></front></TEI><istex><corpusName>iop</corpusName><author><json:item><name>F J Wuilleumier</name><affiliations><json:string>Laboratoire d'Interaction du Rayonnement X avec la Matire (LIXAM), Unit Mixte de Recherche no 8624, Centre Universitaire Paris-Sud, Btiment 350, F-91405 Orsay Cedex, France</json:string></affiliations></json:item><json:item><name>M Meyer</name><affiliations><json:string>Laboratoire d'Interaction du Rayonnement X avec la Matire (LIXAM), Unit Mixte de Recherche no 8624, Centre Universitaire Paris-Sud, Btiment 350, F-91405 Orsay Cedex, France</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>review</json:string><json:string>review</json:string></originalGenre><abstract>The combined use of laser and synchrotron radiations for atomic photoionization studies started in the early 1980s. The strong potential of these pumpprobe experiments to gain information on excited atomic states is illustrated through some exemplary studies. The first series of experiments carried out with the early synchrotron sources, from 1960 to about 1995, are reviewed, including photoionization of unpolarized and polarized excited atoms, and time-resolved lasersynchrotron studies. With the most advanced generation of synchrotron sources, a whole new class of pumpprobe experiments benefiting from the high brightness of the new synchrotron beams has been developed since 1996. 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Phys.</title></host></json:item></refBibs><genre><json:string>review-article</json:string><json:string>research-article</json:string></genre><serie><volume>vol 1</volume><language><json:string>unknown</json:string></language><title>Handbuch der Physik</title></serie><host><volume>39</volume><publisherId><json:string>jpb</json:string></publisherId><pages><total>53</total><last>R477</last><first>R425</first></pages><issn><json:string>0953-4075</json:string></issn><issue>23</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1361-6455</json:string></eissn><title>Journal of Physics B: Atomic, Molecular and Optical Physics</title></host><categories><wos><json:string>science</json:string><json:string>physics, atomic, molecular & chemical</json:string><json:string>optics</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>physics & astronomy</json:string><json:string>general physics</json:string></scienceMetrix></categories><publicationDate>2006</publicationDate><copyrightDate>2006</copyrightDate><doi><json:string>10.1088/0953-4075/39/23/R01</json:string></doi><id>180A52073CAE3E69752AADCB5FE46B867C54C592</id><score>0.06766935</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/180A52073CAE3E69752AADCB5FE46B867C54C592/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/180A52073CAE3E69752AADCB5FE46B867C54C592/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/180A52073CAE3E69752AADCB5FE46B867C54C592/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Pumpprobe experiments in atoms involving laser and synchrotron radiation: an overview</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Institute of Physics Publishing</publisher><availability><p>2006 IOP Publishing Ltd</p></availability><date>2006</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Pumpprobe experiments in atoms involving laser and synchrotron radiation: an overview</title><author xml:id="author-1"><persName><forename type="first">F J</forename><surname>Wuilleumier</surname></persName><affiliation>Laboratoire d'Interaction du Rayonnement X avec la Matire (LIXAM), Unit Mixte de Recherche no 8624, Centre Universitaire Paris-Sud, Btiment 350, F-91405 Orsay Cedex, France</affiliation></author><author xml:id="author-2"><persName><forename type="first">M</forename><surname>Meyer</surname></persName><affiliation>Laboratoire d'Interaction du Rayonnement X avec la Matire (LIXAM), Unit Mixte de Recherche no 8624, Centre Universitaire Paris-Sud, Btiment 350, F-91405 Orsay Cedex, France</affiliation></author></analytic><monogr><title level="j">Journal of Physics B: Atomic, Molecular and Optical Physics</title><title level="j" type="abbrev">J. Phys. B: At. Mol. Opt. Phys.</title><idno type="pISSN">0953-4075</idno><idno type="eISSN">1361-6455</idno><imprint><publisher>Institute of Physics Publishing</publisher><date type="published" when="2006"></date><biblScope unit="volume">39</biblScope><biblScope unit="issue">23</biblScope><biblScope unit="page" from="R425">R425</biblScope><biblScope unit="page" to="R477">R477</biblScope><biblScope unit="production">Printed in the UK</biblScope></imprint></monogr><idno type="istex">180A52073CAE3E69752AADCB5FE46B867C54C592</idno><idno type="DOI">10.1088/0953-4075/39/23/R01</idno><idno type="PII">S0953-4075(06)05870-6</idno><idno type="articleID">205870</idno><idno type="articleNumber">R01</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2006</date></creation><langUsage><language ident="en">en</language></langUsage><abstract><p>The combined use of laser and synchrotron radiations for atomic photoionization studies started in the early 1980s. The strong potential of these pumpprobe experiments to gain information on excited atomic states is illustrated through some exemplary studies. The first series of experiments carried out with the early synchrotron sources, from 1960 to about 1995, are reviewed, including photoionization of unpolarized and polarized excited atoms, and time-resolved lasersynchrotron studies. With the most advanced generation of synchrotron sources, a whole new class of pumpprobe experiments benefiting from the high brightness of the new synchrotron beams has been developed since 1996. A detailed review of these studies as well as possible future applications of pumpprobe experiments using third generation synchrotron sources and free electron lasers is presented.</p></abstract></profileDesc><revisionDesc><change when="2006">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/180A52073CAE3E69752AADCB5FE46B867C54C592/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1"</istex:xmlDeclaration><istex:docType SYSTEM="http://ej.iop.org/dtd/iopv1_5_1.dtd" name="istex:docType"></istex:docType><istex:document><article artid="jpb205870"><article-metadata><jnl-data jnlid="jpb"><jnl-fullname>Journal of Physics B: Atomic, Molecular and Optical Physics</jnl-fullname><jnl-abbreviation>J. Phys. B: At. Mol. Opt. Phys.</jnl-abbreviation><jnl-shortname>JPhysB</jnl-shortname><jnl-issn>0953-4075</jnl-issn><jnl-coden>JPAPEH</jnl-coden><jnl-imprint>Institute of Physics Publishing</jnl-imprint><jnl-web-address>stacks.iop.org/JPhysB</jnl-web-address></jnl-data><volume-data><year-publication>2006</year-publication><volume-number>39</volume-number></volume-data><issue-data><issue-number>23</issue-number><coverdate>14 December 2006</coverdate></issue-data><article-data><article-type type="review" sort="regular">TOPICAL REVIEW</article-type><type-number type="review" artnum="R01">1</type-number><article-number>205870</article-number><first-page>R425</first-page><last-page>R477</last-page><length>53</length><pii>S0953-4075(06)05870-6</pii><doi>10.1088/0953-4075/39/23/R01</doi><copyright>2006 IOP Publishing Ltd</copyright><ccc>0953-4075/06/230425+53$30.00</ccc><printed>Printed in the UK</printed><features colour="none" mmedia="no" suppdata="no"></features></article-data></article-metadata><header><title-group><title>Pump–probe experiments in atoms involving laser and synchrotron radiation: an overview</title><short-title>Topical Review</short-title><ej-title>Topical Review</ej-title></title-group><author-group><author address="jpb205870ad1"><first-names>F J</first-names><second-name>Wuilleumier</second-name></author><author address="jpb205870ad1"><first-names>M</first-names><second-name>Meyer</second-name></author></author-group><address-group><address id="jpb205870ad1" showid="no"><orgname>Laboratoire d'Interaction du Rayonnement X avec la Matière (LIXAM), Unité Mixte de Recherche no 8624, Centre Universitaire Paris-Sud</orgname>, Bâtiment 350, F-91405 Orsay Cedex, <country>France</country></address></address-group><history received="12 July 2006" finalform="6 October 2006" online="17 November 2006"></history><abstract-group><abstract><heading>Abstract</heading><p indent="no">The combined use of laser and synchrotron radiations for atomic photoionization studies started in the early 1980s. The strong potential of these pump–probe experiments to gain information on excited atomic states is illustrated through some exemplary studies. The first series of experiments carried out with the early synchrotron sources, from 1960 to about 1995, are reviewed, including photoionization of unpolarized and polarized excited atoms, and time-resolved laser–synchrotron studies. With the most advanced generation of synchrotron sources, a whole new class of pump–probe experiments benefiting from the high brightness of the new synchrotron beams has been developed since 1996. A detailed review of these studies as well as possible future applications of pump–probe experiments using third generation synchrotron sources and free electron lasers is presented.</p></abstract></abstract-group></header><body numbering="bysection"><sec-level1 id="jpb205870s1" label="1"><heading>Introduction</heading><sec-level2 id="jpb205870s1-1" label="1.1"><heading>General interest</heading><p indent="no">The interaction of photon, electron or ion beams with free atoms, molecules, clusters, liquids or solids serves as a principal tool for experimentalists to obtain information about the structure of matter and the dynamics of the interaction. More specifically, the geometrical and dynamical properties of the electronic motion in the atoms can be explored using the photoionization processes [<cite linkend="jpb205870bib01">1</cite>]. In the absorption of electromagnetic radiation of low intensity by matter, the coupling of the photon to the electron is generally weak. Thus, the photoionization process can usually be treated by perturbation theory [<cite linkend="jpb205870bib02">2</cite>]. Single-electron processes dominate in the photoionization of atoms in the ground state [<cite linkend="jpb205870bib03">3</cite>, <cite linkend="jpb205870bib04">4</cite>], i.e., one electron is excited onto an empty orbital or is ejected into the continuum while all other electrons remain apparently in the same electronic configuration. It has been the success of early studies using synchrotron radiation [<cite linkend="jpb205870bib05" range="jpb205870bib05,jpb205870bib06,jpb205870bib07,jpb205870bib08,jpb205870bib09">5–9</cite>] to show that many-electron interactions (electron correlations) play a major role in describing the experimental behaviour of various photoionization parameters such as cross sections or angular distribution parameters.</p><p>Even before the laser was invented, synchrotron radiation had already been observed [<cite linkend="jpb205870bib10">10</cite>], characterized [<cite linkend="jpb205870bib11">11</cite>] and used for the first inner-shell experiments in atoms in the ground state [<cite linkend="jpb205870bib05">5</cite>, <cite linkend="jpb205870bib12">12</cite>, <cite linkend="jpb205870bib13">13</cite>]. Since the beginning, the great majority of photoionization studies have been undertaken when the initial state of the target is the ground state [<cite linkend="jpb205870bib14">14</cite>, <cite linkend="jpb205870bib15">15</cite>]. Nowadays, several atomic parameters have been measured, providing detailed information about the characteristics of the wavefunctions needed to describe the photoionization process. These wavefunctions, both their amplitude and phase, depend sensitively on the potential used to describe the system. Several experimental [<cite linkend="jpb205870bib16" range="jpb205870bib16,jpb205870bib17,jpb205870bib18,jpb205870bib19,jpb205870bib20">16–20</cite>] and theoretical [<cite linkend="jpb205870bib21">21</cite>, <cite linkend="jpb205870bib22">22</cite>] reviews have presented in detail the different investigations that have been accomplished in the field of photoionization of atoms in the ground state using synchrotron radiation.</p><p>Pump–probe experiments have proven to provide particular advantages, since they enable extension of the experimental studies from ground state targets to well-prepared excited states. In general, in such an experiment the system under investigation is prepared in an excited state using a selected excitation (photonic, electronic, ionic excitation, high-voltage discharges)—the ‘pump’—and is subsequently investigated by a beam of particles (photons, electrons, ions, neutral atoms or molecules)—the ‘probe’. The products of this process (electrons, photons, ions, fragments) are analysed using an appropriate spectroscopic technique (absorption, mass spectrometry, electron or ion spectroscopy, fluorescence spectroscopy).</p><p>Particularly interesting is the combination of two-photon sources, since dipole selection rules enable a very well defined preparation of the target. In figure <figref linkend="jpb205870fig01">1</figref>, we show two examples illustrating different pump–probe excitation schemes. The left panel describes the situation where the atom in the ground state is first brought into an excited state using photons available from the pump and the excited atomic state is either directly ionized into the continuum by the probe or resonantly excited to a doubly excited state, usually an autoionizing state. The right panel considers the situation where the ‘pump’ initiates a process, for example the electronic relaxation of an inner-shell resonance or the dissociation of a molecule into its atomic constituents, followed by the probing of the final products. In this case, a particular interest of the pump–probe experiment relies on the possibility of using pulsed sources opening access to the dynamics of a photoinduced process by time-resolved spectroscopy.
<figure id="jpb205870fig01"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig01.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig01.jpg"></graphic-file></graphic><caption id="jpb205870fc01" label="Figure 1"><p indent="no">Excitation schemes for pump–probe experiments.</p></caption></figure></p><p>Pump–probe experiments using synchrotron and laser radiations were initiated according to the first scheme (figure <figref linkend="jpb205870fig01">1</figref>), for the determination of photoexcitation and photoionization cross sections of laser-excited Na and Ba atoms [<cite linkend="jpb205870bib23" range="jpb205870bib23,jpb205870bib24,jpb205870bib25,jpb205870bib26">23–26</cite>]. Later on these measurements have been extended to studies of direct non-resonant photoionization in polarized laser-excited states (e.g. [<cite linkend="jpb205870bib27">27</cite>]) as well as to studies of polarized ground state atoms (e.g. [<cite linkend="jpb205870bib28">28</cite>]), which have been aligned or oriented by optical pumping. Similar to angle-resolved measurements and spin-resolved studies, a more complete description of the photoionization process can be obtained by making use of the alignment and orientation of the laser-excited intermediate state. Measurements of the dichroism in the electron spectrum provide an excellent tool to determine the relative amplitudes for the different dipole matrix elements and the relative phases of the outgoing electrons [<cite linkend="jpb205870bib29">29</cite>]. In addition, the detailed analysis of the polarization dependence and the comparison with theoretical predictions is very sensitive to the different electron interactions in the electronic cloud. The appropriate coupling scheme for the theoretical description of the electronic configuration can be found, since the dichroism spectra are more sensitive to the model used than conventional photoelectron spectra.</p><p>Even though photoionization experiments on atoms in the ground state are still widely pursued, it should be remembered that most of the visible matter in the universe is not in the neutral ground state, since this mass appears to be concentrated in stars or in the interstellar medium in excited or ionized states, and the investigation of excited species remains challenging and important. The use of lasers and the application of pump–probe techniques have given access to this new research field and transformed many aspects of scientific research with synchrotron radiation. The intensity and the well-defined polarization of the laser make it possible to prepare and control accurately the quantum state of excited atoms. The limitations introduced by dipole selection rules into the accessibility from the ground state to a complete class of excited states can be circumvented. The study of photoionization of atoms from excited states is already 25 years old, as described in detail in previous reviews [<cite linkend="jpb205870bib30" range="jpb205870bib30,jpb205870bib31,jpb205870bib32">30–32</cite>], but new techniques make it now a more tractable research endeavour than the huge effort required at the beginning to obtain the first data on excited atoms.</p></sec-level2><sec-level2 id="jpb205870s1-2" label="1.2"><heading>History</heading><p indent="no">With the invention of lasers at the end of the 1950s [<cite linkend="jpb205870bib33">33</cite>, <cite linkend="jpb205870bib34">34</cite>], experimentalists at last had available an intense source for pump–probe experiments to start measurements on excited or ionic systems in the laboratory. In the first experiments combining two laser systems to excite in 2p<sup>6</sup>3s<sup>2 1</sup>S<sub>0</sub> magnesium atoms both outer electrons to the 3p orbital, the resonant absorption cross section was measured around the energy of the 2p<sup>6</sup>3p<sup>2 3</sup>P<sub>2</sub> autoionizing state [<cite linkend="jpb205870bib35">35</cite>, <cite linkend="jpb205870bib36">36</cite>]. Within a few years, a significant amount of photoionization cross sections involving the outer electron in laser-excited atoms, mainly in alkali [<cite linkend="jpb205870bib37" range="jpb205870bib37,jpb205870bib38,jpb205870bib39">37–39</cite>] and alkaline-earth [<cite linkend="jpb205870bib40">40</cite>, <cite linkend="jpb205870bib41">41</cite>] atoms, were measured and compared to the results of the central field Hermann–Skillmann approximation [<cite linkend="jpb205870bib42">42</cite>, <cite linkend="jpb205870bib43">43</cite>]. Further improvements in the laser techniques added the ability to determine the angular distribution of the laser-ionized outer electron in these atoms [<cite linkend="jpb205870bib44">44</cite>]. Laser excitation of the outer electron in other atoms was, however, difficult at that time and even impossible in the rare gases because of their high excitation energies (at least 10 eV). To extend the measurements to these atoms and, in general, to access higher photon energies, other sources had to be used. The first attempts to go beyond the narrow energy range above the first ionization threshold of atoms were achieved by using the XUV continuum emitted by discharge lamps such as the Ballofet–Roman–Vodar (BRV) lamp [<cite linkend="jpb205870bib45">45</cite>]. When synchronized with powerful, pulsed lasers, the use of this continuum allowed the observation of the first inner-shell photoionization features in laser-excited lithium [<cite linkend="jpb205870bib46">46</cite>] and sodium [<cite linkend="jpb205870bib47">47</cite>] atoms. With the discovery of the emission of an intense XUV continuum radiation from the plasma produced when a solid target is hit by an intense pulsed laser, leading to the development of the dual laser-produced plasma (DLPP) technique [<cite linkend="jpb205870bib48">48</cite>], there was some hope to widely extend the field of pump–probe experiments to study the photoionization of laser-excited atoms. The development of the DLPP method, however, was mainly exploited to measure photoabsorption spectra of singly and multiply charged ions and was not much used for photoionization of excited atoms. The situation changed dramatically with the advent of synchrotron radiation. Moreover, the nature and quality of the measurements developed and improved strongly with each new type of synchrotron radiation source.</p><p>The first generation of synchrotron radiation sources was electron synchrotrons or storage rings built for the study of collisions between charged particles. Thus, they were not optimized for the production of this radiation. Despite the low intensity of the photon beams emitted by these sources (monochromatized photon flux in the 10<sup>9</sup>–10<sup>10</sup> photons s<sup>−1</sup> range), the results of the first series of experiments were so promising that the second generation of sources was built during the 1980s all over the world as dedicated sources of photons. The high electron current (several hundreds of milliamperes) in these machines increased the photon flux available into the 10<sup>11</sup>–10<sup>12</sup> photons s<sup>−1</sup> range, without much improving, however, the spectral resolution practically usable. During this period, new magnetic devices, the undulators, were designed and successfully tested, being able to provide the users with up to 10<sup>13</sup> monochromatized photons s<sup>−1</sup>. Then, new low-emittance storage rings delivering this photon flux with a spectral resolution of 10<sup>−4</sup> were designed and built during the last decade of the twentieth century. Today, there are more than 12 of these third generation synchrotron radiation sources operating, or under construction, in the world. We refer to two previous reviews [<cite linkend="jpb205870bib49">49</cite>, <cite linkend="jpb205870bib50">50</cite>] to obtain detailed information on these sources.</p><p>In parallel to this impressive development of the sources, the nature of the experiments and the quality of the results were also dramatically improved, especially for pump–probe experiments combining laser and synchrotron radiation beams. The first results of a two-photon experiment combining synchrotron and laser radiations [<cite linkend="jpb205870bib51">51</cite>] have been obtained at DESY in Hamburg in 1980 on solid krypton, using synchrotron radiation to excite excitons and a pulsed laser beam to photoionize the excitons within their lifetime. A few months later, the first successful pump–probe experiment was achieved for atomic physics studies in combining the synchrotron radiation beam emitted by the first generation storage ring ACO in Orsay with a continuous wave laser [<cite linkend="jpb205870bib52">52</cite>, <cite linkend="jpb205870bib53">53</cite>]. The experiment was performed on laser-excited sodium atoms. As we will see throughout this review, sodium with its ground state 2p<sup>6</sup>3s <sup>2</sup>S<sub>1/2</sub> is the most favourable candidate for such experiments, because the 2.11 eV photons necessary to excite the 3s-electron onto a 3p-orbital are delivered at the optimum of the efficiency curve of the easily manageable Rhodamine 6G dye used for the laser.
</p><p>The energy diagram of the excited Na levels is shown in figure <figref linkend="jpb205870fig02">2</figref> and will be frequently referred to in the following. In the first experiment, energy-resolved electron spectroscopy was used to detect the photoelectrons resulting from photoionization with synchrotron radiation. Figure <figref linkend="jpb205870fig03">3</figref> shows the original results obtained in this experiment [<cite linkend="jpb205870bib53">53</cite>, <cite linkend="jpb205870bib54">54</cite>]. In the upper part of the left panel, a photoelectron spectrum of sodium atoms in the ground state measured without the laser is shown. The intense photoelectron peak at 38 eV binding energy is due to direct photoionization of a 2p-electron leading to the unresolved 2p<sup>5</sup>3s <sup>1,3</sup>P ionic states. The low-intensity structure extending between 42 and 44 eV binding energy groups together the 2p<sup>5</sup>3p <sup>1,3</sup>L satellites arising from interchannel coupling. This structure is composed of ten unresolved fine structure levels. In the lower frame of the left panel, the photoelectron spectrum recorded when the laser was also present in the interaction volume is shown. In addition to the photoelectron lines from photoionization of atoms in the ground state, still present since only about 10% of the atoms in the vapour had been transferred to the 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> level, a new structure is observed around 40 eV binding energy, i.e., at the expected energy position of the main lines resulting from single photoionization of the 2p-electron from the excited 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> state into one of the [2p<sup>5</sup>3p <sup>1,3</sup>L] <italic>ϵl</italic> continua. Taking into account the low resolution of the experiment related to the low photon flux (about 10<sup>10</sup> photons s<sup>−1</sup> were available at 75 eV), the fine structure levels composing the 2p<sup>5</sup>3p <sup>1,3</sup>L structure in the excited state are not resolved, as in the ground state spectrum. They are shifted to lower binding energies by 2.11 eV, which is the energy brought by the laser. With this type of experiments it was demonstrated that it is possible to observe and to study modifications induced by changes of the outer electronic shells in both the direct photoionization process and the resonant photoexcitation of core electrons. All further studies on laser-excited atoms follow closely this excitation scheme described for sodium. As a comparison, one of the best spectra measured with synchrotron and laser radiations at the second generation Super ACO storage ring [<cite linkend="jpb205870bib25">25</cite>] in Orsay is shown in the right panel of figure <figref linkend="jpb205870fig03">3</figref>. The electron line intensities are significantly increased, but not the spectral resolution, underlining that major progress in this research had to wait until low-emittance high-brightness third generation synchrotron sources would be available.
<figure id="jpb205870fig02"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig02.eps" width="15.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig02.jpg"></graphic-file></graphic><caption id="jpb205870fc02" label="Figure 2"><p indent="no">Simplified energy level diagram of atomic Na.</p></caption></figure><figure id="jpb205870fig03"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig03.eps" width="21.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig03.jpg"></graphic-file></graphic><caption id="jpb205870fc03" label="Figure 3"><p indent="no">Photolectron spectra of Na atoms in the ground 2p<sup>6</sup>3s <sup>2</sup>S<sub>1/2</sub> (upper panels) and excited 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> (lower panels) states measured with 75 eV photons emitted by the first generation ACO (left part) and second generation storage ring Super-ACO (right part), respectively. Reprinted with permission from [<cite linkend="jpb205870bib54">54</cite>], copyright 1982 by the American Institute of Physics and with permission from [<cite linkend="jpb205870bib25">25</cite>], copyright 1989 by the American Physical Society.</p></caption></figure></p><p>By taking advantage of the laser polarization, the first studies of aligned or oriented excited atoms [<cite linkend="jpb205870bib55" range="jpb205870bib55,jpb205870bib56,jpb205870bib57">55–57</cite>] were performed a few years later in 1987 at the second generation synchrotron radiation source BESSY I in Berlin. In order to not destroy the laser-induced polarization by collisions and radiation trapping, the density of the atoms in the ground state had to be kept in the range of some 10<sup>10</sup> atoms cm<sup>−3</sup>. The two-photon double-resonant excitation scheme leads to a strong increase in the photoelectron signal and allowed thereby measurements with reasonably high statistics in order to deduce the relevant information. The possibility of populating the magnetic sublevels of the laser-excited state in a non-statistical way (Δ<italic>m</italic> = 0 and Δ<italic>m</italic> = ±1 transitions are favoured by linearly and circularly polarized laser light, respectively) provided access to the symmetry of core-hole excited resonances and tested successfully the theoretical predictions. Strong differences of the intensities of the Li 1s<italic>nln′l′</italic> <sup>2</sup>S, <sup>2</sup>P, <sup>2</sup>D resonances were observed after laser excitation to the 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> state, when switching the laser polarization from a direction parallel to that perpendicular to the polarization vector of the synchrotron radiation [<cite linkend="jpb205870bib55">55</cite>]. The <sup>2</sup>S resonances were much more affected than the <sup>2</sup>P or <sup>2</sup>D resonances illustrating the sensitivity of these measurements to the symmetry of the resonances.</p><p>Before moving into the various parts of this review, we like to show two examples of recent experiments. One illustrates the improvements introduced by the advent of third generation storage rings and the second highlights the new observables and phenomena becoming experimentally accessible by pump–probe experiments combining laser and synchrotron radiations. In figure <figref linkend="jpb205870fig04">4</figref>, two photoelectron spectra of atomic sodium are displayed, which were recorded after direct photoionization into the 2p<sup>−1</sup>-continuum. In the upper panel, a low-resolution photoelectron spectrum taken with 60 eV photons of the second generation source Super-ACO [<cite linkend="jpb205870bib25">25</cite>] is shown, resulting from photoionization of sodium atoms in both the ground (Na) and laser-excited 3p <sup>2</sup>P<sub>3/2</sub> (Na*) states. The second spectrum, shown in the lower frame, has been obtained recently at the third generation synchrotron source, the Advanced Light Source in Berkeley [<cite linkend="jpb205870bib58">58</cite>]. Here, a high-resolution electron spectrometer was used to measure the 2p-photoelectron spectra of Na and Na*. Most of the photoelectron lines corresponding to the various final ionic states in both atomic states are now fully resolved. The total resolution (10 meV) is such that J-resolved studies, i.e., a detailed analysis of the photoionization process and a very stringent test of the theory, are now achievable [<cite linkend="jpb205870bib59">59</cite>].
<figure id="jpb205870fig04"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig04.eps" width="21.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig04.jpg"></graphic-file></graphic><caption id="jpb205870fc04" label="Figure 4"><p indent="no">Photoelectron spectra of Na atoms in the ground 2p<sup>6</sup>3s <sup>2</sup>S<sub>1/2</sub> and excited 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> states measured with 60 eV photons at Super-ACO (upper panel) and at the ALS (lower panel) in the region of 2p-ionization. Reprinted with permission from [<cite linkend="jpb205870bib58">58</cite>], copyright 2003 by the American Institute of Physics.</p></caption></figure></p><p>The sodium atom was initially chosen mainly for feasibility experiments and the spectra do not show, at first sight, a strong qualitative difference in the behaviour of photoionization of atoms in the ground and the excited states. To conclude this introduction, a more spectacular case, the photoionization of excited chromium atoms [<cite linkend="jpb205870bib60">60</cite>], is presented. Studied 15 years later, these measurements took advantage of the improved experimental conditions provided by the use of the synchrotron radiation emitted by an undulator of the second generation BESSY I storage ring. The results are shown in figure <figref linkend="jpb205870fig05">5</figref>. The dashed line represents the photoexcitation spectrum of chromium atoms in the 3p<sup>6</sup>3d<sup>5</sup>4s <sup>7</sup>S<sub>3</sub> ground state. It displays a set of well-developed Rydberg series in the energy range around 45 eV where the 3p → <italic>n</italic>d excitations occur. The spectrum measured when a linearly polarized laser beam excites about 10% of the atoms from the ground state to the 3d<sup>5</sup>4p <sup>7</sup>P<sub>4</sub> excited state is represented by the solid line in the figure. The 3d partial cross section does not show the Rydberg series and the so-called giant 3p–3d resonance is broadened for the laser-excited chromium atoms. These results demonstrate the exceptional sensitivity of the chromium atoms to slight changes in the electron distribution.
<figure id="jpb205870fig05"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig05.eps" width="21.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig05.jpg"></graphic-file></graphic><caption id="jpb205870fc05" label="Figure 5"><p indent="no">Partial 3d-photoionization cross sections of ground state Cr 3p<sup>6</sup>3d<sup>5</sup> 4s <sup>7</sup>S<sub>3</sub> (dashed line) and laser excited Cr* 3p<sup>6</sup>3d<sup>5</sup> 4p <sup>7</sup>P<sub>4</sub> (full line) atoms in the region of 3p-excitations. Reprinted with permission from [<cite linkend="jpb205870bib60">60</cite>], copyright 1995 by the American Institute of Physics.</p></caption></figure></p><p>This review is organized in the following way. Section <secref linkend="jpb205870s2">2</secref> summarizes the theoretical calculations that have been developed for predicting some special features expected in the photoionization of excited atoms. Section <secref linkend="jpb205870s3">3</secref> describes the continuous progress made in the experimental technique to adapt the potentialities of the experiments to the performances of the various generations of synchrotron radiation sources. Section <secref linkend="jpb205870s4">4</secref> presents the main results that have been obtained using first and second generation sources. Section <secref linkend="jpb205870s5">5</secref> is dedicated to the presentation of the new results that have been made possible and actually obtained over the past 10 years by using advanced second and third generation light sources. Finally, in section <secref linkend="jpb205870s6">6</secref> we present some suggestions for future developments.</p></sec-level2></sec-level1><sec-level1 id="jpb205870s2" label="2"><heading>Theoretical background</heading><sec-level2 id="jpb205870s2-1" label="2.1"><heading>Atomic structures and dynamics</heading><p indent="no">With synchrotron radiation, multiphoton processes cannot occur, because of the poor photon intensity available in one single pulse, even when emitted from the most advanced undulators installed on third generation storage rings. Because of the broad energy range available, however, inner/outer-shell one-photon photoionization measurements have allowed many new processes to be discovered, such as the delayed onset of the maximum of the 4d-photoionization cross sections in Xe to Ba atoms [<cite linkend="jpb205870bib12">12</cite>, <cite linkend="jpb205870bib61">61</cite>] and their ions [<cite linkend="jpb205870bib62">62</cite>], the ‘collapse’ of the 3d and 4f wavefunctions in the transition elements [<cite linkend="jpb205870bib63">63</cite>] and in the lanthanides [<cite linkend="jpb205870bib64">64</cite>, <cite linkend="jpb205870bib65">65</cite>], respectively, threshold effects including post-collision interaction [<cite linkend="jpb205870bib66">66</cite>], and the Raman–Auger effect [<cite linkend="jpb205870bib67">67</cite>]. These studies have demonstrated the major role played by many-electron interactions, specifically by electron–electron correlations, to account for most of the observed phenomena. In particular, the two-electron processes are key points to our understanding of atomic structure and dynamics.</p><p>In parallel, many theoretical models have been developed, from the simplest Hermann–Skilmann [<cite linkend="jpb205870bib42">42</cite>] and Hartree–Fock [<cite linkend="jpb205870bib68">68</cite>] one-electron approximations to the most sophisticated highly correlated methods, mainly the many-body perturbation theory (MBPT) [<cite linkend="jpb205870bib02">2</cite>], the random-phase approximation with (RPAE) [<cite linkend="jpb205870bib69">69</cite>] and without (RPA, RRPA [<cite linkend="jpb205870bib70">70</cite>]) exchange, and the <italic>R</italic>-matrix theory [<cite linkend="jpb205870bib71">71</cite>].</p><p>The information obtained from photoionization studies on atoms in the ground state, however, while having a great value, is somewhat restrictive because the dipole selection rules are strictly limiting the parity of the accessible final states. Only a reduced class of them can be probed. With the advent of high-power frequency-tunable dye lasers, it has become possible to prepare the initial state in a specific way with well-defined LSJ quantum numbers and to reach highly excited states that were not previously accessible. Atomic photoionization can then be probed by two-photon, two-colour experiments. It is possible to study, e.g., by stepwise excitations, autoionizing states having the same parity as the ground state, and to obtain experimental information on their geometrical and dynamical properties. These highly excited states may be of great importance in fields such as plasma physics, astrophysics and photochemistry.</p><p>The wavefunctions, which are a measure of the potential, governing the photoionization process, can be probed over a larger range of the radial coordinates. The excitation of a valence electron onto an optical orbital can significantly modify the effective potential acting on core electrons with relatively high orbital quantum numbers (<italic>l</italic> = 2, 3), eventually resulting in a radical redistribution of the oscillator strength density. When the total potential of an atom whose atomic number <italic>Z</italic> is near that corresponding to the opening of a shell (e.g., the lanthanides, for the 4f-shell [<cite linkend="jpb205870bib64">64</cite>], and the transition elements for the 3d shell [<cite linkend="jpb205870bib63">63</cite>]), the excitation/ionization of a valence electron can modify dramatically the effective potential experienced by the (<italic>l</italic> = 2) inner electrons [<cite linkend="jpb205870bib61">61</cite>]. Then the radial distribution of the atomic wavefunctions can be changed in a controlled way by the severe contraction, sometimes called ‘collapse’, of the atomic orbitals towards the nucleus.</p><p>The general techniques for photoionization calculations are the same as for photoionization of atoms in the ground state. Many calculations on excited states have dealt first with photoionization of outer-shell electrons. For inner-shell photoionization, some new features have been discovered [<cite linkend="jpb205870bib25">25</cite>] and confirmed later by theoretical calculations [<cite linkend="jpb205870bib72">72</cite>], some other theoretical predictions [<cite linkend="jpb205870bib73">73</cite>] have been most recently verified [<cite linkend="jpb205870bib74">74</cite>]. Indeed, theory and experiment have to go hand in hand to bring new insight into the knowledge of atomic photoionization from excited states.</p><p>For photoionization of atoms in the excited state, the multiconfiguration Hartree–Fock [<cite linkend="jpb205870bib73">73</cite>], the <italic>R</italic>-matrix [<cite linkend="jpb205870bib75">75</cite>] and the saddle-point approximation [<cite linkend="jpb205870bib76">76</cite>] have been the mostly used approximations in calculating the photoionization cross sections for one- and two-electron processes. Specific calculations aiming to interpret some experimental data will be introduced and commented throughout the text of this review. Here we would like to emphasize two new features which were predicted before experimental data became available.</p><p>The calculations of photoionization cross sections and angular distribution from unpolarized atomic targets predicted a weak sensitivity to variations in screening for the photoionization of inner-shell electrons for excited alkali (sodium, potassium) atoms [<cite linkend="jpb205870bib77">77</cite>, <cite linkend="jpb205870bib78">78</cite>]. Interchannel interactions between the 2p → ϵd and 2p → ϵs transitions and four initial states were included in the Hartree–Fock calculations to estimate the effect due to the changing outer-shell electronic environment: the ground state of sodium (1s<sup>2</sup>2s<sup>2</sup>2p<sup>6</sup>3s <sup>2</sup>S<sub>1/2</sub>), the excited state of neutral sodium with the valence electron in a 3p orbit (2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub>), and a 3d orbit (2p<sup>6</sup>3d <sup>2</sup>D<sub>3/2,5/2</sub>), and the ground state of ionic sodium (2p<sup>6 1</sup>S<sub>0</sub>). In figure <figref linkend="jpb205870fig06">6</figref> the calculated cross sections are displayed as a function of the photoelectron energy. The left and right panels of the figure show separately the cross section for the 2p → ϵd and 2p → ϵs transitions. These results reveal that both the 2p-photoionization cross sections in sodium (and the 3p in potassium) and the asymmetry parameter β (not shown here) should practically not vary (to within 5%) at a fixed photoelectron energy for transitions from all initial atomic states included in the study, thus validating the expectation that the photoionization of the inner-shell 2p-electron is practically independent of the atomic orbit that the valence electron occupies. The different processes that were implicitly included in the calculations of the cross sections (i.e., only single photoionization or also multiple photoexcitation–photoionization) were not specifically defined. We will see later that the results of experiments were able to selectively determine differential variations of the various partial cross sections, as confirmed later by additional calculations [<cite linkend="jpb205870bib72">72</cite>, <cite linkend="jpb205870bib79">79</cite>].
<figure id="jpb205870fig06"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig06.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig06.jpg"></graphic-file></graphic><caption id="jpb205870fc06" label="Figure 6"><p indent="no">The calculated photoionization cross sections for the 2p<sup>6</sup><italic>nl</italic> → 2p<sup>5</sup><italic>nl</italic> + ϵd transitions in Na(<italic>nl</italic>) atoms: <italic>nl</italic> = 3s, open triangles; 3p, plus symbols; 3d, open circles (left panel). The cross section for the 2p<sup>6</sup><italic>nl</italic> → 2p<sup>5</sup><italic>nl</italic> + ϵs transitions (right panel). Reprinted with permission from [<cite linkend="jpb205870bib77">77</cite>], copyright 1982 by the American Institute of Physics.</p></caption></figure></p><p>Some years later, similar theoretical predictions were extended to situations where the principal quantum number of the excited orbital has even higher values. The calculations were performed for high-lying excited states of atomic lithium [<cite linkend="jpb205870bib73">73</cite>]. Partial cross sections were calculated for single and multiple 1s-ionization in the 1s<sup>2</sup>2p <sup>2</sup>P and 1s<sup>2</sup>3p <sup>2</sup>P excited states within the multi-configuration Hartree–Fock (MCHF) approximation, using the Fischer code for the wavefunctions of the discrete initial excited atomic and the final ionic states. In figure <figref linkend="jpb205870fig07">7</figref> we show these results for the partial photoionization cross sections involving at least one 1s electron from 1s<sup>2</sup>2p <sup>2</sup>P (left panel) and 1s<sup>2</sup>3p <sup>2</sup>P (right panel). The outstanding feature of these results is that the dominant cross sections from the 1s<sup>2</sup>3p <sup>2</sup>P excited state are found in the 1s4p <sup>3</sup>P and <sup>1</sup>P channels. For photon energies up to 100 eV above threshold, the calculations establish that there is a probability of 76% that the final state is a shake-up satellite state containing a 4p electron, and that in only 13% of the transitions the 3p electron remains in the 3p orbital, which is opposite to the general consensus that single-electron transitions dominate the photoionization process. A simple explanation is that the overlap of the 3p wavefunction in the initial 1s<sup>2</sup>3p <sup>2</sup>P state is greater with the 1s4p <sup>2</sup>P state wavefunction in the ionic state than with that of the 1s3p <sup>2</sup>P state because of the strong perturbation due to the removal of one 1s electron. A similar conclusion was also reached later by using the <italic>R</italic>-matrix approximation [<cite linkend="jpb205870bib75">75</cite>], and has just been experimentally confirmed this year [<cite linkend="jpb205870bib74">74</cite>].
<figure id="jpb205870fig07"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig07.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig07.jpg"></graphic-file></graphic><caption id="jpb205870fc07" label="Figure 7"><p indent="no">Photoionization cross sections calculated for 1s ionization in the Li* 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> (upper panel) and 1s<sup>2</sup>3p <sup>2</sup>P<sub>3/2</sub> (lower panel) excited states to various <italic>n</italic><sup>3</sup>P and <italic>n</italic><sup>1</sup>P states (<italic>n</italic> = 2, 3, 4) of the Li<sup>+</sup> ion versus photon energy.</p></caption></figure></p></sec-level2><sec-level2 id="jpb205870s2-2" label="2.2"><heading>Polarization</heading><p indent="no">The experimental techniques for pump–probe experiments combining laser and synchrotron radiation have increasingly made use of the polarization of both light sources. The possibility of varying at will the angle between the laser and synchrotron radiation polarization vectors add more information on the photoionization process, since the excited states can be laser/synchrotron aligned or oriented, thus giving rise to the observation of linear and circular dichroism effects [<cite linkend="jpb205870bib27">27</cite>]. The angular distribution of the electrons photoionized from an atomic excited state will reflect the symmetry of that state and yield phase information about the continuum wavefunctions. In addition, the ground state of the atom can be laser-prepared in a polarized state [<cite linkend="jpb205870bib28">28</cite>]. Also, the theoretical descriptions have been extended towards inclusion of alignment and orientation effects.</p><p>Starting with some early, general theoretical studies [<cite linkend="jpb205870bib80">80</cite>, <cite linkend="jpb205870bib81">81</cite>], the theory of photoionization of polarized targets has been treated in detail for direct comparison with experiments in the early 1990s [<cite linkend="jpb205870bib82">82</cite>, <cite linkend="jpb205870bib83">83</cite>]. The strong interplay between theory and experiments has allowed us to get a much deeper insight into the interaction mechanism and relaxation processes present in a multi-electron system. As for the experiments measuring the angular distribution of the outgoing electrons or their spin polarization, the investigation of polarized targets provides an additional parameter, which can be varied in a precise and controlled way. As a consequence, the measured variation of a two-photon signal is very sensitive to the photoionization dynamics and the electronic interaction, but the interpretation relies strongly on an adequate theoretical support.</p><p>In the theoretical treatment of the photoionization process, it has been convenient to use the formalism of density matrix and statistical tensors in order to describe the polarization and correlation phenomena. In this formalism, the polarization state of the atom and the photon is described by statistical tensors, which are connected with the atomic density matrix and the Stokes parameters describing the polarization of the light. The detailed derivation of all equations has been outlined in different publications [<cite linkend="jpb205870bib82">82</cite>, <cite linkend="jpb205870bib84">84</cite>, <cite linkend="jpb205870bib85">85</cite>].</p><p>In general, the differential cross section for photoionization in this formalism is given by
<display-eqn id="jpb205870eqn01" eqnnum="1"></display-eqn>where σ is the angle-integrated photoionization cross section of an unpolarized target. The <inline-eqn></inline-eqn> are the reduced tensors describing the polarization of the intermediate state, the <inline-eqn></inline-eqn> are the generalized anisotropy coefficients containing the dipole amplitudes and therefore the dynamical information about the photoionization process, and, finally, the <inline-eqn></inline-eqn> comprise the information about the particular experimental geometry.</p><p>The dichroism measurements provide as result the differences between cross sections for two directions of the atomic polarization. Only odd statistical tensors <italic>A</italic><sub>10</sub>, <italic>A</italic><sub>30</sub>,…have to be considered for measurements of the magnetic dichroism, determined by the orientation of the atom. On the other hand, even statistical tensors <italic>A</italic><sub>20</sub>, <italic>A</italic><sub>40</sub>,…contribute to the linear alignment. Starting from a particular experimental configuration and geometry and defining the adequate coupling scheme for the wavefunction of the electronic states, the general formula can be simplified. Some examples are given in the specific publications [<cite linkend="jpb205870bib86" range="jpb205870bib86,jpb205870bib87,jpb205870bib88">86–88</cite>] or in the theoretical study considering the angular distribution of photoelectrons in the resonant photoionization of polarized atoms [<cite linkend="jpb205870bib82">82</cite>]. Explicit expressions are given there for experiments performed either with a cylindrical mirror electron analyser or with an angle-resolved hemispherical analyser.</p><p>In figure <figref linkend="jpb205870fig08">8</figref>, four different types of dichroism measurements are summarized that have been applied and that can be distinguished by the way of combining different polarization for the laser and synchrotron radiation. Two counter-propagating beams are considered and the electrons are collected in a direction perpendicular to the photon propagation axis. If linearly polarized laser radiation is used for aligning the intermediate state, the linear alignment dichroism (LAD) can be measured, when the ionizing synchrotron radiation is also linearly polarized. The LAD is obtained by changing the relative angle η between the polarization vector of the laser and the synchrotron radiation. The dichroism is then given by the difference of measurements, where the two polarization vectors are perpendicular to each other. Two independent measurements at, in principle, any mutual angles can be performed. In practice, differences <italic>I</italic> (η = 0°) − <italic>I</italic>(η = 90°) and <italic>I</italic>(η = 45°) − <italic>I</italic> (η = −45°) are used which provide the quantities LAD(cos) and LAD(sin), respectively, where the notation indicates a cosine or sine dependence on the angle 2η.
<figure id="jpb205870fig08"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig08.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig08.jpg"></graphic-file></graphic><caption id="jpb205870fc08" label="Figure 8"><p indent="no">Examples of dichroisms using different polarizations of the laser and synchrotron radiations (from [<cite linkend="jpb205870bib82">82</cite>]).</p></caption></figure></p><p>If for the excitation circularly polarized light is used, the intermediate state is oriented and the linear magnetic dichroism in the angular distribution (LMDAD) and the circular magnetic dichroism (CMD) can be determined, when the synchrotron radiation in the second step is linearly or circularly polarized. In particular, the CMD has only been applied in very recent years due to the new developments of special undulators in the synchrotron radiation storage rings providing circularly polarized light also in the VUV and XUV regime.</p><p>The combination of the different dichroism measurements provides a much more detailed insight into the photodissociation dynamics. For simple systems, independent measurements result in the determination of the partial dipole matrix elements and phase differences of the outgoing electrons, leading in this way to an almost ‘complete’ description of the photoionization process. For example, the emission of a ‘p’ electron is described by the emission of an ϵs wave and an ϵd wave. Together with the relative phase, three parameters have to be determined in order to obtain a ‘complete’ description. This is of course valid only if single configuration approximations are used and relativistic effects leading to a spin–orbit coupling of the ϵd electron (ϵd<sub>3/2</sub> and ϵd<sub>5/2</sub>) are neglected. Otherwise the determination of at least five parameters will be necessary in order to obtain a complete description of the photoionization process. Therefore, it is clear that the term complete has a clear meaning only within a particular model.</p></sec-level2></sec-level1><sec-level1 id="jpb205870s3" label="3"><heading>Experimental background</heading><sec-level2 id="jpb205870s3-1" label="3.1"><heading>Characteristics of the photon sources</heading><p indent="no">Lasers and synchrotron radiation storage rings are very different sources of photons. While lasers are characterized by their high intensity, i.e., by a huge number of photons delivered per pulse (for pulsed lasers) or per second (for cw lasers), as well as by their very high monochromaticity but narrow tunability range—limited to the infrared, visible and VUV regions—synchrotron sources provide photon beams with opposite qualities: low intensity and weak number of photons per pulse, modest spectral resolution (at best 10<sup>−4</sup> with reasonable intensities) but large tunability range from the infrared to the x-ray range. In table <tabref linkend="jpb205870tab01">1</tabref>, we have listed the main characteristics of these sources. One can note that the very low number of photons available per pulse with the first generation synchrotron sources together with the limited repetition rate of the pulsed lasers made totally inefficient any attempt of combining these two sources in atomic physics. Thus, until undulators became available to users at advanced second and third generation synchrotron sources, pump–probe experiments were limited to the cw mode of operation.
<table id="jpb205870tab01" frame="topbot" indent="no"><caption id="jpb205870tc01" label="Table 1"><p indent="no">Main characteristics of laser and synchrotron radiation sources.</p></caption><tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><thead><row><entry></entry><entry>Pulsed dye laser</entry><entry>cw dye laser</entry><entry>Synchrotron radiation</entry></row></thead><tbody><row><entry>Tunability range</entry><entry>0.5 to 15 eV</entry><entry>0.8 to 6 eV</entry><entry>0.01 to 20 000 eV</entry></row><row><entry>Spectral resolution</entry><entry>10<sup>−4</sup> to 10<sup>−5</sup></entry><entry>Better than 10<sup>−8</sup></entry><entry>10<sup>−2</sup> (first generation) to 10<sup>−4</sup> (third generation)</entry></row><row><entry>Photons/pulse</entry><entry>10<sup>16</sup> to 10<sup>18</sup></entry><entry></entry><entry>10<sup>4</sup> (1 ns pulsewidth, first generation) to 10<sup>6</sup></entry></row><row><entry></entry><entry></entry><entry></entry><entry>(30 ps pulsewidth, third generation)</entry></row><row><entry>Photons/s</entry><entry></entry><entry>10<sup>18</sup>–10<sup>20</sup></entry><entry>10<sup>11</sup> (first generation) to 10<sup>13</sup> (third generation</entry></row><row><entry></entry><entry></entry><entry></entry><entry>in 10<sup>−4</sup> spectral bandwith)</entry></row><row><entry>Repetition rate</entry><entry>Hz to MHz</entry><entry></entry><entry>1 to 10 MHz</entry></row><row><entry>Pulse width</entry><entry>fs to ns</entry><entry></entry><entry>30 ps (at best 1 ps at low flux in the low α-mode)</entry></row><row><entry>Polarization</entry><entry>linear or</entry><entry>linear or</entry><entry>linear (circular at low intensity, first generation),</entry></row><row><entry></entry><entry>circular</entry><entry>circular</entry><entry>linear or circular (third generation)</entry></row></tbody></tgroup></table></p></sec-level2><sec-level2 id="jpb205870s3-2" label="3.2"><heading>Experimental set-ups for pump–probe studies</heading><p indent="no">The simplest measurement to analyse photoionization processes is to detect the photoions produced by the interaction of the photons with the atoms being studied. For photoionization of excited states, however, a significant, even dominant, part of the target atoms is still in the ground state. Consequently, measuring photoions does, in general, not allow us to distinguish between ionization of atoms in the ground and the excited states. The only experimental technique able to provide precise information is electron spectrometry [<cite linkend="jpb205870bib09">9</cite>], since electrons have different kinetic energies as a result of photoionization with a monochromatic radiation. In this way, it is possible to selectively detect photoionization in every subshell having a binding energy lower than the photon energy, and thus to determine the partial photoionization into different channels and over extended energy ranges. Photoelectron spectrometry also eliminates spurious results eventually resulting from other radiations with photon energies differing from the monochromatic beam eventually transmitted by the monochromator.</p><sec-level3 id="jpb205870s3-2-1" label="3.2.1"><heading>Target preparation and detection system</heading><p indent="no">The set-up that was chosen for the first pump–probe experiment consists of a monochromator, a laser whose output is tailored for the particular experiment, an electron spectrometer and an oven to produce the atoms to be studied, as displayed in figure <figref linkend="jpb205870fig09">9</figref> [<cite linkend="jpb205870bib52" range="jpb205870bib52,jpb205870bib53,jpb205870bib54">52–54</cite>]. Synchrotron radiation from the first generation ACO storage ring was monochromatized by a high-transmission toroidal grating monochromator delivering up to 10<sup>12</sup> photons s<sup>−1</sup> in a 1% spectral band width for photon energies between 20 eV and 100 eV. The output of the monochromator was focused by a toroidal mirror into the source volume of a cylindrical mirror analyser (CMA). A resistively heated oven, collinear to the common axis of the CMA and photon beam, was emitting a weakly collimated beam of metallic vapour towards the source volume of the CMA at densities up to 10<sup>13</sup> atoms cm<sup>−3</sup>. The laser beam was produced by a cw argon-ion pumped dye laser operating in the mono-mode regime. It was defocused to fit the size of the source volume of the CMA (2 × 2 × 4 mm<sup>3</sup>). A small amount of the laser beam was sent into an auxiliary furnace. The resulting fluorescence, recorded with a photomultiplier, was used to lock the wavelength of the laser to the desired transition. The electrons produced from the ground and the excited states by photoionization were energy analysed at the magic angle.
<figure id="jpb205870fig09"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig09.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig09.jpg"></graphic-file></graphic><caption id="jpb205870fc09" label="Figure 9"><p indent="no">Experimental setup for the first laser-synchrotron pump–probe experiments. A cylindrical mirror analyser was used to energy analyse the electrons produced by photoionization of the laser excited Na atoms with the synchrotron radiation emitted by the first generation ACO storage ring. The fluorescence measured in an auxiliary Na oven served to lock the laser to the 2p<sup>6</sup>3s <sup>2</sup>S<sub>1/2</sub> → 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> transition (adapted from [<cite linkend="jpb205870bib54">54</cite>]).</p></caption></figure></p><p>In this experiment, like in all experiments dedicated to the determination of partial cross sections in excited states using first and second generation synchrotron sources, the atomic density in the interaction zone was kept high, between 10<sup>12</sup> and 10<sup>13</sup> atoms cm<sup>−3</sup>, and any alignment induced by the laser in the intermediate state was lost by collisions and radiation trapping. Due to this high density, associative ionization and energy pooling resulting from collisions between excited atoms produced a huge number of low-energy electrons [<cite linkend="jpb205870bib89">89</cite>]. These electrons can undergo super-elastic collisions with excited sodium atoms and gain energy in 2.11 eV steps [<cite linkend="jpb205870bib90">90</cite>, <cite linkend="jpb205870bib91">91</cite>]. Electrons accelerated by up to three successive collisions have been observed [<cite linkend="jpb205870bib89">89</cite>]. The production of these electrons is a troublesome source of high background and may mask the photoionization spectrum resulting from processes with cross sections two orders of magnitude lower than the collisions. The presence of electrons and positive ions transforms the vapour in a low temperature plasma, as a plasma shift is observed in the photoelectron spectra from excited states, decreasing the measured kinetic energies of the electrons by as much as 1 eV (when about 30% of the atoms are initially in the excited state with a density in the order of 10<sup>13</sup> atoms cm<sup>−3</sup>).</p><p>To analyse the angular distribution of the photoelectrons emitted from unpolarized targets, a modified CMA was used for determination of the asymmetry parameter β [<cite linkend="jpb205870bib72">72</cite>]. In the detection system, the channeltron previously placed on the CMA axis in the measurements of partial cross sections was removed and a set of six identical channeltrons was installed in the focal plan of the CMA between the two inner cylinders. The advantage of such a device as compared to a rotating electron spectrometer is that at each angle the full spectrum is simultaneously measured, eliminating the effect of any variation in the density of atoms in the excited state.</p><p>For the early experiments on laser-polarized excited atoms, the polarization of the fluorescence emitted by the active volume was analysed as a function of the density of atoms in the ground state [<cite linkend="jpb205870bib57">57</cite>]. This polarization is shown in the left part of figure <figref linkend="jpb205870fig10">10</figref>, for the case of lithium atoms excited into the 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> state. It is decreasing with increasing density, reaching a value close to zero between 10<sup>11</sup> and 10<sup>12</sup> atoms cm<sup>−3</sup>. Thus, the experiments were performed at atomic densities between 10<sup>10</sup> and 10<sup>11</sup> atoms cm<sup>−3</sup> using at the beginning an angle-integrating CMA to detect the electrons [<cite linkend="jpb205870bib55">55</cite>, <cite linkend="jpb205870bib56">56</cite>]. The synchrotron beam was counter-propagating to the laser beam, as shown in figure <figref linkend="jpb205870fig11">11</figref>. The atomic vapour beam propagated in the <italic>x</italic>-direction perpendicularly to the synchrotron and laser. The axis of the spectrometer was perpendicular to this direction. The polarization axis of the laser lied in the <italic>x</italic>–<italic>z</italic> plane at an angle η with respect to the <italic>z</italic>-axis. For the first angular distribution studies [<cite linkend="jpb205870bib92">92</cite>], the general scheme was the same, but the CMA was replaced by a movable electron spectrometer, which was rotated around the laser and synchrotron beams (figure <figref linkend="jpb205870fig11">11</figref>).
<figure id="jpb205870fig10"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig10.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig10.jpg"></graphic-file></graphic><caption id="jpb205870fc10" label="Figure 10"><p indent="no">Left: degree of polarization of the fluorescence from the Li* 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> excited state as a function of the particle density. Reprinted with permission from [<cite linkend="jpb205870bib57">57</cite>], copyright 1990 by the Royal Swedish Academy of Sciences. Right: two photoelectron spectra from the Na 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> excited state into the final ionic states 2p<sup>5</sup>3p <sup>(2S + 1)</sup>L<sub>J</sub> measured at the ALS for two different relative orientations (parallel, full line, and perpendicular, dashed line) of the polarization vectors of the laser and synchrotron radiations at target densities of 10<sup>12</sup>–10<sup>13</sup> atoms cm<sup>−3</sup>.</p></caption></figure><figure id="jpb205870fig11"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig11.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig11.jpg"></graphic-file></graphic><caption id="jpb205870fc11" label="Figure 11"><p indent="no">Scheme of the arrangement in the angle-resolved photoionization experiments on laser-prepared polarized atomic states. Laser and synchrotron radiations propagate in opposite directions along the <italic>y</italic>-axis. Both photon beams intersect the atomic beam in the source volume of a rotatable electron spectrometer. Reprinted with permission from [<cite linkend="jpb205870bib92">92</cite>], copyright 1992 by the American Physical Society.</p></caption></figure></p></sec-level3><sec-level3 id="jpb205870s3-2-2" label="3.2.2"><heading>New features with third generation sources</heading><p indent="no">The improvements in the performances of the synchrotron radiation sources (undulators at second and third generation sources) had to be accompanied by a similar progress in the detection system. In order to fully exploit the high spectral resolution, in the 10 meV range, also a high-resolution electron spectrometer had to be used. This was given by the specific development of a hemispherical analyser and its position sensitive detection system, the Scienta analyser [<cite linkend="jpb205870bib93">93</cite>], which became commercially available at this time. It was used at the ALS [<cite linkend="jpb205870bib58">58</cite>, <cite linkend="jpb205870bib59">59</cite>] for J-resolved photoionization (see figure <figref linkend="jpb205870fig04">4</figref>) and for cross section measurements as well as at BESSY II and DESY [<cite linkend="jpb205870bib87">87</cite>, <cite linkend="jpb205870bib88">88</cite>] for resonant and continuum photoionization of polarized atoms. This new experimental set-up served especially for the investigation of the linear alignment dichroism in magnetic 3d-atoms laser-aligned either in the ground or in the excited state.</p><p>In addition, with the advent of third generation storage rings, polarization effects could also be observed at high atomic densities, as it has been measured in recent experiments at the ALS [<cite linkend="jpb205870bib59">59</cite>]. In the right part of figure <figref linkend="jpb205870fig10">10</figref> are shown two photoelectron spectra recorded upon photoionization of sodium atoms excited in the 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> state, and measured at an atomic density close to 10<sup>13</sup> atoms cm<sup>−3</sup>. The linear polarization of the laser was either parallel (spectrum in full line) or perpendicular (spectrum in dashed line) to the linear polarization of the synchrotron beam. For some of the final ionic states, the relative intensities of the corresponding photolines depend strongly on the angle between the two polarizations, demonstrating that the excited atoms are still polarized. This effect results from a strong reduction of the radiation trapping in the source volume seen by the electron spectrometer as a consequence of the quite reduced size of this volume (the diameter perpendicular to the propagation direction of the synchrotron radiation is less than 100 µm).</p></sec-level3></sec-level2><sec-level2 id="jpb205870s3-3" label="3.3"><heading>Techniques of synchronization</heading><p indent="no">Already in the very beginning of pump–probe experiments combining laser and synchrotron radiation, the idea came up to use a pulsed laser synchronized to the pulses of the synchrotron. This would provide the experimental access to time-resolved experiments as well as increase substantially the duty cycles, i.e., the general temporal overlap between laser and synchrotron radiation.</p><p>We take as a concrete example the characteristics of the installation at the Super-ACO storage ring (figure <figref linkend="jpb205870fig12">12</figref>), where some of the early experiments in the gas phase have been performed [<cite linkend="jpb205870bib94" range="jpb205870bib94,jpb205870bib95,jpb205870bib96">94–96</cite>]. The synchrotron radiation was characterized by a pulsed structure with a repetition rate of 8.32 MHz in the two-bunch mode and a temporal width of about 500 ps for the individual synchrotron pulses. The later value has been strongly improved for the third generation sources characterized by pulse widths of about 30–50 ps. Ideally, the pulsed laser should have very similar characteristics. For the experiments at Super-ACO, a mode-locked Ar-ion laser (repetition rate of 74.88 MHz and pulse width of 230 ps) was used. In order to obtain synchronization two main conditions have to be fulfilled: (i) the ratio between both repetition rates has to be exactly equal to an integer number (at Super-ACO <italic>f</italic>(SR)/<italic>f</italic>(laser) ≡ 9) and (ii) the two pulsed sources have to rely on the same time standard in order to counterbalance possible drifts in only one of them (at Super-ACO the 10 MHz master clock of the storage ring was also used as reference for the mode-locker of the laser). The absolute time delay between laser and synchrotron pulses was controlled inside the experimental vacuum chamber, by a small fast photodiode providing a first ‘coarse’ calibration as well as an indication for the spatial overlap in the interaction volume for the experiment. The optimal conditions and time delay ‘zero’ were finally determined by the experiment itself, i.e., by monitoring a typical two-photon signal as a function of the temporal delay.
<figure id="jpb205870fig12"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig12.eps" width="15pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig12.jpg"></graphic-file></graphic><caption id="jpb205870fc12" label="Figure 12"><p indent="no">Experimental setup used to synchronize the light pulses of a linear dye laser and of the synchrotron radiation emitted by the Super-ACO storage ring (from [<cite linkend="jpb205870bib128">128</cite>]).</p></caption></figure></p><p>After the demonstration of stable synchronization using the 514 nm line of the mode-locked Ar-ion laser for ionizing excited He atoms, which had been prepared before by resonant excitation with the synchrotron radiation, the technique was further improved by the installation of a linear dye laser and a cavity dumper [<cite linkend="jpb205870bib97">97</cite>]. The dye laser, which was synchronously pumped by the Ar-ion laser, has the same pulse structure, but a much smaller temporal width (5–10 ps) due to its larger spectral range. In addition, a cavity dumper allowed us to select only a particular number of pulses and thereby to obtain an equal repetition rate for both sources. With this extension, time-resolved experiments on the picosecond time scale with two wavelength-tunable sources are feasible. In particular, two-photon double-resonant excitation schemes via short-lived intermediate states can be investigated. Comparing the use of a continuous wave with a pulsed synchronized laser, an increase of the two-photon intensity by almost two orders of magnitude has been determined for the investigation of even parity states of Xe [<cite linkend="jpb205870bib97">97</cite>, <cite linkend="jpb205870bib98">98</cite>]. In general, the advantage of the technique is maximized when the temporal width of both sources (synchrotron and laser) is very similar to the lifetime of the excited intermediate state.</p></sec-level2></sec-level1><sec-level1 id="jpb205870s4" label="4"><heading>The early experiments</heading><p indent="no">In this section, we will present and discuss the experiments performed using first and second generation synchrotron radiation sources, i.e., with sometimes high intensity but low resolution of the synchrotron beam. Some of the given examples have been the pioneering experiments preparing the ground for the full exploitation of the method using third generation sources. We sub-divide this presentation into four parts: photoionization of unpolarized excited atoms, first studies on polarized targets, synchronization experiments and photoionization of atomic fragments following dissociation of small molecules.</p><sec-level2 id="jpb205870s4-1" label="4.1"><heading>Photoionization of unpolarized excited atoms</heading><p indent="no">For the measurements described thereafter, the low-resolution CMA electron spectrometer described in section <secref linkend="jpb205870s3">3</secref> was used to energy analyse the electrons. The alkali (Li, Na and K) and alkaline-earth (Ba) atoms were the only atomic systems which could be laser-excited with a significant efficiency at this time.</p><p>As mentioned in the introduction, sodium is the best candidate for quantitative studies in pump–probe experiments because of the easiness to excite the Na* 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> state. Following the first experiments (see figure <figref linkend="jpb205870fig03">3</figref>), the absolute values of the oscillator strengths for transitions to the Na<sup>**</sup> 2p<sup>5</sup>3s3p <sup>(2S + 1)</sup>L<sub>J</sub> autoionizing states were determined [<cite linkend="jpb205870bib23">23</cite>] by normalization of the relative data to the photoabsorption cross section for Na atoms in the ground state [<cite linkend="jpb205870bib99">99</cite>]. The sum of the measured oscillator strengths was 0.22 (4), in good agreement with the results of a calculation for neon providing a value of 0.23 [<cite linkend="jpb205870bib100">100</cite>]. The close correspondence between the experimental and calculated values was satisfactory and demonstrated the validity of the experimental approach [<cite linkend="jpb205870bib23">23</cite>].</p><p>For the determination of partial photoionization cross sections in excited sodium, photoelectron spectra similar to the one shown in figure <figref linkend="jpb205870fig03">3</figref> (right part, lower panel) served to establish a valid basis for the relative intensities of the various photoionization processes in excited sodium. After comparison between the main lines, shake-up and interchannel coupling satellites, relative cross sections were determined. The first results [<cite linkend="jpb205870bib25">25</cite>] showing the branching ratios between the two groups of main lines (2p<sup>5</sup>3p <sup>1,3</sup>S, P, D compared to 2p<sup>5</sup>3s <sup>1,3</sup>P final ionic states) are presented in the upper panel (left part) of figure <figref linkend="jpb205870fig13">13</figref>. On average, single photoionization in the excited sodium atoms is systematically lower than that for atoms in the ground state. The experimental ratio of 0.80(4) between these two cross sections apparently did not confirm the theoretical predictions [<cite linkend="jpb205870bib77">77</cite>, <cite linkend="jpb205870bib78">78</cite>]. However, the experimental results for the relative intensities of the shake-up satellites (2p<sup>5</sup>4p <sup>1,3</sup>S, P, D/2p<sup>5</sup>3p <sup>1,3</sup>S, P, D) and 2p<sup>5</sup>4s <sup>1,3</sup>P (mixed with 2p<sup>5</sup>3d)/2p<sup>5</sup>3s <sup>1,3</sup>P final ionic states reveal a strong enhancement of these satellites in the photoionization of the excited state, as shown in the right part of figure <figref linkend="jpb205870fig13">13</figref>: about 40% against less than 20% in the ground state. These data were further corroborated by theoretical calculations carried out within the <italic>R</italic>-matrix approximation [<cite linkend="jpb205870bib72">72</cite>] which are in excellent agreement with the experimental data (solid line in figure <figref linkend="jpb205870fig13">13</figref>), while some MCHF calculations [<cite linkend="jpb205870bib101">101</cite>] are rather in poor agreement, confirming the need of highly correlated calculations to reproduce the experimental results. Physically, the behaviour of the shake-up satellite intensities in the excited atom is due to a larger overlap [<cite linkend="jpb205870bib73">73</cite>] of the orbital occupied by the shake electron with the orbital occupied by this electron in the initial state following the formation of a core hole, which creates differences in the contraction of the various orbitals.
<figure id="jpb205870fig13"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig13.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig13.jpg"></graphic-file></graphic><caption id="jpb205870fc13" label="Figure 13"><p indent="no">Left: ratio between the single 2p photoionization cross sections in the 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> excited and the 2p<sup>6</sup>3s <sup>2</sup>S<sub>1/2</sub> ground states (upper panel) and between the total 2p cross sections (lower panel) versus photon energy. Right: relative intensity of the shake-up satellites for sodium atoms in the ground state (lower series of points) and in the 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> excited state (upper series of points) versus photon energy. Theoretical results are from the <italic>R</italic>-matrix (full lines) and MCHF (dashed lines) approximations. Reprinted with permission from [<cite linkend="jpb205870bib25">25</cite>, <cite linkend="jpb205870bib72">72</cite>], copyright 1989 and 1995 by the American Physical Society.</p></caption></figure></p><p>In contrast, the relative intensities of the interchannel coupling (IC) satellites do not show any significant variation when comparing atoms in the ground and excited states, as illustrated in figure <figref linkend="jpb205870fig14">14</figref>. The left part shows the energy dependence of the relative intensity of the 2p<sup>5</sup>3p IC satellites from the ground state [<cite linkend="jpb205870bib102">102</cite>] (branching ratio between 2p<sup>5</sup>3p <sup>1,3</sup>S, P, D and 2p<sup>5</sup>3s <sup>1,3</sup>S final ionic states) and the right part the relative intensity of the IC satellites in photoionization of the 2p<sup>6</sup>3p excited atoms [<cite linkend="jpb205870bib103">103</cite>] (branching ratio between 2p<sup>5</sup>4s <sup>1,3</sup>P together with the unresolved 2p<sup>5</sup>3d and 2p<sup>5</sup>3p <sup>1,3</sup>S, P, D final ionic states). The absolute values of the branching ratios as well as their expected photon energy dependences (slowly decreasing from 14% to 7% with increasing photon energies) are the same, within the experimental accuracy.
<figure id="jpb205870fig14"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig14.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig14.jpg"></graphic-file></graphic><caption id="jpb205870fc14" label="Figure 14"><p indent="no">Relative intensities of the interchannel coupling satellites lines produced with a change in the angular momentum of the excited electron in photoionization of Na in the ground state (Na 3s, left panel, and in the first excited state (Na 3p, right panel). Reprinted with permission from [<cite linkend="jpb205870bib102">102</cite>], copyright 1991 by Les Editions de Physique.</p></caption></figure></p><p>Finally, the contribution of the double ionization cross section (1 to 3% [<cite linkend="jpb205870bib104">104</cite>]) for sodium atoms in the ground state was added in the branching ratio. Then, for the branching ratios between the total 2p-photoionization cross sections in the excited and ground states, respectively, the data do not suggest any photon energy dependence, but they are now quite close to 100%. Thus, the picture emerging from this detailed comparison for the case of sodium is that the many-body predictions are valid, provided the total photoabsorption cross section is considered, and not just the partial 2p → ϵd and 2p → ϵs cross section. It suggests that the MBPT calculations implicitly include the contribution of all processes in the calculation of the 2p → <italic>ϵl</italic> transitions.</p><p>Probing photoionization in the 2s-subshell of laser-excited sodium atoms leads to a similar conclusion [<cite linkend="jpb205870bib105">105</cite>]. The same kind of studies was performed in laser-excited lithium [<cite linkend="jpb205870bib106">106</cite>] and potassium [<cite linkend="jpb205870bib107">107</cite>] atoms. These measurements confirm the enhancement of the relative intensity of shake-up satellites in excited atoms. It should be noted, however, that the smaller <italic>Z</italic>, the higher is this enhancement: 60% in lithium, against 40% as measured in sodium, and 15 to 20% in potassium atoms. This trend is easily understandable since the removal of one inner electron out of a total of three electrons from lithium evidently creates a much stronger perturbation than removing one 3p electron out of 19 electrons in potassium.</p><p>The first determination of the absolute value of an inner-shell photoionization cross section over a broad photon energy range in an excited atomic state was made for laser-excited barium atoms [<cite linkend="jpb205870bib26">26</cite>]. Photoelectron spectra following photoionization of 4d-, 5s-, 5p-, 5d- and 6s electrons in barium atoms laser-excited into the 4d<sup>10</sup>5s<sup>2</sup>5p<sup>6</sup>6s6p <sup>1</sup>P<sub>1</sub> state were observed using synchrotron radiation from the ACO [<cite linkend="jpb205870bib108">108</cite>] and BESSY I [<cite linkend="jpb205870bib109">109</cite>] storage rings. A cw single-mode ring dye laser was locked to the 6s<sup>2 1</sup>S → 6s6p <sup>1</sup>P transition at 553.5 nm. Under steady-state conditions, however, it was found that most of the excited atoms were accumulated in the 6s5d <sup>1,3</sup>D metastable states via radiative decay. This situation is reflected in the spectrum [<cite linkend="jpb205870bib26">26</cite>, <cite linkend="jpb205870bib108">108</cite>] shown in figure <figref linkend="jpb205870fig15">15</figref>. It was recorded at a photon energy of 43 eV on barium atoms in the ground state 6s<sup>2 1</sup>S<sub>o</sub> (upper part) and in the ground and 6s5d <sup>1,3</sup>D excited states (lower part) as demonstrated by the observation of the photoelectron line that was produced by ionization of the 5d electrons (binding energy of 3.8 eV) by first-order photons. The other photoelectron lines result from the emission of 5p and 4d electrons by third-order, and 5s electrons by second-order photons transmitted by the monochromator. After normalization to the 5p photoionization cross section measured for ground state atoms [<cite linkend="jpb205870bib110">110</cite>], the energy variation of the 5d (figure <figref linkend="jpb205870fig16">16</figref>, left part, [<cite linkend="jpb205870bib26">26</cite>]) and 5p (right part, [<cite linkend="jpb205870bib111">111</cite>]) cross sections was determined. The experimental data are compared with the results of two different calculations: a local density approximation (LDA, a single-electron model) and a local-density-based random-phase approximation (LDRPA). In the photon energy range below 40 eV, both models reproduced the general non-resonant behaviour of the 5d cross section rather satisfactorily. Between 80 eV and 110 eV, the 5d and 5p cross sections undergo a strong enhancement after the opening of the 4d ionization channels. Similar resonance effects have been first observed for photoionization of xenon [<cite linkend="jpb205870bib08">8</cite>] and barium atoms in the ground state. They are reproduced only by the LDRPA model (solid lines in figure <figref linkend="jpb205870fig16">16</figref>), taking into account inner-shell interactions with the 4d-subshell. The dashed line shown for the 5p-cross section is the result of an earlier one-electron model calculation [<cite linkend="jpb205870bib112">112</cite>] predicting a continuously decreasing cross section towards high photon energy.
<figure id="jpb205870fig15"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig15.eps" width="15pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig15.jpg"></graphic-file></graphic><caption id="jpb205870fc15" label="Figure 15"><p indent="no">Photoelectron spectra of Ba atoms in the 5p<sup>6</sup>6s<sup>2 1</sup>S<sub>o</sub> ground state (upper panel) and in a mixture of Ba atoms in the ground and 5p<sup>5</sup>6s5d <sup>1,3</sup>D excited states (lower panel) taken at a photon energy of 43 eV (from [<cite linkend="jpb205870bib26">26</cite>]).</p></caption></figure><figure id="jpb205870fig16"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig16.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig16.jpg"></graphic-file></graphic><caption id="jpb205870fc16" label="Figure 16"><p indent="no">Photoionization cross sections in the 5d (left panel) and 5p (right panel) subshells of Ba atoms excited in the 6s5d <sup>1,3</sup>D states. The theoretical results are from the LDRPA approximation (full line) and the one-electron LDA calculation (dashed line). Left panel: reprinted with permission from [<cite linkend="jpb205870bib26">26</cite>], copyright 1986 by the American Physical Society; right panel: reprinted with permission from [<cite linkend="jpb205870bib111">111</cite>], copyright 1987 by Les Editions de Physique.</p></caption></figure></p><p>As already discussed in the introduction (figure <figref linkend="jpb205870fig05">5</figref>), the measurements of the 3d cross section have been performed on a relative scale for chromium atoms in the ground state and in the first excited state [<cite linkend="jpb205870bib60">60</cite>]. They demonstrated the sensitivity of the cross section to small changes in the electronic cortege. To the best of our knowledge, there were no other significant determinations of cross sections in excited atoms made at this time. In one case, the angular distribution of photoelectrons emitted from unpolarized excited atoms was measured [<cite linkend="jpb205870bib72">72</cite>] using the photon beam emitted by a bending magnet of the Super-ACO storage ring to photoionize Na atoms excited in the 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> state. The variation of the angular distribution parameter β of the photoelectrons ejected in single 2p-photoionization was obtained as a function of photon energy between 50 and 115 eV, in good agreement with the results of the <italic>R</italic>-matrix calculations. This shows that the correlations between the core and the excited valence electrons are weak, while the excitation of the outer electron has a strong influence on the correlation effects within the core electrons.</p><p>An attempt was also made to reach highly excited atomic states below the first ionization threshold. Two laser beams populating either the 4d or 5s excited states of Na were used in combination with synchrotron radiation [<cite linkend="jpb205870bib24">24</cite>, <cite linkend="jpb205870bib113">113</cite>]. When exciting these highly excited states, however, radiative decay occurs and also populates, after the excitation of the 4d <sup>2</sup>D<sub>5/2</sub> state, the 4p <sup>2</sup>P<sub>3/2</sub>, 4s <sup>2</sup>S<sub>1/2</sub> and 3d <sup>2</sup>D<sub>5/2,3/2</sub> states. Following excitation of the 5s <sup>2</sup>S<sub>1/2</sub> state, mainly the 4p <sup>2</sup>P<sub>3/2</sub> and, to a lesser extent, the 4s <sup>2</sup>S<sub>1/2</sub> states were populated. Exciting an inner 2p-electron from these various laser-excited states provided rather complicated spectra. With the two lasers and the synchrotron photon beam, a huge background, originating from collisions in the beam between atoms excited in various excited states, was masking the electron lines due to direct photoionization into the continuum. Strong autoionization lines were emerging only above the sea of low-energy electrons. Large improvements in the experimental techniques were necessary in order to be able to observe direct photoionization from the individually resolved, optically excited states.</p></sec-level2><sec-level2 id="jpb205870s4-2" label="4.2"><heading>First studies on polarized targets</heading><p indent="no">In addition to the possibilities brought along by using the spectral properties of laser and synchrotron radiation, the polarization has also been exploited. The polarization of the laser light can be changed rather easily, i.e., it can be switched from linear to circular polarization, and the direction of the linear polarization vector as well as the sense of the helicity of the circularly polarized light can be freely chosen. The synchrotron radiation in the first experiments was linearly polarized with rather high purity and with the main axis in the horizontal plane. The photoexcitation with polarized radiations induces an unequal population of the magnetic sublevels of the excited state, i.e., an alignment or an orientation of the target. In this way, by making use of the dipole selection rules, not only for the total angular momentum <italic>J</italic>, but also for the magnetic momentum <italic>m<sub>J</sub></italic>, the photo-excitation and ionization processes can be studied in much greater detail.</p><p>In general, linearly polarized light induces transitions between magnetic sublevels, which are characterized by the selection rule Δ<italic>m<sub>J</sub></italic> = 0. For circularly polarized light, only transitions with Δ<italic>m<sub>J</sub></italic> = −1 and +1 are allowed for left- and right-handed helicity of the radiation, respectively. An illustrative example is given in figure <figref linkend="jpb205870fig17">17</figref> by the excitation from an atomic ground state with the total angular momentum <italic>J</italic> = 1/2 to an excited state with <italic>J</italic> = 3/2. Linearly polarized light will populate the <italic>m<sub>J</sub></italic> = ±1/2 levels only and thereby introduce an alignment of the excited state. Right-handed circularly polarized light induces population of the <italic>m<sub>J</sub></italic> = +1/2, +3/2 levels and thereby introduces directionality, i.e., orientation, to the system. In practice, the situation can be more complicated and various other processes have to be considered. In the experiments using a continuous wave laser, many excitation and relaxation processes take place during the time the atom is in the region of the laser beam and a final effective polarization is produced. This can be different from the one produced after the first excitation, in particular for cases where states of higher angular momenta are involved. Rate equations have to be solved in order to obtain the final polarization. Furthermore a possible hyperfine structure of the states has to be taken into account. In the relaxation of the excited state, this might lead to population of ground state levels, which are not pumped by the laser radiation and are therefore lost for the excitation process.
<figure id="jpb205870fig17"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig17.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig17.jpg"></graphic-file></graphic><caption id="jpb205870fc17" label="Figure 17"><p indent="no">Scheme for alignment and orientation of atoms with linearly and circularly polarized light, respectively.</p></caption></figure></p><p>Low target densities have been compensated rather efficiently by making use of the much higher cross section for resonant excitation. Therefore the first results on laser-aligned atoms [<cite linkend="jpb205870bib55">55</cite>] were obtained by studying the double-resonant excitation of atomic Li following the excitation scheme:
<display-eqn id="jpb205870ueq01" number="no" eqnalign="left"></display-eqn>For some close-lying resonances (left panel of figure <figref linkend="jpb205870fig18">18</figref>) the result of the alignment has been demonstrated. After excitation to the 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> excited state, the relative intensities of the resonant features depend strongly on the relative orientation of the linear polarization vector of the laser with respect to that of the synchrotron radiation. These relative changes could be described by a theoretical treatment of the process predicting only very small changes for <sup>2</sup>P<sub>3/2</sub> → <sup>2</sup>D<sub>3/2,5/2</sub> transitions, but changes by a factor of 4 for <sup>2</sup>P<sub>3/2</sub> → <sup>2</sup>S<sub>1/2</sub> transitions. In this way, it was possible to identify the symmetry of the excited states and to control the theoretical predictions for the high-lying doubly excited autoionization resonances of the Li atom. This method has, in the following, been applied to the analysis of Ca<sup>**</sup> 3p<sup>5</sup>3d4s4p resonances after laser excitation to the Ca* 3p<sup>6</sup>4s4p <sup>1</sup>P<sub>1</sub> state [<cite linkend="jpb205870bib114">114</cite>] and, with inclusion of circularly polarized light, for the Na<sup>**</sup> 2p<sup>5</sup>3s3p <sup>2</sup>S, <sup>2</sup>P and <sup>2</sup>D resonances excited from the Na* 2p<sup>6</sup>3p <sup>2</sup>P<sub>1/2,3/2</sub> laser-excited state [<cite linkend="jpb205870bib57">57</cite>].
<figure id="jpb205870fig18"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig18.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig18.jpg"></graphic-file></graphic><caption id="jpb205870fc18" label="Figure 18"><p indent="no">Left: Li* 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> → 1s<italic>nln</italic>′<italic>l</italic>′ absorption (uppermost curve) and partial autoionization cross sections for excitation via the <sup>2</sup>P<sub>1/2</sub> (spectrum 2) and <sup>2</sup>P<sub>3/2</sub> (spectra 3 and 4) intermediate states. The polarization vector of the laser was oriented parallel (spectra 2 and 3) or perpendicular (spectrum 4) to the polarization vector of the synchrotron radiation. Reprinted with permission from [<cite linkend="jpb205870bib55">55</cite>], copyright 1987 by the American Physical Society. Right: relative intensity of the electrons emitted upon the process Li 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> → 1s2p<sup>2 2</sup>D<sub>3/2,5/2</sub> for three different values (0°, 45°, 90°) of the angle η between the polarization vectors of the laser and synchrotron radiations. Reprinted with permission from [<cite linkend="jpb205870bib92">92</cite>], copyright 1992 by the American Physical Society.</p></caption></figure></p><p>A further technical development has initiated an extension of the method, which now uses the measurement of the angular distribution of the photoelectrons. Triggered by the much higher photon intensities available using new insertion devices, experiments taking only electrons emitted in a small solid angle became possible. Again, laser-excited aligned Li atoms and the 1s<italic>nln′l′</italic> <sup>2</sup>S, <sup>2</sup>P, <sup>2</sup>D resonances were chosen as test case in order to demonstrate the potential of the method [<cite linkend="jpb205870bib92">92</cite>]. By monitoring the intensity of the main Li<sup>+</sup> 1s<sup>2 1</sup>S<sub>0</sub> photoelectron line, for example for the resonant transition:
<display-eqn id="jpb205870ueq02" number="no"></display-eqn>as a function of the angle Θ between the axis of the electron spectrometer and the polarization vector of the ionizing synchrotron radiation for different relative angles η between the polarization vectors of the laser and the synchrotron radiation (see figure <figref linkend="jpb205870fig11">11</figref>), a more detailed analysis of the resonances has been possible. The specific character of the resonance manifests itself in the characteristic distribution of the Θ-scans (right panel of figure <figref linkend="jpb205870fig18">18</figref>), when the relative angle between the light polarizations is fixed and the spectrometer is turned around the propagation axis of the light beams, as well as of the η-scans when the polarization of the laser is turned with respect to that of the synchrotron, and the electrons are recorded in a fixed geometry. In this way, the symmetry of the highly excited autoionizing resonances is not only deduced from global changes of the intensity when changing the polarization of the target, but is now directly derived from the angular distribution and the changes in the angular distribution for different polarizations.</p><p>Following the same idea as for Li, the Na<sup>**</sup> 2p<sup>5</sup>3s3p [<cite linkend="jpb205870bib115">115</cite>, <cite linkend="jpb205870bib116">116</cite>] and the Ca<sup>**</sup> 3p<sup>5</sup>3d4s4p states [<cite linkend="jpb205870bib86">86</cite>, <cite linkend="jpb205870bib117">117</cite>] have also been reinvestigated by angular distribution studies. In the case of laser-excited Na, the measurements confirmed the assignment of excited states of <sup>2</sup>S and <sup>2</sup>D symmetry. For the <sup>2</sup>P resonances, in particular the Na 2p<sup>5</sup>(3s3p <sup>3</sup>P) <sup>2</sup>P<sub>3/2</sub> resonance at 31.5 eV, a strong perturbation in the angular distribution of the photoelectron was discovered showing only very small variation of the electron intensity in the η-scans [<cite linkend="jpb205870bib115">115</cite>, <cite linkend="jpb205870bib116">116</cite>]. These findings have been explained by a reduction of the electronic alignment due to the hyperfine coupling with the nuclear spin during the autoionization process. The relative long lifetime of the state results in an alignment transfer from the electronic to the nuclear system and thereby in a loss in <italic>m<sub>J</sub></italic> alignment.</p><p>For the more complex Ca atom [<cite linkend="jpb205870bib86">86</cite>, <cite linkend="jpb205870bib117">117</cite>], the method was finally fully explored, in the experiment, by the combination of two different electron analysers, an angle integrating CMA with fixed entrance apertures and an angle-resolving electron spectrometer, as well as in theory by explicitly deducing formulae to extract full information from the experimental data. In particular, the so-called phase-tilt method was introduced describing the laser polarization for which, under fixed analyser geometry, the maximal electron intensity is measured. This quantity does not depend on the alignment of the intermediate state and is, in this sense, much less sensitive to experimental imperfections introduced when switching from one configuration to another. Despite the strong energy dependence of the 4s-photoline (figure <figref linkend="jpb205870fig19">19</figref>) in the region of the manifold of 3p<sup>5</sup>3d(<sup>1</sup>P)4s4p resonances at 33 eV, the phase tilt shows a constant behaviour with a mean value at δ<sup>CMA</sup> = −15.5°. As deduced from the theoretical model, this can be explained by the fact that only contributions from one channel with the total angular momentum <italic>J</italic> = 2 contribute to the formation of the 4s line. In this way it was possible to extract in a model-independent way the anisotropy parameter β from the phase tilt measurements. This is not the case for the also investigated 4p and 3d photolines, which show a more complex energy dependence, and only a qualitative interpretation of the experimental results was obtained.
<figure id="jpb205870fig19"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig19.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig19.jpg"></graphic-file></graphic><caption id="jpb205870fc19" label="Figure 19"><p indent="no">Photoionization cross section of the Ca atoms laser-excited to the 3p<sup>6</sup>4s4p <sup>2</sup>P<sub>3/2</sub> state in the 3p → 3d resonance region (upper panel) and phase tilt in the 4s-channel (lower panel) measured as a function of photon energy. Reprinted with permission from [<cite linkend="jpb205870bib86">86</cite>], copyright 1997 by the American Physical Society.</p></caption></figure></p></sec-level2><sec-level2 id="jpb205870s4-3" label="4.3"><heading>Synchronization experiments</heading><p indent="no">Since synchrotron radiation is produced as light bursts of some 10 to 100 ps temporal width and a repetition rate of typically some MHz, advantage can be taken from the use of a pulsed synchronized laser, especially, when the synchrotron radiation is used for the pumping processes to short-lived excited states. After the very first investigations on solid krypton using a temporally broad, low repetition rate N<sub>2</sub> laser in combination with the synchrotron radiation of the DORIS ring in Hamburg [<cite linkend="jpb205870bib51">51</cite>], some further experiments using synchronized MHz lasers were performed later on solid or liquid targets [<cite linkend="jpb205870bib118" range="jpb205870bib118,jpb205870bib119,jpb205870bib120">118–120</cite>]. Using the Super-ACO synchronization system [<cite linkend="jpb205870bib94">94</cite>] to show the feasibility of such experiments for diluted gas targets, the two-photon ionization of atomic He via the short-lived He*1s3p <sup>1</sup>P state was studied [<cite linkend="jpb205870bib94">94</cite>, <cite linkend="jpb205870bib121">121</cite>]. Monochromatized synchrotron radiation was used to excite the resonance below the first ionization threshold (left part of figure <figref linkend="jpb205870fig20">20</figref>). The photon energy of the optical laser is now sufficient to induce the ionization of the atom, but photoelectrons are only detected when the laser pulses arrive on the sample within the 1.72 ns lifetime of the excited state. As experimental proof of successful synchronization and as a way to determine the lifetime of the excited He*1s3p <sup>1</sup>P state, the intensity of the photoelectrons was recorded as a function of the time delay between the laser and the synchrotron radiation pulses (right part of figure <figref linkend="jpb205870fig20">20</figref>). The experimental data points can be approximated by an asymmetric profile, which is the convolution of the temporal widths of the laser and of the synchrotron radiation with the exponential decay curve of the excited He*1s3p <sup>1</sup>P state. Although only a low flux bending magnet beamline on a second generation synchrotron source was used in these experiments, the possibility of time-resolved experiments in the gas phase was clearly demonstrated. Since the lifetimes of the excited states of rare gases have already been determined very accurately by other experimental techniques, further studies on atomic Xe at Super-ACO [<cite linkend="jpb205870bib97">97</cite>, <cite linkend="jpb205870bib98">98</cite>] and on He at the UVSOR storage ring in Okazaki (Japan) [<cite linkend="jpb205870bib122">122</cite>] did mainly focus on the demonstration of the synchronization process. Similarly, experiments on laser-excited calcium using the synchronization between the synchrotron radiation pulses of BESSY in Berlin (Germany) and a mode-locked Ti:Sa laser concentrated on the technical aspects [<cite linkend="jpb205870bib123">123</cite>].
<figure id="jpb205870fig20"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig20.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig20.jpg"></graphic-file></graphic><caption id="jpb205870fc20" label="Figure 20"><p indent="no">Time-resolved laser-ionization of the synchrotron-radiation-excited He* 1s3p <sup>1</sup>P state. Left: scheme of the excitation-ionization processes using synchronized pulses from both radiations. Right: variation of the electron intensity as a function of the delay between the synchrotron and laser pulses. Reprinted with permission from [<cite linkend="jpb205870bib121">121</cite>], copyright 1996 by Elsevier.</p></caption></figure></p><p>In the following, the advantage of high pump–probe efficiency has been further explored, in particular in combination with a synchronized, wavelength-tunable laser. At Super-ACO, the even-parity autoionization states of atomic Xe have been studied in the region between the two lowest ionization thresholds, 5p<sup>5 2</sup>P<sub>3/2</sub> and <sup>2</sup>P<sub>1/2</sub> [<cite linkend="jpb205870bib97">97</cite>, <cite linkend="jpb205870bib98">98</cite>]. In this energy region, the 5p<sup>5</sup> (<sup>2</sup>P<sub>1/2</sub>) <italic>n</italic>s′ and <italic>m</italic>d′ Rydberg series have been extensively studied for a long time using one-photon excitation and have been considered as showcases for the study of autoionizing resonances, i.e., for the demonstration of coupling between highly excited states and underlying continua. The application of the two-photon double-resonant excitation scheme has provided a direct access to the Xe*5p<sup>5</sup>(<sup>2</sup>P<sub>1/2</sub>) <italic>n</italic>p′ and <italic>m</italic>f′ resonances, which cannot be excited by one-photon absorption from the ground state due to parity selection rules. In a first step, the Xe* 5p<sup>5</sup>(<sup>2</sup>P<sub>3/2</sub>) 5d[3/2]<sub>1</sub> or 6d[3/2]<sub>1</sub> intermediate states were excited by the synchrotron radiation (left part of figure <figref linkend="jpb205870fig21">21</figref>). In a second step, a synchronized tunable dye laser induced the subsequent excitation to the <italic>n</italic>p′, <italic>m</italic>f′ autoionization states, and the ion signal was recorded as a function of the laser wavelength. In this way, the 4f′[5/2]<sub>2</sub> and the <italic>n</italic>f′[5/2]<sub>2</sub> (<italic>n</italic> = 7–13) resonances could be measured with the high spectral resolution given by the laser (right part of figure <figref linkend="jpb205870fig21">21</figref>) and the asymmetry parameters <italic>q</italic> and the line widths Γ were determined for these resonances. The two-photon excitation via a well-defined photoexcited intermediate state, here the <italic>n</italic>d[3/2]<sub>1</sub> resonances, enables in some cases a more precise analysis of the autoionizing resonances than the analysis based on other techniques such as multi-photon excitation [<cite linkend="jpb205870bib124">124</cite>, <cite linkend="jpb205870bib125">125</cite>] or photoexcitation from metastable intermediate states [<cite linkend="jpb205870bib126">126</cite>].
<figure id="jpb205870fig21"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig21.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig21.jpg"></graphic-file></graphic><caption id="jpb205870fc21" label="Figure 21"><p indent="no">Two-photon double-resonant excitation of the Xe* 5p<sup>5</sup><italic>n</italic>f′, <italic>m</italic>p′ autoionizing states using synchronized laser and synchrotron radiation pulses. Left: energy diagram indicating the two-photon excitation pathways. Right: two-photon ionization spectrum of the Xe* 5p<sup>5</sup><italic>n</italic>f′ [5/2]<sub>2</sub> resonances via the Xe* 5p<sup>5</sup>6d [3/2]<sub>1</sub> resonance. The energy positions of the Xe* 5p<sup>5</sup><italic>m</italic>p′[3/2]<sub>1</sub> resonances are marked by vertical lines (from [<cite linkend="jpb205870bib97">97</cite>]).</p></caption></figure></p><p>The most remarkable result of the investigation of the even parity states of Xe is given by the dramatic differences between the intensities of the <italic>n</italic>p′ and <italic>m</italic>f′ resonances (figure <figref linkend="jpb205870fig22">22</figref>). Unlike the intense asymmetric profiles of Xe* 5p<sup>5</sup>(<sup>2</sup>P<sub>1/2</sub>) <italic>m</italic>f′ resonances, which are dominating the spectrum, no clear indication was found in the experiment for the Xe* 5p<sup>5</sup>(<sup>2</sup>P<sub>1/2</sub>) <italic>n</italic>p′ resonances. The oscillator strengths for d → f transitions seem to exceed by far those for the also dipole-allowed d → p transitions. The observed differences can be explained by theoretical studies, based on a configuration-interaction Pauli–Fock approach with inclusion of core polarization [<cite linkend="jpb205870bib127">127</cite>]. This theoretical model, developed in the case of highly excited Ar, was able to reproduce the experimental findings for Xe [<cite linkend="jpb205870bib128">128</cite>]. In the theoretical spectrum (figure <figref linkend="jpb205870fig22">22</figref>), the Xe*5p<sup>5</sup>(<sup>2</sup>P<sub>1/2</sub>) 11p′[1/2]<sub>0,1</sub> and [3/2]<sub>1,2</sub> resonances are characterized by rather large line widths compared to the <italic>m</italic>f′[5/2]<sub>2</sub> resonances and by small asymmetry parameters <italic>q</italic> giving rise to window-type Fano profiles. For the investigated transitions 6d[3/2]<sub>1</sub> → 7f′, 8f′[5/2]<sub>2</sub> and 6d[3/2]<sub>1</sub> → 11p′[K]<italic><sub>J</sub></italic> these differences result in an effective suppression of the 11p′ resonances by a factor of about 200, explaining thereby the absence of these resonances in the experimental spectrum. The correct theoretical interpretation of the experimental results reveals the importance of a strong configuration interaction in the intermediate as well as in the final state.
<figure id="jpb205870fig22"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig22.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig22.jpg"></graphic-file></graphic><caption id="jpb205870fc22" label="Figure 22"><p indent="no">Comparison between experimental (upper panel) and computed (lower panel) resonance profiles of the Xe* 5p<sup>5</sup>7f′, 8f′[(5/2] and 11p′[K]<italic><sub>J</sub></italic> autoionizing states excited via the 5p<sup>5</sup>6d[3/2]<sub>1</sub> intermediate state (from [<cite linkend="jpb205870bib128">128</cite>]).</p></caption></figure></p><p>Similar experimental investigations have been undertaken later on other rare gases demonstrating that the strong differences observed in the Xe spectra are less pronounced for the corresponding series in Ar [<cite linkend="jpb205870bib129">129</cite>]. By applying the synchronization between a pulsed Ti:S laser and the synchrotron radiation pulses of NSRRC synchrotron ring in Taiwan, it was possible to measure, in the energy range between the Ar<sup>+</sup> 3p<sup>5 2</sup>P<sub>3/2</sub> and <sup>2</sup>P<sub>1/2</sub> ionization thresholds, three autoionization series assigned to the Ar* 3p<sup>5</sup><italic>n</italic>f′[5/2]<sub>2</sub>, 3p<sup>5</sup><italic>n</italic>p′[3/2]<sub>2</sub> and 3p<sup>5</sup><italic>n</italic>p′[1/2]<sub>0</sub> Rydberg states (figure <figref linkend="jpb205870fig23">23</figref>). The 3p<sup>5</sup><italic>n</italic>p′ resonances show up clearly after initial excitation of the Ar* 3p<sup>5</sup>(<sup>2</sup>P<sub>1/2</sub>) 3d′[3/2]<sub>1</sub> intermediate state. As discussed for other rare gases [<cite linkend="jpb205870bib130">130</cite>], the profiles of the autoionization resonances strongly depend on the intermediate state. The Ar 3p<sup>5</sup><italic>n</italic>f′[5/2]<sub>2</sub> resonances show a very asymmetric profile, when excited via the Ar* 3p<sup>5</sup>(<sup>2</sup>P<sub>3/2</sub>)3d [3/2]<sub>1</sub> intermediate state indicating a relative strong direct ionization process, but an almost symmetric profile after excitation from the Ar* 3p<sup>5</sup>(<sup>2</sup>P<sub>1/2</sub>)3d′[3/2]<sub>1</sub> level. A further, more detailed discussion of the electronic interaction governing the electronic relaxation of the even-parity autoionization states of rare gases has certainly to be accompanied by a theoretical support.
<figure id="jpb205870fig23"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig23.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig23.jpg"></graphic-file></graphic><caption id="jpb205870fc23" label="Figure 23"><p indent="no">Two colour double-resonance photoionization spectra of Ar measured with synchronized laser and synchrotron photon beams: two-photon ionization of the <italic>n</italic>p′ and <italic>n</italic>f′ resonances via the Ar* 3p<sup>5</sup>(<sup>2</sup>P<sub>1/2</sub>)3d′[3/2]<sub>1</sub> Rydberg state. Reprinted with permission from [<cite linkend="jpb205870bib129">129</cite>], copyright 2005 by Elsevier.</p></caption></figure></p></sec-level2><sec-level2 id="jpb205870s4-4" label="4.4"><heading>Photoionization of atoms following dissociation of diatomic molecules</heading><p indent="no">An interesting application of pump–probe experiments is the ability to provide access to the study of photoionization processes in atoms that are difficult to prepare but can be produced by dissociation of small molecules. More generally, photoionization of free radicals is an important topic to be investigated because of their abundance in the upper atmosphere or in the interstellar medium. While the determination of absolute and partial cross sections is of great interest in astrophysics, photoionization of free radicals is also an important tool to analyse photoionization in open-shell atoms.</p><p>Good examples of these are the halogen and chalcogen atoms. Their production is difficult. For many years they have been generated by various techniques having a low efficiency [<cite linkend="jpb205870bib131" range="jpb205870bib131,jpb205870bib132,jpb205870bib133">131–133</cite>]. In an experiment performed in 1980 [<cite linkend="jpb205870bib134">134</cite>], a laser was used to photodissociate iodine molecules into iodine atoms in both fine-structure states I (5p<sup>5 2</sup>P<sub>3/2</sub> and <sup>2</sup>P<sub>1/2</sub>) inside the laser cavity in order to get a high laser power (60 W). The target was photoionized by unpolarized HeI (58.4 nm) radiation. By extracting differences between spectra recorded with and without laser it was possible to isolate the photoelectrons from purely atomic origin and to measure relative partial cross sections, in good agreement with previous works [<cite linkend="jpb205870bib132">132</cite>].</p><p>The first tentative of pump–probe experiments using a laser to dissociate iodine molecules into atomic fragments and the synchrotron radiation to probe the residual fragments was achieved about 10 years later. In these experiments [<cite linkend="jpb205870bib135">135</cite>, <cite linkend="jpb205870bib136">136</cite>], iodine atoms in the ground state were produced by a multiline cw Ar<sup>+</sup> ion laser, and photoionized in the VUV range by the synchrotron radiation emitted by the Super-ACO storage ring. The laser beam was supposed to dissociate, <italic>in situ</italic>, the molecular iodine, by inducing mainly a transition from the <sup>1</sup>Σ<sub>g</sub><sup>+</sup> ground state into the <sup>1</sup>Π<sub>1u</sub> repulsive state, which is correlated to two atoms in the <sup>2</sup>P<sub>3/2</sub> ground state. Collinear to the laser beam a monochromatized beam of synchrotron radiation photoionized the halogen atoms and/or molecules. Photoelectrons were then collected in a 127° cylindrical analyser. With a laser power of about 8 W, dissociation of I<sub>2</sub> was observed; in fact, more than 95% of the signal was seen to originate from iodine atoms produced in their ground state.</p><p>The 4d excitations and decay dynamics of neutral atomic iodine were investigated first to determine the role of the 5p hole on the photoexcitation and/or photoionization of the shallow 4d-inner shell in an open shell atom. The total ion yield spectrum of atomic iodine [<cite linkend="jpb205870bib136">136</cite>, <cite linkend="jpb205870bib137">137</cite>], recorded in the region of the 4d → 5p excitations, is shown in the left part of figure <figref linkend="jpb205870fig24">24</figref>. The spectrum is dominated by two strong resonances corresponding to the 4d<sup>10</sup>5s<sup>2</sup>5p<sup>5 2</sup>P<sub>3/2</sub> → 4d<sup>9</sup>5s<sup>2</sup>5p<sup>6 2</sup>D<sub>5/2</sub>, <sup>2</sup>D<sub>3/2</sub> transitions, which brings out the good spatial overlap between the 4d and 5p orbitals. The analysis of the photoelectron spectra demonstrated that these states decay primarily by direct autoionization into the outer-shell channels because of the valence character of the 5p orbital. For the region above the 5s threshold, <italic>ab initio</italic> calculations pointed out that the 5s5p<sup>5</sup> configuration is strongly mixed with the [5s<sup>2</sup>5p<sup>3 2</sup>P] 5d and [5s<sup>2</sup>5p<sup>3 2</sup>D] 5d configurations, so that the observed photoelectron lines could not be separated into main and satellite lines. Photoexcitation and photoionization of bromine atoms [<cite linkend="jpb205870bib137">137</cite>, <cite linkend="jpb205870bib138">138</cite>] as well as autoionization of the 5s → <italic>n</italic>p resonances of atomic iodine [<cite linkend="jpb205870bib139">139</cite>] produced in a similar way were also studied. In the right part of figure <figref linkend="jpb205870fig24">24</figref>, the photoion yield following 3d excitation and ionization in bromine atoms is given. Here, only 75% of the molecules were found to be transferred in two states of the bromine atom. Both the iodine and the bromine spectra are quite similar, although not identical, in particular in the near-threshold region.
<figure id="jpb205870fig24"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig24.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig24.jpg"></graphic-file></graphic><caption id="jpb205870fc24" label="Figure 24"><p indent="no">Photoionyield spectra following photoabsorption in the 4d- and 3d-subshells of atomic iodine (left panel) and bromine (right panel), respectively. Reprinted with permission from [<cite linkend="jpb205870bib137">137</cite>], copyright 1994 by Kluwer.</p></caption></figure></p><p>The 4d-shell photoionization cross section of the iodine atom was also determined [<cite linkend="jpb205870bib140">140</cite>] in these pump–probe experiments. It belongs to the general scheme of the delayed onset of cross section maxima as mentionned in section <secref linkend="jpb205870s2">2</secref>. The experimental results determined from the measurements of the 4d-photoelectron lines, after normalization to the experimental value of the phototoabsorption cross section for the iodine molecule [<cite linkend="jpb205870bib141">141</cite>], are shown in figure <figref linkend="jpb205870fig25">25</figref> as a series of black squares culminating at about 7.5 Mb. These data confirmed the existence of the delayed onset maximum in the 4d-photoionization cross section of atomic iodine. For comparison, the theoretical results of RPAE calculations for I<sup>−</sup> [<cite linkend="jpb205870bib142">142</cite>], I [<cite linkend="jpb205870bib143">143</cite>] and I<sup>+</sup> [<cite linkend="jpb205870bib144">144</cite>] are also shown in figure <figref linkend="jpb205870fig25">25</figref>. Together with the experimental determinations for I<sup>−</sup> and I<sup>+</sup> [<cite linkend="jpb205870bib145">145</cite>] ions as well as with the experimental [<cite linkend="jpb205870bib146">146</cite>, <cite linkend="jpb205870bib147">147</cite>] and theoretical [<cite linkend="jpb205870bib148">148</cite>, <cite linkend="jpb205870bib149">149</cite>] results for the neighbouring Xe atom, they are converging towards a total 4d-cross section between 25 and 30 Mb for these atomic systems.
<figure id="jpb205870fig25"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig25.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig25.jpg"></graphic-file></graphic><caption id="jpb205870fc25" label="Figure 25"><p indent="no">Total 4d-photoionization cross section into the continuum calculated using the RPAE approximation for I<sup>−</sup> (dotted line), atomic iodine I (full curve) and I<sup>+</sup> (dashed curve) in the region of the 4d-subshell ionization, together with the results of the experiments (full dots) (adapted from [<cite linkend="jpb205870bib143">143</cite>]).</p></caption></figure></p><p>The large discrepancy (almost a factor of 4) between the experimental values for the 4d-cross section of atomic iodine and the theoretical results as well as the studies on the neighbour atomic systems, deserves special attention [<cite linkend="jpb205870bib143">143</cite>, <cite linkend="jpb205870bib144">144</cite>]. It seems quite unlikely that such a strong disagreement is due to uncertainties in the data for an iodine molecule [<cite linkend="jpb205870bib141">141</cite>]. Therefore, two other points should be mentioned. First, it was assumed in the normalization procedure that the 4d-cross section in atomic iodine is exactly equal to half the 4d-molecular cross section. This may not be true, since inter-shell correlation effects differ in both cases. The bonding of the iodine atoms in the iodine molecule should likely modify the height of the potential barrier that is very sensitive to small changes in the electronic environment. Taking into account the low value also measured in CH<sub>3</sub>I [<cite linkend="jpb205870bib150">150</cite>], one may expect that the 4d-cross section of the iodine atom bound in a molecule is somewhat smaller than in the free iodine atom. Second, it is quite likely that some of the iodine atoms were produced also by thermal dissociation, since the laser was focused in the experiment very close to the extremity of the oven, thus overheating it. This can lead also to a change of the size of the ‘effective’ source volume and to changes of the contact potential. Therefore, despite the clear advantage of these pump–probe experiments to provide an efficient source of reactive atoms, further experiments are necessary in order to solve the discrepancies and to address the quantitative aspects of such experiments.</p></sec-level2></sec-level1><sec-level1 id="jpb205870s5" label="5"><heading>Recent results obtained at advanced synchrotron radiation sources</heading><p indent="no">In the past few years the two-photon experiments have largely taken benefits of the new developments realized at the synchrotron radiation sources in terms of the quality of the photon beam, i.e., its brightness, and in terms of the undulator performances allowing us to freely adjust the polarization of the synchrotron radiation. The effect of variable polarization of the laser as well as of the synchrotron radiation has been explored mainly in experiments at undulator beam lines of second generation sources, such as Super-ACO in Orsay and DESY in Hamburg. The first high-brightness dedicated storage rings available to synchrotron users were the European Synchrotron Radiation Facility (ESRF) in Grenoble and the ALS in Berkeley. The ESRF (6 GeV electron energy) was built almost exclusively for high-energy x-rays studies on condensed matter and biological species. In contrast, the ALS (1.9 GeV maximum energy) was <italic>a priori</italic> dedicated to soft x-rays and XUV experiments. One of its undulator beamlines is dedicated to atomic and molecular physics over the 10–300 eV photon energy range, which is ideal for exploring the potentials of the third generation synchrotron radiation sources [<cite linkend="jpb205870bib58">58</cite>, <cite linkend="jpb205870bib59">59</cite>, <cite linkend="jpb205870bib151">151</cite>]. It was used for this purpose starting about 10 years ago [<cite linkend="jpb205870bib151">151</cite>]. More recently, pump–probe experiments on laser excited atoms have also been started at MAX II in Lund [<cite linkend="jpb205870bib152" range="jpb205870bib152,jpb205870bib153,jpb205870bib154,jpb205870bib155">152–155</cite>] and at BESSY II in Berlin [<cite linkend="jpb205870bib74">74</cite>, <cite linkend="jpb205870bib156">156</cite>].</p><sec-level2 id="jpb205870s5-1" label="5.1"><heading>Photoionization of unpolarized excited states</heading><sec-level3 id="jpb205870s5-1-1" label="5.1.1"><heading>High-resolution measurements of partial photoionization cross sections</heading><p indent="no">While high spectral resolution was already provided, high-resolution detectors were not yet available for pump–probe experiments. Thus, the initial studies of laser-excited atoms by photoelectron spectrometry were still obtained using a CMA of moderate resolution. A well-resolved photoelectron spectrum for direct photoionization into the continuum of laser-excited lithium atoms [<cite linkend="jpb205870bib157">157</cite>], shown in the left part of figure <figref linkend="jpb205870fig26">26</figref> (lower panel), illustrates the huge improvement in the spectral resolution for the various final ionic states by comparison with the results previously obtained with the second generation source Super-ACO (left part of figure <figref linkend="jpb205870fig26">26</figref>, upper panel) [<cite linkend="jpb205870bib158">158</cite>]. The increase in the spectral resolution has a more pronounced impact on the determination of the energy dependence of partial photoionization cross sections, which are obtained by CIS (constant ionic state) spectra. In fact, when measurements are conducted in the CIS mode, only the spectral resolution plays a role in the quality of the data; the resolution of the electron detectors has no influence at all.
<figure id="jpb205870fig26"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig26.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig26.jpg"></graphic-file></graphic><caption id="jpb205870fc26" label="Figure 26"><p indent="no">Left: photoelectron spectra resulting from photoionization of Li atoms in the 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> excited state measured at Super-ACO (upper panel) and from a mixture of atoms in the ground state, and in the excited state (lower panel, black area) taken at the ALS at a photon energy of 90 eV. In the upper panel, the spectrum from the ground state has been substracted. Reprinted with permission from [<cite linkend="jpb205870bib157">157</cite>], copyright 1998 by Elsevier. Right: experimental (upper panel) and <italic>R</italic>-matrix calculated (lower panel) cross sections for photoionization of the Li 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> excited state into the 1s2p <sup>1</sup>P state of the Li<sup>+</sup> ion at the excitation energy of the 2s2p<sup>2 2</sup>P hollow state. Reprinted with permission from [<cite linkend="jpb205870bib151">151</cite>], copyright 1996 by the American Physical Society.</p></caption></figure></p><p>Investigations on hollow lithium were, at this time, extensively performed since their discovery in 1994 with the help of a laser-produced plasma source [<cite linkend="jpb205870bib159">159</cite>]. The ALS was first exploited for high-resolution studies of hollow atoms produced by double and triple excitations of lithium atoms in the ground state [<cite linkend="jpb205870bib160" range="jpb205870bib160,jpb205870bib161,jpb205870bib162">160–162</cite>]. In 1996, the first measurements of even-parity hollow lithium states produced by double and triple excitation of laser-excited lithium atoms were successfully carried out [<cite linkend="jpb205870bib151">151</cite>]. A cw dye laser tuned to the wavelength of the 1s<sup>2</sup>2s <sup>2</sup>S<sub>1/2</sub> → 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> transition in lithium transferred a fraction of the lithium atoms into this excited state, and synchrotron radiation produced the hollow states 2s2p<sup>2 2</sup>P and <sup>2</sup>D by double excitation of the excited atoms. <italic>R</italic>-matrix calculations predicted [<cite linkend="jpb205870bib151">151</cite>] the existence of these resonances above 140 eV photon energy. The theoretical values of the energies and natural lifetimes of these even-parity triply excited states are shown in table <tabref linkend="jpb205870tab02">2</tabref> (columns 3 to 7), including results obtained by using the saddle-point complex rotation method [<cite linkend="jpb205870bib163">163</cite>]. Partial photoionization cross sections were measured in this energy region. An example of the experimental results obtained at the energy of the 2s2p<sup>2 2</sup>P hollow state [<cite linkend="jpb205870bib151">151</cite>] is shown in the right part of figure <figref linkend="jpb205870fig26">26</figref> (upper panel). The profile obtained by the <italic>R</italic>-matrix calculations (shown in the lower panel) are in amazing agreement with the experimental results. The <italic>ab initio</italic> calculated and experimentally determined energy positions and lifetimes of this hollow state are almost identical, within the error bars. Moreover, within the experimental uncertainty, the absolute value of the experimental cross section at the top of the profile, obtained by normalization of the data to the photoabsorption cross section previously measured for lithium atoms in the ground state [<cite linkend="jpb205870bib164">164</cite>], agrees rather well with the calculated cross section. A similar agreement between experiment and theory is noted in the case of the 2s2p<sup>2 2</sup>D hollow state [<cite linkend="jpb205870bib165" range="jpb205870bib165,jpb205870bib166,jpb205870bib167">165–167</cite>], shown in the left part of figure <figref linkend="jpb205870fig27">27</figref>. For both the <sup>2</sup>P and the <sup>2</sup>D hollow state, the Fano-profile of the resonances is strongly asymmetric. This is not the case for the 2s<sup>2</sup>2p <sup>2</sup>P hollow state excited from lithium atoms in the ground state [<cite linkend="jpb205870bib157">157</cite>, <cite linkend="jpb205870bib165">165</cite>, <cite linkend="jpb205870bib166">166</cite>], as seen in the right part of figure <figref linkend="jpb205870fig27">27</figref>. The profile of this resonance into the 1s2p <sup>3</sup>P (and <sup>1</sup>P) decay channel is quasi-Lorentzian, resulting from the fact that the cross section for direct photoionization into this channel in the vicinity of the resonance is extremely weak. The results on the laser-excited lithium atoms confirmed that direct photoionization of the laser-excited lithium atoms into the <sup>1,3</sup>P ionic channels is greatly enhanced by the laser preparation of the lithium atoms in the 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> state, since the shape of the profile demonstrates the existence of strong interferences between the direct and the resonant pathways******Partial cross sections for direct photoionization of the excited lithium atom into all 1s<italic>nl</italic> ionic channels up to <italic>n</italic> = 4 have also been measured with an unprecedented resolution. In particular, the results confirmed the highest enhancement of the intensity of shake-up satellites in the excited 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> lithium atoms, as compared to other alkali atoms [<cite linkend="jpb205870bib32">32</cite>].
<figure id="jpb205870fig27"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig27.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig27.jpg"></graphic-file></graphic><caption id="jpb205870fc27" label="Figure 27"><p indent="no">Photoionization cross sections of Li in the excited 1s<sup>2</sup>2p <sup>2</sup>P<sub>3/2</sub> (left panel) and in the ground 1s<sup>2</sup>2s <sup>2</sup>S<sub>1/2</sub> (right panel) states to the 1s2p <sup>3</sup>P ionic state in the vicinity of the 2s2p<sup>2 2</sup>D and 2s<sup>2</sup>2p <sup>2</sup>P hollow states, respectively. The experimental results are given as the solid lines and black points, and the results of the <italic>R</italic>-matrix calculations as dashed lines. Reprinted with permission from [<cite linkend="jpb205870bib165">165</cite>], copyright 1996 by the American Institute of Physics and from [<cite linkend="jpb205870bib158">158</cite>], copyright 1996 by the American Physical Society.</p></caption></figure><table id="jpb205870tab02" frame="topbot" indent="no"><caption id="jpb205870tc02" label="Table 2"><p indent="no">Measured and calculated parameters for the hollow states 2s2p<sup>2 2</sup>P and 2s2p<sup>2 2</sup>D in Li* atoms (from [<cite linkend="jpb205870bib161">161</cite>]).</p></caption><tgroup cols="7"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><colspec colnum="6" colname="col6" align="left"></colspec><colspec colnum="7" colname="col7" align="left"></colspec><spanspec spanname="2to3" namest="col2" nameend="col3" align="center"></spanspec><spanspec spanname="4to5" namest="col4" nameend="col5" align="center"></spanspec><spanspec spanname="6to7" namest="col6" nameend="col7" align="center"></spanspec><spanspec spanname="1to7" namest="col1" nameend="col7" align="center"></spanspec><thead><row><entry></entry><entry spanname="2to3">Energy (eV)</entry><entry spanname="4to5">Line width (meV)</entry><entry spanname="6to7"><italic>q</italic>-parameter</entry></row><row><entry></entry><entry spanname="2to3"></entry><entry spanname="4to5"></entry><entry spanname="6to7"></entry></row><row><entry>State</entry><entry>Experimental</entry><entry>Theoretical</entry><entry>Experimental</entry><entry>Theoretical</entry><entry>Experimental</entry><entry>Theoretical</entry></row></thead><tbody><row><entry>2s2p<sup>2 2</sup>P</entry><entry>145.08 (5)</entry><entry>145.00<sup>a</sup></entry><entry> 47 (5)</entry><entry>48<sup>b</sup></entry><entry>−2.1 (2)</entry><entry>−2.09<sup>b</sup></entry></row><row><entry></entry><entry></entry><entry>145.07<sup>b</sup></entry><entry></entry><entry></entry><entry></entry><entry></entry></row><row><entry>2s2p<sup>2 2</sup>D</entry><entry>142.92 (5)</entry><entry>142.76<sup>a</sup></entry><entry>103 (10)</entry><entry>90<sup>b</sup></entry><entry></entry><entry></entry></row><row><entry></entry><entry></entry><entry>142.91<sup>b</sup></entry><entry></entry><entry></entry><entry></entry><entry></entry></row></tbody><tfoot><sup>a</sup> <italic>R</italic>-matrix (Voky [<cite linkend="jpb205870bib161">161</cite>]).</tfoot><tfoot><sup>b</sup> From [<cite linkend="jpb205870bib163">163</cite>].</tfoot></tgroup></table></p></sec-level3><sec-level3 id="jpb205870s5-1-2" label="5.1.2"><heading>J-resolved photoionization</heading><p indent="no">As already seen in figure <figref linkend="jpb205870fig04">4</figref>, the photoelectron spectrum following photoionization from the 2p-subshell of sodium atoms is almost fully resolved with the high spectral resolution of the synchrotron radiation, provided that the same resolution is available in the photoelectron spectrometer. The influence of the total angular momentum <italic>J</italic><sub>0</sub> of the initial atomic state on transitions to final fine structure ionic states can then be analysed and interpreted, revealing the existence of dynamically and quasiforbidden transitions in open-shell atoms [<cite linkend="jpb205870bib59">59</cite>]. Figure <figref linkend="jpb205870fig28">28</figref> presents in the upper panel a view of the interchannel coupling satellite spectrum (2p<sup>5</sup>3p <sup>1,3</sup>S, P, D ionic states) taken for sodium atoms in the ground state at 48 eV photon energy [<cite linkend="jpb205870bib58">58</cite>, <cite linkend="jpb205870bib59">59</cite>]. The <sup>3</sup>S satellite dominates the spectrum. The relative intensities of the lines within the <sup>3</sup>D<sub>1,2,3</sub> manifold is distributed according to the statistical ratio 7:5:3. In the middle and bottom panels of figure <figref linkend="jpb205870fig28">28</figref> are displayed the photoelectron spectra (shifted along the kinetic energy axis by the amount of energy brought by the laser 2.106 and 2.104 eV, respectively) to 2p<sup>5</sup>3p <sup>1,3</sup>S, P, D final ionic states from the excited 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> and <sup>2</sup>P<sub>1/2</sub> states. The relative line intensities differ considerably. Compared to the ground state, the intensity of the <sup>1,3</sup>S lines is strongly reduced in the spectra from both excited states. In the spectrum from the <sup>2</sup>P<sub>3/2</sub> excited state, the <sup>3</sup>D<sub>3</sub> line dominates, the relative intensities of the <sup>3</sup>D<sub>1</sub> and <sup>3</sup>D<sub>2</sub> lines are very weak. The intensity of the <sup>1</sup>D<sub>2</sub> line is strong, while the <sup>1</sup>P<sub>1</sub> line is significantly reduced. After <sup>2</sup>P<sub>1/2</sub> excitation, there is a pronounced redistribution of the oscillator strength within the manifold. The cross section to the <sup>3</sup>D<sub>3</sub> and <sup>1</sup>D<sub>2</sub> state has completely vanished or is drastically reduced, and the <sup>1</sup>P<sub>1</sub> (indicating a large transfer of oscillator strength from the <sup>3</sup>P to the <sup>1</sup>P lines) and <sup>3</sup>D<sub>2</sub> lines dominate the spectrum. The interpretation of these new features was based on the concept of quasi- and dynamically forbidden transitions, the later resulting from mutual cancellation of terms in the dipole matrix elements, and the former referring to the earlier predictions of such transitions in open-shell atoms [<cite linkend="jpb205870bib168">168</cite>].
<figure id="jpb205870fig28"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig28.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig28.jpg"></graphic-file></graphic><caption id="jpb205870fc28" label="Figure 28"><p indent="no">Photoelectron spectra into the Na<sup>+</sup> 2p<sup>5</sup>3p <sup>(2S + 1)</sup>L<italic><sub>J</sub></italic> ionic states measured at 48 eV photon energy from Na atoms in the 2p<sup>6</sup>3s <sup>2</sup>S<sub>1/2</sub> ground state (upper curve), and from the 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> (centre curve), and 2p<sup>6</sup>3p <sup>2</sup>P<sub>1/2</sub> (lower curve) excited states, respectively. Reprinted with permission from [<cite linkend="jpb205870bib58">58</cite>], copyright 2003 by the American Institute of Physics.</p></caption></figure></p><p>Calculations carried out in the single-configuration Hartree-Fock approximation using the Cowan code [<cite linkend="jpb205870bib169">169</cite>] accurately reproduce the experimental data in terms of relative cross sections and variations between the <sup>2</sup>P<sub>1/2</sub> and <sup>2</sup>P<sub>3/2</sub> cases. To go further in the interpretation, a series of calculations investigated sequentially the effects of the angular momentum coupling scheme by assuming either a pure LS coupling scheme for the atomic/ionic states (the geometrical model) or the intermediate coupling (the so-called generalized geometrical model). In the two lower panels of figure <figref linkend="jpb205870fig28">28</figref>, the results of the calculations are presented as black vertical bars for the generalized geometrical model. The agreement between the later and the measured relative intensities is excellent, confirming its validity for the case of 2p-ionization of excited sodium. The observed break-up of the pure geometrical model was explained by a violation of the LSJ-coupling scheme in the final ionic state. The almost complete suppression of the line <sup>1</sup>D<sub>2</sub> in the <sup>2</sup>P<sub>1/2</sub> spectrum (lower panel) results from a negative interference between product terms corresponding to different LS components in the theoretical expression for the line intensities. This effect was shown to be independent of the photon energy. Such lines were given the name of dynamically forbidden lines, since dynamical atomic structure calculations are needed to find that the corresponding cross section vanishes. The same phenomena were observed in the shake-up satellite spectrum, since these satellites should mimic the main line spectrum. It was indeed the case, as shown in figure <figref linkend="jpb205870fig29">29</figref> [<cite linkend="jpb205870bib58">58</cite>]. The exceptional overall resolution (10 meV in total, including all contributions) in the photoelectron spectra was the key point to observe accurately the new features.
<figure id="jpb205870fig29"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig29.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig29.jpg"></graphic-file></graphic><caption id="jpb205870fc29" label="Figure 29"><p indent="no">Shake-up satellites to Na<sup>+</sup> 2p<sup>5</sup>4p <sup>(2S + 1)</sup>L<italic><sub>J</sub></italic> ionic states accompanying single photoionization to the Na<sup>+</sup> 2p<sup>5</sup>3p <sup>(2S + 1)</sup>L<italic><sub>J</sub></italic> states of sodium atoms excited in the 2p<sup>6</sup>3p <sup>2</sup>P<sub>1/2</sub> (dashed line) and <sup>2</sup>P<sub>3/2</sub> (full line), respectively. Reprinted with permission from [<cite linkend="jpb205870bib58">58</cite>], copyright 2003 by the American Institute of Physics.</p></caption></figure></p><p>In order to check the general validity of this concept, the measurements were extended to potassium [<cite linkend="jpb205870bib156">156</cite>], rubidium [<cite linkend="jpb205870bib153">153</cite>] and cesium [<cite linkend="jpb205870bib155">155</cite>] atoms laser-excited into the K 3p<sup>6</sup>4p <sup>2</sup>P<sub>1/2</sub>, <sup>2</sup>P<sub>3/2</sub>, Rb 4p<sup>6</sup>5p <sup>2</sup>P<sub>1/2</sub>, <sup>2</sup>P<sub>3/2</sub> and Cs 5p<sup>6</sup>6p <sup>2</sup>P<sub>1/2</sub>, <sup>2</sup>P<sub>3/2</sub> states, respectively. The same kind of photoelectron spectra, again with a strong variation in the intensities of similar photoelectron lines, was measured for the final ionic configurations K<sup>+</sup> 3p<sup>5</sup>4p and Rb<sup>+</sup> 4p<sup>5</sup>5p in laser-excited potassium and rubidium atoms, respectively. The calculations were performed in both the pure jK coupling scheme and the generalized geometrical model for both atoms. The results of the generalized geometrical model were found to be in excellent agreement with the experimental intensity data only in the case of potassium. Figure <figref linkend="jpb205870fig30">30</figref> shows, as an example, the calculated photoelectron spectra [<cite linkend="jpb205870bib156">156</cite>] of potassium (upper panel) and rubidium (lower panel) in the region of the <italic>n</italic>p<sup>5</sup>(<italic>n</italic> + 1)p lines after excitation to the <sup>2</sup>P<sub>1/2</sub> state. For potassium, the difference between the two models is prominent: the dynamically forbidden 4p[3/2]<sub>2</sub> line is completely suppressed in the generalized model, whereas the jK coupling predicts a large intensity; the lines 4p′[3/2]<sub>2</sub> and 4p[1/2]<sub>0</sub> are strictly forbidden in jK coupling, while the experiment and the generalized geometrical model show a pronounced structure. In the case of rubidium, the difference of the results for the two models is meaningful only in the region of the 5p[3/2]<sub>2</sub> line: the generalized model calculation gives much less intensity than the jK model and brings this part of the spectrum in better agreement with the experiment. In conclusion, the three studies demonstrate that, for potassium, the generalized geometrical model is still in excellent agreement with the experimental data, as for sodium. The K<sup>+</sup> 3p<sup>5</sup>4p spectrum is not well described in any pure coupling scheme, being, however, closer to the case of sodium than to rubidium, while the Rb<sup>+</sup> 4p<sup>5</sup>5p spectrum and also the Cs<sup>+</sup> 5p<sup>5</sup>6p spectrum [<cite linkend="jpb205870bib155">155</cite>] are closely approximated in the jK-coupling model.
<figure id="jpb205870fig30"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig30.eps" width="19.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig30.jpg"></graphic-file></graphic><caption id="jpb205870fc30" label="Figure 30"><p indent="no">Calculated photoelectron spectra of K (upper panel) and Rb (lower panel) in the region of the <italic>n</italic>p<sup>5</sup>(<italic>n</italic> + 1)p lines after laser excitation to the 3p<sup>6</sup>4p <sup>2</sup>P<sub>1/2</sub> and 4p<sup>6</sup>5p <sup>2</sup>P<sub>1/2</sub> states, respectively: the solid and dashed lines are the results of the calculations using the generalized geometrical and jK coupling models, respectively (from [<cite linkend="jpb205870bib156">156</cite>]).</p></caption></figure></p><p>Besides studying the detailed spin–orbit structure of the core-excited states in the direct photoionization process, the high resolution in the electron spectra can also be exploited for studies of the resonant Auger decay starting from laser-excited states. The first attempt in this direction has been undertaken through the investigation of the 2p Auger decay of laser-excited K* 3p<sup>6</sup> 4p atoms [<cite linkend="jpb205870bib154">154</cite>]. Compared to the normal Auger decay, which is mainly described by the process K<sup>+</sup> 2p<sup>5</sup> 3s<sup>2</sup> 3p<sup>6</sup> 4s → K<sup>2+</sup> 2p<sup>6</sup> 3s<sup>2</sup> 3p<sup>4</sup> 4s + <italic>ϵl</italic>, the Auger decay of the laser excited states following K<sup>+</sup> 2p<sup>5</sup> 3s<sup>2</sup> 3p<sup>6</sup> 4p → K<sup>2+</sup> 2p<sup>6</sup> 3s<sup>2</sup> 3p<sup>4</sup> 4p + ϵ<italic>l</italic> was investigated giving a direct access to the K<sup>2+</sup> 3p<sup>4</sup> 4p final states. The analysis is unfortunately complicated by the fact that the direct photoionization already produces the same singly ionized state, K<sup>+</sup> 2p<sup>5</sup> 3s<sup>2</sup> 3p<sup>6</sup> 4p, through the formation of the conjugate shake-up satellites, and therefore the same Auger decay. In consequence, the Auger decay of the laser-excited states is difficult to separate from the Auger decay of ground state atoms and further studies in this direction are certainly necessary in order to show the entire potential of this type of studies.</p></sec-level3><sec-level3 id="jpb205870s5-1-3" label="5.1.3"><heading>Lifetime measurements of short-lived autoionizing states</heading><p indent="no">Another example of pump–probe photoionization experiments taking the best advantage of the very high spectral resolution achievable at third generation synchrotron beam lines is the measurement of the lifetimes of core-excited autoionizing states in alkali atoms [<cite linkend="jpb205870bib58">58</cite>]. Lifetimes of the deep inner shells of an atom are usually determined at best by photoabsorption (with lifetimes in the femtosecond range and spectral width larger than 100 meV) or, for the outer-shell excited states, by radiative decay measurements (lifetimes in the nanosecond range and spectral width smaller than 100 µeV). In contrast, the lifetimes of core-excited autoionizing states in the low and middle <italic>Z</italic>-elements are the most difficult ones to be determined, because they lie in the range of several hundreds of femtoseconds, i.e., a natural width of about 1 meV. This is precisely the ultimate energy resolution accessible by the third generation sources in the soft x-ray range below 100 eV. For instance, until quite recently, the lifetime of the 2p<sup>5</sup>3s<sup>2 2</sup>P<sub>1/2,3/2</sub> autoionizing states for sodium atoms in the ground state was not known: only an upper limit has been set at about 20 meV from electron impact experiments [<cite linkend="jpb205870bib170">170</cite>]. We show in figure <figref linkend="jpb205870fig31">31</figref> a spectrum of several autoionizing states excited from the 2p<sup>6</sup>3p <sup>2</sup>P<sub>3/2</sub> state, and experimentally resolved, by using monochromatized synchrotron radiation from the ALS, in the region of the [(2p<sup>5</sup>)<sup>2</sup>P(3s3p)<sup>3</sup>P]<sup>2</sup>D<sub>5/2</sub> state [<cite linkend="jpb205870bib171">171</cite>]. The energies of these states were known from pump–probe experiments combining the VUV radiation emitted from a BRV lamp and a pulsed dye laser [<cite linkend="jpb205870bib172">172</cite>]. The spectrum in figure <figref linkend="jpb205870fig31">31</figref> was recorded in the CIS mode of operation. We have already seen that only the spectral resolution plays a role in this case and should be set to a value comparable to the value of the lifetime(s) under investigation. In figure <figref linkend="jpb205870fig32">32</figref>, we present an example of the analysis [<cite linkend="jpb205870bib171">171</cite>] made to determine the lifetime from the measured data, taking the case of the the [(2p<sup>5</sup>)<sup>2</sup>P (3s3p)<sup>1</sup>P] <sup>2</sup>D<sub>5/2</sub> autoionizing state. Representing the experimental function by a Gaussian profile (with a FWHM G) and the natural lifetime by a Lorentzian profile (FWHM L), the convolution of both providing a Voigt profile with total width Γ equal to the width of the experimentally measured CIS spectrum. In the example chosen in figure <figref linkend="jpb205870fig32">32</figref>, the optimized values of G and L are 1.4(2) meV and 1.0(3) meV, respectively. Several theoretical calculations of these lifetimes have been made using the MCHF [<cite linkend="jpb205870bib116">116</cite>], term-dependent HF [<cite linkend="jpb205870bib173">173</cite>] and MCFH including the semi-relativistic Breit–Pauli [<cite linkend="jpb205870bib174">174</cite>] approximations. The various results differ considerably, sometimes by one order of magnitude. As an example, we show in table <tabref linkend="jpb205870tab03">3</tabref> the resulting values for three different core-excited autoionizing states in laser-excited sodium atoms. For the <sup>2</sup>D<sub>5/2</sub> state (first column), all experimental and theoretical results are in agreement, within the experimental uncertainty, while the situation is different for the <sup>2</sup>S<sub>1/2</sub> state. Only the semi-relativistic MCHF value is in reasonable agreement with the experimental result. For the other <sup>2</sup>D<sub>5/2</sub> state (third column), the MCHF and R-MCHF results are in agreement with the experiment. It is worthwhile to note that the natural lifetimes of the three states presented here are all in the sub-picosecond range and that working with a spectral resolution of 1 meV or less was absolutely necessary to determine experimental values in this range of lifetimes.
<figure id="jpb205870fig31"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig31.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig31.jpg"></graphic-file></graphic><caption id="jpb205870fc31" label="Figure 31"><p indent="no">Autoionization spectra in the region of 2p-resonances from laser excited Na atoms in the 32.675–32.722 eV energy range (from [<cite linkend="jpb205870bib171">171</cite>]).</p></caption></figure><figure id="jpb205870fig32"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig32.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig32.jpg"></graphic-file></graphic><caption id="jpb205870fc32" label="Figure 32"><p indent="no">Deconvolution of the resonance profile measured in the non-radiative decay of the [(2p<sup>5</sup>)<sup>2</sup>P (3s3p)<sup>1</sup>P] <sup>2</sup>D<sub>5/2</sub> into the natural lifetime (Lorentzian) and experimental (Gaussian) contributions (from [<cite linkend="jpb205870bib171">171</cite>]).</p></caption></figure><table id="jpb205870tab03" frame="topbot"><caption id="jpb205870tc03" label="Table 3"><p indent="no">Measured and calculated natural lifetimes for three core-excited autoionizing states produced by inner-shell excitation of laser-excited sodium atoms.</p></caption><tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><thead><row><entry>State</entry><entry>[(2p<sup>5</sup>)<sup>2</sup>P(3s3p)<sup>1</sup>P]<sup>2</sup>D<sub>5/2</sub></entry><entry>[(2p<sup>5</sup>)<sup>2</sup>P(3s3p)<sup>1</sup>P]<sup>2</sup>S<sub>1/2</sub></entry><entry>[(2p<sup>5</sup>)<sup>2</sup>P(3s3p)<sup>3</sup>P]<sup>2</sup>D<sub>5/2</sub></entry></row></thead><tbody><row><entry>Energy (eV)</entry><entry>31.395</entry><entry>31.780</entry><entry>32.680</entry></row><row><entry>Exp. (meV)</entry><entry>0.9 (3)</entry><entry>4.4 (8)</entry><entry>1.2 (3)</entry></row><row><entry>MCHF [<cite linkend="jpb205870bib116">116</cite>]</entry><entry>0.86</entry><entry>33.26</entry><entry>1.51</entry></row><row><entry>TDHF [<cite linkend="jpb205870bib173">173</cite>]</entry><entry>0.82</entry><entry>1.65</entry><entry>0.55</entry></row><row><entry>R-MCHF [<cite linkend="jpb205870bib174">174</cite>]</entry><entry></entry><entry>5.47</entry><entry>1.96</entry></row></tbody></tgroup></table></p></sec-level3></sec-level2><sec-level2 id="jpb205870s5-2" label="5.2"><heading>Photoionization of polarized targets</heading><sec-level3 id="jpb205870s5-2-1" label="5.2.1"><heading>Highly excited states of the rare gases</heading><p indent="no">For experiments using the synchrotron radiation as the pump and the laser as the probe, recent developments are closely connected to the possibility of using variable polarization, i.e., linear polarization with freely adjustable direction of the polarization vector, and circular polarization with left- and right-handed helicity, for both the laser and the synchrotron radiation. This feature, already used much earlier for many studies on laser-excited atoms, allows us to obtain further insights into the symmetry of the continua, which are coupled to the autoionization resonances excited in the two-photon process.</p><p>For example, the polarization dependence of the photoionization of the Ar* 3p<sup>5</sup> <italic>n</italic>s, <italic>m</italic>s Rydberg states has been studied using an intense Nd:Yag laser at a fixed wavelength in combination with the synchrotron radiation of the UVSOR storage ring in Okasaki [<cite linkend="jpb205870bib175">175</cite>]. Synchrotron radiation was used to excite the Rydberg states below the first ionization threshold, and the laser to project these excited states into the Ar<sup>+</sup> 3p<sup>5 2</sup>P<sub>3/2</sub> and <sup>2</sup>P<sub>1/2</sub> continua. The photoelectrons produced by the laser were energy analysed in order to separate the contributions from both continua, while the synchrotron radiation was scanned through the energy region of the intermediate resonances. By measuring the angular distribution of the photoelectrons with respect to the electric field vector of the laser and by comparison with results of a theoretical analysis for photoionization of polarized targets, it was possible to deduce the different components of the photoionization process via an intermediate resonance. For example, for the Ar* 3p<sup>5</sup>3d[1/2]<sub>1</sub> resonance at 13.863 eV excitation energy, the measured value β = 0.64 ± 0.04 corresponds to a ratio between p-wave (<italic>l</italic> = 1) and f-wave (<italic>l</italic> = 3) emission of 0.60, when the phase difference between both is neglected. On the other hand, for the Ar* 3p<sup>5</sup>3d′[1/2]<sub>1</sub> resonance at 14.304 eV, the β value of 0.98 ± 0.07 would suggest that the f-partial wave is much stronger than the p-partial wave.</p><p>In a further attempt towards complete analysis, the investigation of the partial cross section for the two-photon double resonant ionization of Xe [<cite linkend="jpb205870bib176">176</cite>] was undertaken. In these studies, linearly as well as circularly polarized synchrotron and laser light was used allowing us to induce either an alignment or an orientation of the intermediate state. The combination of measurements for the linear and circular dichroism and the careful inclusion of depolarization effects, mainly due to hyperfine interaction in the Xe atom, has made it possible to extract, e.g., the partial photoionization cross sections <italic>σ<sub>J</sub></italic> for the process:
<display-eqn id="jpb205870ueq03" lines="block" number="no" eqnalign="left"></display-eqn>In figure <figref linkend="jpb205870fig33">33</figref>, the final result of the deconvolution procedure is given. The two spectra on top of the figure illustrate the amplitude of relative changes in the photoionization spectrum on variation of the linear polarization. The remaining intensity for the Xe* 5p<sup>5</sup>8p′[1/2]<sub>0</sub> resonance for a perpendicular orientation of the polarization vectors (ϕ = 90°) demonstrates the importance of depolarization. Ideally, the intensity should drop completely to zero for this orientation. For the partial cross sections seen in the three lower panels of figure <figref linkend="jpb205870fig33">33</figref>, a clear relation between the total angular momenta <italic>J</italic> of the Xe* 5p<sup>5</sup>8p′[K]<italic><sub>J</sub></italic> resonances and the continuum is observed. In this way it was possible to resolve, in the partial cross sections, the close lying Xe* 5p<sup>5</sup>8p′[1/2]<sub>1</sub> and Xe* 5p<sup>5</sup>8p′[3/2]<sub>2</sub> resonances, which are not resolved in the total ion yield due to their inherent lifetime broadenings. Further applications of the combination of circular and linear polarization of both the synchrotron radiation and the laser will provide, in some cases, complete information on the photoionization process, i.e., the determination of the intensity of all partial waves and their relative phases, and precise comparison with theoretical descriptions will be possible.
<figure id="jpb205870fig33"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig33.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig33.jpg"></graphic-file></graphic><caption id="jpb205870fc33" label="Figure 33"><p indent="no">Photoionization spectra in the region of the Xe* 5p<sup>5</sup>8p′[K]<italic><sub>J</sub></italic> resonances excited from the 7s[3/2]<sub>1</sub> state using linearly polarized laser and synchrotron radiations of parallel (0°) and perpendicular (90°) relative orientation of their electric field vectors (upper panel), and deduced partial photoionization cross sections σ<sub>0</sub>, σ<sub>1</sub> and σ<sub>2</sub> in the same energy region (three lower panels, respectively) (from [<cite linkend="jpb205870bib176">176</cite>]).</p></caption></figure></p></sec-level3><sec-level3 id="jpb205870s5-2-2" label="5.2.2"><heading>Electron correlation in open-shell 3d and 4f atoms</heading><p indent="no">The interest of pump–probe studies combining laser and synchrotron radiations for the investigations of many-electron systems such as the 3d and 4f transition metals has been briefly discussed already in the introduction (cf figure <figref linkend="jpb205870fig05">5</figref>). Laser excitation of the outer 4s electron in the Cr 3p<sup>6</sup>3d<sup>5</sup>4s <sup>7</sup>S<sub>3</sub> ground state atom to the Cr* 3p<sup>6</sup>3d<sup>5</sup>4p <sup>7</sup>P<sub>4</sub> has strong consequences for the 3p → <italic>n</italic>d, <italic>n</italic>s excitations, in particular for the 3p → 3d giant resonance [<cite linkend="jpb205870bib177">177</cite>]. The resonance profile of the partial 3d cross section is much larger for laser-excited chromium (Γ = 1.15 eV) than for ground-state chromium (Γ = 0.75 eV). This can be explained by a different screening of the core, which prevents the anti-collapse of the 3d↓ wavefunction, which was suggested [<cite linkend="jpb205870bib178">178</cite>] as the main reason for the smaller resonance width of Cr with respect to Mn with a 3d↓ wavefunction fully localized in the core region. A further consequence of the anti-collapse is the suppression of the 3p → <italic>n</italic>d Rydberg series in the 3d cross section of laser-excited Cr. In general, the laser-excited Cr* 3p<sup>6</sup>3d<sup>5</sup>4p can be considered to occupy an intermediate position between ground-state Cr and Mn and provides an ideal possibility of proving theoretical description of the complex electronic interactions in a multi-electron system.</p><p>But the laser radiation can also serve to modify and prepare the electronic ground state of the atom. Since many cycles of laser excitation and subsequent radiative relaxation are possible within the time period in which the atoms cross the region of interaction with the laser beam, the polarization of the laser can be used to polarize the ground state. By using for example a linearly polarized laser for the excitation Cr 3p<sup>6</sup>3d<sup>5</sup>4s <sup>7</sup>S<sub>3</sub> → Cr* 3p<sup>6</sup>3d<sup>5</sup>4p <sup>7</sup>P<sub>2</sub> (figure <figref linkend="jpb205870fig34">34</figref>) an unequal population of the magnetic sublevels is induced [<cite linkend="jpb205870bib177">177</cite>]. The relative population of the sublevels is transferred from small to large <italic>m<sub>J</sub></italic> values. In the present example, <italic>m<sub>J</sub></italic> = ±3 of the ground state cannot be re-excited by the linearly polarized laser light (only Δ<italic>m</italic> = 0 transitions), and their population grows due to spontaneous decay (Δ<italic>m</italic> = ± 1) of the <italic>m<sub>J</sub></italic> = ±2 levels from the Cr* 3p<sup>6</sup>3d<sup>5</sup>4p <sup>7</sup>P<sub>2</sub> laser-excited state. After several pumping cycles and when collisional processes can be neglected, the ground state atoms are aligned. In a similar way, the excitation with circularly polarized laser light results in an orientation of the ground state. This method is particularly interesting for studies of open-shell systems having a high angular momentum <italic>J</italic> already in the ground state. The first application has been performed on Cr and Eu atoms, which were aligned by optical pumping of the transitions Cr 3p<sup>6</sup>3d<sup>5</sup> 4s <sup>7</sup>S<sub>3</sub> → Cr* 3p<sup>6</sup>3d<sup>5</sup> 4p <sup>7</sup>P<sub>2</sub> and Eu 4d<sup>10</sup>4f<sup>7</sup> 6s<sup>2 8</sup>S<sub>7/2</sub> → Eu* 4d<sup>10</sup>4f<sup>7</sup> 6s6p <sup>8</sup>P<sub>5/2</sub>, respectively. The half-filled outer shells considerably simplify the theoretical approaches and both atoms were chosen as representative testing ground for the 3d and 4f transition metals, which are the important constituents of magnetic materials in the solid phase.
<figure id="jpb205870fig34"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig34.eps" width="18pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig34.jpg"></graphic-file></graphic><caption id="jpb205870fc34" label="Figure 34"><p indent="no">Ground state populations and scheme of the pump–probe process used to align the Cr atoms in the 3p<sup>6</sup>3d<sup>5</sup>4s <sup>7</sup>S<sub>3</sub> state (adapted from [<cite linkend="jpb205870bib28">28</cite>]).</p></caption></figure></p><p>Investigations of atomic Cr started in 1996 [<cite linkend="jpb205870bib27">27</cite>, <cite linkend="jpb205870bib177">177</cite>]. The linear dichroism in the 3d photoemission was measured in the region of the 3p → 4s resonances, Cr* 3p<sup>5</sup>3d<sup>5</sup>4s<sup>2 7</sup>P<sub>4</sub>, <sup>7</sup>P<sub>3</sub> and <sup>7</sup>P<sub>2</sub>, and of the 3p → 3d giant resonance. The resonances autoionize into the Cr<sup>+</sup>3p<sup>6</sup>3d<sup>5</sup> + ϵ<italic>l</italic> and Cr<sup>+</sup>3p<sup>6</sup>3d<sup>4</sup>4s + <italic>ϵl</italic> continua with the total angular momentum <italic>J</italic> = 2, 3 and 4 and interferences with the direct photoionization of the 3d and 4s electron leads to asymmetric Fano-type resonance profiles. The 3d photoemission spectra recorded as a function of the photon energy with the linear polarization vector of the laser parallel (η = 0°) or perpendicular (η = 90°) to that of the synchrotron radiation show marked differences in the relative intensities of the Cr* 3p<sup>5</sup>3d<sup>5</sup>4s<sup>2</sup> resonances as shown in the left part (upper panel) of figure <figref linkend="jpb205870fig35">35</figref>. The linear dichroism A<sub>20</sub>β<sub>LD</sub> deduced from these data (centre panel) is in good agreement with calculation based on spin-polarized random phase approximation with exchange (SP RPAE) [<cite linkend="jpb205870bib178">178</cite>]. Sign and profiles of the structures in the linear dichroism curves allow for a detailed comparison with theory, in particular for the partial ionization cross section σ(<italic>J</italic> = 4), σ(<italic>J</italic> = 3) and σ(<italic>J</italic> = 2) and their Fano-profiles (see the lower panel of the left part of figure <figref linkend="jpb205870fig35">35</figref>).
<figure id="jpb205870fig35"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig35.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig35.jpg"></graphic-file></graphic><caption id="jpb205870fc35" label="Figure 35"><p indent="no">Left: dichroism (experimental points and theoretical line) in the 3p–4s excitation resonances of ground state Cr atoms (centre panel) determined from the measured intensity of the 3p photoelectrons (upper panel) for η = 0° (black squares) and 90° (open losanges); the partial cross sections σ<sub>2</sub>, σ<sub>3</sub> and σ<sub>4</sub> calculated within the SPRPAE approximation are shown in the lower panel. Reprinted with permission from [<cite linkend="jpb205870bib28">28</cite>], copyright 1997 by the American Physical Society. Right: Cr 3p<sup>5</sup>3d<sup>5</sup>4s <sup>8</sup>P + <italic>ϵl</italic> photoelectron spectra measured at 76 eV photon energy for two perpendicular atomic alignments (upper panel), linear dichroism LD (centre panel) and normalized linear dichroism together with the theoretical (dashed line) calculations (lower panel, from [<cite linkend="jpb205870bib27">27</cite>]).</p></caption></figure></p><p>A more detailed analysis of the photoionization process can be obtained by measuring the linear dichroism (LD) and the linear magnetic dichroism in the angular distribution (LMDAD) for direct photoionization [<cite linkend="jpb205870bib27">27</cite>, <cite linkend="jpb205870bib29">29</cite>]. As a result of the laser-induced polarization of the ground state, the intensities of the 3p photolines Cr<sup>+</sup>3p<sup>5</sup>3d<sup>5</sup>4s <sup>8</sup>P<sub>9/2</sub>, <sup>8</sup>P<sub>7/2</sub> and <sup>8</sup>P<sub>5/2</sub> vary strongly (see the right part, upper panel in figure <figref linkend="jpb205870fig35">35</figref>) when the relative angle η between the linear polarization vectors of laser and synchrotron radiation is changed from η = 0° to η = 90°. The difference of both spectra represents the linear dichroism, defined as LD = <italic>I</italic>(0°) − <italic>I</italic>(90°), and is given in the centre panel of the figure. In order to be able to compare the data with other experiments or with theory, the normalized LD is given in the right part (lower panel), which takes into account the cross section and the polarization of the atom and the ionizing radiation. For the case of Cr 3p photoionization to the Cr<sup>+</sup> 3p<sup>5</sup>3d<sup>5</sup>4s <sup>8</sup>P, <sup>6</sup>P + ϵs, ϵd continua the LD makes it possible to determine the ratio of the reduced dipole matrix elements <italic>D</italic><sub>s</sub> and <italic>D</italic><sub>d</sub> describing the emission of an ϵs and ϵd electron, respectively. From the presented data, a ratio |<italic>D</italic><sub>s</sub>|/|<italic>D</italic><sub>d</sub>| = 2.0(+1, − 0.5) was determined underlining the importance of ϵs continuum electrons in the 3p photoionization process at 76 eV, i.e., close to the Cooper minimum of the 3p → ϵd cross section. In addition to the ratio of the matrix elements, the phase difference (δ<sub>s</sub> – δ<sub>d</sub>) between the outgoing s and d waves is also accessible through the measurement of the LMDAD, which depends not only on the ratio of the reduced matrix elements but also on the phase difference. A value of sin(δ<sub>s</sub> – δ<sub>d</sub>) = 0.95 ± 0.05 was determined in the present experiment [<cite linkend="jpb205870bib27">27</cite>].</p><p>Similar studies were undertaken for the 5p photoemission of atomic Eu [<cite linkend="jpb205870bib29">29</cite>]. The combination of LMDAD, LDAD and phase tilt measurements was used to determine the photoionization parameters into the Eu<sup>+</sup> 4d<sup>10</sup>5p<sup>5</sup>4f<sup>7</sup>6s<sup>2 9</sup>P<sub>5</sub>, <sup>9</sup>P<sub>4</sub>, <sup>9</sup>P<sub>3</sub> + ϵs, ϵd continua at photon energies between 43 and 58 eV. Although the two measurements of the dichroism are enough to determine the relative amplitudes of the matrix elements for the ϵs and ϵd continua and the relative phase between both wavefunctions, the additional phase tilt measurement allows for a strong reduction of the error bars, since the phase tilt δ does not depend on the absolute value of the alignment parameters and is therefore a quantity which can easily be measured experimentally with high precision. A typical phase tilt measurement for the Eu 5p photoline is displayed in the left part of figure <figref linkend="jpb205870fig36">36</figref> showing the modulation of the photoelectron signal as a function of the angle η of the laser polarization direction. The phase tilt can be determined from the laser polarization angle, where maximal electron emission is observed, i.e., δ = 2η<sub>max</sub> = 87(3)° in the present case. The combination of the three measurements for photon energies of 53 eV (in the right panel of figure <figref linkend="jpb205870fig36">36</figref>) results in a very precise determination of dipole amplitudes x = |<italic>D</italic><sub>s</sub>|/|<italic>D</italic><sub>d</sub>| and the phase differences (δ<sub>s</sub> – δ<sub>d</sub>) given as the intersection (black area in figure <figref linkend="jpb205870fig36">36</figref>) of all three measurements. In general, the experiments show that it is possible to obtain ‘complete’ information on the photoionization process by dichroism measurements of polarized targets.
<figure id="jpb205870fig36"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig36.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig36.jpg"></graphic-file></graphic><caption id="jpb205870fc36" label="Figure 36"><p indent="no">Photoemission from laser-polarized Eu atoms: phase tilt measurements for the 5p<sup>5</sup>6s<sup>2 9</sup>P<sub>5</sub> level showing the modulation of the photoelectron signal as a function of the angle η between the laser and synchrotron polarization vectors (left panel), and polar plot of the different sets of values for the relative magnitude of the dipole continuum amplitudes <italic>x</italic>, the phase difference (δ<sub>s</sub> − δ<sub>d</sub>) derived from measurements of LDAD, LMDAD and phase tilt for the outgoing electron waves ϵs, ϵd at a photon energy of 53 eV (right panel); the area where all three sets intersect is the small area marked in black. Reprinted with permission from [<cite linkend="jpb205870bib29">29</cite>], copyright 1998 by the American Physical Society.</p></caption></figure></p><p>For laser-polarized ground state Cr atoms, the investigation of dichroism effects in the photoemission has been further extended to the 3p Auger spectrum [<cite linkend="jpb205870bib179">179</cite>] (showing striking similarities to the 3p photoemission) and to the 2p excitation region [<cite linkend="jpb205870bib87">87</cite>]. For example, the LMDAD of the 2p photoemission at a photon energy of 706 eV has been measured and compared to similar spectra of Cr atoms bound to an Fe surface. This direct comparison between investigations of free and bound Cr atoms allows for a clear separation of intra-atomic and inter-atomic interactions and thereby for a determination of the relative importance of both contributions. For investigations of the magnetic properties of solid 3d metals and thin films this information is of great importance. The experimental results of the linear magnetic dichroism in the 2p photoelectron spectra of free Cr atoms are explained by strong Coulomb interaction between the 2p core hole and the 3d valence electrons in the final ionic state. Since the spectra of the Cr surface layer show similar behaviour in the LMDAD, the importance of the 2p–3d Coulomb interaction is also shown for the 2p photoemisson of 3d metal thin films.</p><p>A further analysis of the linear alignment dichroism (LAD) in the 2p photoemission of free laser aligned Cr atoms demonstrates that the intermediate coupling scheme is more appropriate than the jK coupling model for the description of 2p photoelectron spectra [<cite linkend="jpb205870bib87">87</cite>]. This underlines again that measurements of different types of dichroism enable a deep analysis of the photoionization process and provide a proof for the theoretical models used to describe the many-electron interactions. As a direct result the relative values for the reduced dipole matrix elements and relative phases of the continuum wavefuntions can be determined. In the case of 2p photoionization of Cr atoms at 706 eV, the ratio between ϵs and ϵd continua was determined to be |<italic>D</italic><sub>s</sub>|/|<italic>D</italic><sub>d</sub>| = 0.173 and the phase difference to be (δ<sub>s</sub> – δ<sub>d</sub>) = 63° ± 5°.</p><p>For laser-aligned Eu, the photoemission of the 4d [<cite linkend="jpb205870bib180">180</cite>] and 4f [<cite linkend="jpb205870bib88">88</cite>, <cite linkend="jpb205870bib181">181</cite>] sub-shells has been investigated. The results of the LMDAD spectra in the 4d photoelectron spectrum of atomic Eu [<cite linkend="jpb205870bib180">180</cite>] are closely related and important for the interpretation of the circular magnetic dichroism (CMD) of solid Gd, for which the ionic state is also described by the configuration 4f<sup>7 8</sup>S. The similarity is quite obvious from the corresponding spectra (figure <figref linkend="jpb205870fig37">37</figref>) and remaining differences can be attributed to the influence of the valence electrons. The 4d photoelectron spectrum of atomic Eu (upper panel) recorded at a photon energy of 455 eV, i.e., well above the 4d ionization threshold of 136.3 eV, shows an unresolved multiplet structure assigned to the Eu<sup>+</sup> 4d<sup>9</sup>(<sup>2</sup>D) 4f<sup>7</sup>(<sup>8</sup>S) 6s<sup>2 9</sup>D states as well as to levels Eu<sup>+</sup> 4d<sup>9</sup>(<sup>2</sup>D)4f<sup>7</sup>(<sup>6</sup>L)6s<sup>2 7</sup>D resulting from the recoupling of the 4f shell. A detailed comparison of the LMDAD curve (centre panel) with theoretical predictions using the LS-coupling model as well as single configuration HF calculations shows clearly the remaining differences, in particular for the maximum of the positive lobe. Mixing with Eu<sup>+</sup> 4d<sup>9</sup>4f<sup>7</sup>5d<sup>2</sup> configurations has to be taken into account in order to reduce these differences, demonstrating the high sensitivity of dichroism measurements to electron correlations in the final state. The CMD in the 4d-photoemission of solid Gd (lower panel) shows a very similar structure.
<figure id="jpb205870fig37"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig37.eps" width="15pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig37.jpg"></graphic-file></graphic><caption id="jpb205870fc37" label="Figure 37"><p indent="no">Upper part: 4d-photoelectron spectra for parallel (open rectangles) and antiparallel (black rectangles) orientations in comparison with the results of a Hartree–Fock calculation (vertical lines) in the upper panel, and the Eu LMDAD in comparison with the same calculation in the lower panel. Lower part: CMD in the 4d-photoemission of solid Gd (from [<cite linkend="jpb205870bib180">180</cite>]).</p></caption></figure></p><p>In a similar way, the 3d partial cross section of laser-prepared Cu atoms has been investigated in the region of the 3p threshold [<cite linkend="jpb205870bib182">182</cite>]. Here a UV laser is used to prepare the copper atoms in the Cu* 3d<sup>9</sup>4s<sup>2</sup> metastable state before photoionization with the synchrotron radiation. After laser excitation from the Cu 3d<sup>10</sup>4s <sup>2</sup>S<sub>1/2</sub> ground state to the Cu* 3d<sup>10</sup>4p <sup>2</sup>P<sub>3/2</sub> excited state, there exists a small probability (about 1%) for relaxation to the Cu* 3d<sup>9</sup>4s<sup>2 2</sup>D<sub>5/2,3/2</sub> states due to an admixture of Cu*3d<sup>9</sup>4s4p in the laser-excited state. In this way, i.e., via the intermediate laser-excited state, about 5–10% of the atoms can be prepared in the Ni-like configuration Cu 3d<sup>9</sup>4s<sup>2</sup>. The experimental spectra of the partial 3d cross section (figure <figref linkend="jpb205870fig38">38</figref>) show pronounced differences in the photon energy region between 65 and 80 eV. For the laser-prepared Cu* 3d<sup>9</sup>4s<sup>2</sup> a broad asymmetric Fano-profile is observed, which is caused by the interference between the resonant Cu<sup>**</sup>3p<sup>5</sup>(<sup>2</sup>P<sub>3/2</sub>)3d<sup>10</sup>4s<sup>2</sup> excitation with following super Coster–Kronig decay and the direct ionization into the Cu<sup>+</sup> 3p<sup>6</sup>3d<sup>9</sup>4s<sup>2</sup> continuum. The spectrum is almost identical to the 3d cross section of nickel atoms with the ground state configuration Ni 3p<sup>6</sup>3d<sup>9</sup>4s. The additional 4s electron seems to have only very little effect on the resonance profile. In contrast, the partial 3d cross section of Cu 3p<sup>6</sup>3d<sup>10</sup>4s ground state atoms shows dramatic differences, since only a very little structure is observed in the region of the 3p threshold. The additional 3d electron has of course a very strong influence, since it leads to the completion of the 3d shell and therefore to a complete absence of 3p → 3d transitions.
<figure id="jpb205870fig38"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig38.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig38.jpg"></graphic-file></graphic><caption id="jpb205870fc38" label="Figure 38"><p indent="no">Experimental 3d cross sections of Ni-like Cu (black points), Ni (open losanges) and Cu (open circles) in the region of the 3p inner-shell excitations. The Cu and Ni spectra were scaled and shifted to match the Ni-like Cu spectrum, respectively. Reprinted with permission from [<cite linkend="jpb205870bib182">182</cite>], copyright 1999 by the American Physical Society.</p></caption></figure></p></sec-level3></sec-level2></sec-level1><sec-level1 id="jpb205870s6" label="6"><heading>Future developments</heading><p indent="no">Throughout this review, we have illustrated how the improved characteristics of synchrotron radiation sources had a direct impact on the quality of pump–probe experiments and lead almost immediately to deeper and more complete insight into the different mechanisms of electron correlation and photon–matter interaction. Especially, we have shown (and will show in this section) through the example of pump–probe experiments in laser excited sodium, how the use of a new generation of synchrotrons directly provided more and more new information. In view of the stable and reliable characteristics of third generation synchrotron radiation sources, such as the ALS, BESSY II, MAX II, ELETTRA, SPRING-8 and SOLEIL, the survey of laser-excited targets will certainly be continued. Some studies will be directly pursued on a refined level making use of the improved characteristics of these sources and of advanced spectroscopic techniques. High-resolution photoelectron spectroscopy on laser-excited targets (atoms and molecules) and investigations of different dichroism effects, by making use of the well-defined polarizations of the exciting light sources, are an obvious research field in the future. Somewhat more sophisticated is the development and application of more complex excitation schemes using two (or more) lasers. This will allow for a refined investigation of the influence of the outer electrons to inner-shell ionization processes, in particular of the highly excited levels and of higher orbital momenta. Finally, the probably most exciting extension of present two-photon pump–probe experiments will explore time-resolved phenomena and strong field effects opened up by the sometimes-called fourth generation sources, the VUV or x-ray free electron lasers [<cite linkend="jpb205870bib183">183</cite>, <cite linkend="jpb205870bib184">184</cite>]. In general, the combination of laser and synchrotron radiation will address in the future many exciting and unexplored research areas.</p><sec-level2 id="jpb205870s6-1" label="6.1"><heading>High-resolution and dichroism studies</heading><p indent="no">The latest experiments on laser excited alkali atoms have shown that many new aspects of electron interactions and correlations can now be brought under experimental investigation. Systematic studies are possible, as highlighted for the alkaline atoms Li [<cite linkend="jpb205870bib75">75</cite>, <cite linkend="jpb205870bib158">158</cite>], Na [<cite linkend="jpb205870bib59">59</cite>], K [<cite linkend="jpb205870bib156">156</cite>], Rb [<cite linkend="jpb205870bib153">153</cite>] and Cs [<cite linkend="jpb205870bib155">155</cite>], as well as for Cr [<cite linkend="jpb205870bib177" range="jpb205870bib177,jpb205870bib178,jpb205870bib179">177–179</cite>]. Similar studies on the more complex open-shell atoms of the 3d and 4f transition metal group will show in a much larger detail the influences of the different electronic interactions. In particular, experiments on laser-excited atoms will bring out the role of the outer electronic shell for electronic correlation and for excitation and ionization processes in deeper subshells. The possibility of resolving the different multiplet states of a particular electronic configuration will certainly trigger further theoretical efforts leading to a more complete picture of the photoionization process in its different facets.</p><p>The studies of laser-excited and laser-polarized targets (Cr, Cu, Eu) have shown that pump–probe experiments using polarized radiation constitute an ideal tool to get more insight into the photoionization mechanism. It looks quite natural that these studies will be continued and extended to other atoms in order to obtain more reliable data on the effect of aligned and/or oriented targets. A particular application is connected to the determination of partial cross sections and, eventually, even of the relative phases for the outgoing electrons. These measurements will mainly aim to probe on an advanced level the theoretical description of many-electron systems and to obtain complete information on the photoionization process for some particular cases.</p><p>More promising is the continuation of studies comparing the results of laser-prepared atomic states with those of solid targets or thin films (Cr [<cite linkend="jpb205870bib28">28</cite>], Eu [<cite linkend="jpb205870bib180">180</cite>]). In many cases the interpretation of magnetic effects in solids is based on atomic models. The study of laser-excited atoms enables here a clear distinction between intra-atomic and inter-atomic effects, i.e., to disentangle atomic and solid state effects. A particular interest will certainly be given to the strong 3p → 3d and 4d → 4f resonances for the 3d-transition metals and the lanthanides, respectively. A reliable and confirmed basis of experimental and theoretical results on atomic samples seems to be an indispensable prerequisite for the success of further developments and applications to magnetic phenomena, and experiments combining laser and synchrotron radiation provide many advantages for obtaining new results in these energy regions.</p></sec-level2><sec-level2 id="jpb205870s6-2" label="6.2"><heading>Highly excited states</heading><p indent="no">A quite new research field can be opened up by using not only one laser for the excitation of the excited atoms, but by using two or more lasers. We have seen that a first study has already been undertaken on laser-excited Na using a first generation synchrotron radiation source [<cite linkend="jpb205870bib26">26</cite>, <cite linkend="jpb205870bib113">113</cite>]. At that time, the Na* 2p<sup>6</sup>4d level was excited from the Na 2p<sup>6</sup>3s ground state via the Na* 2p<sup>6</sup> 3p by the interaction with two lasers. The main difficulties in the experiment resulted from the large number of different excited states which were populated by the radiative cascades, making the analysis very difficult. The higher spectral resolution and higher brilliance of the synchrotron radiation available nowadays makes this type of studies actually feasible. In addition, the use of pulsed and synchronized laser sources (at least for one step of the excitation ladder) would provide the possibility of introducing a time-marker in the cascade processes and therefore to (partially) select or to favour a particular excited state.</p><p>More generally, this type of experiments will enable the study of the influence of higher orbital momenta. Systematic investigations of the dependence of inner-shell photoionization processes on the main quantum number <italic>n</italic> and, more specifically, on the magnetic orbital <italic>l</italic> of the outer electron can be undertaken in order to separate clearly the particular importance of the different interactions in a complex multi-electron system. Additionally, two (or more)-electron excitations can be explored, making it possible to introduce an interaction with many electrons at the same time. A concrete application is given by the simultaneous promotion of the two outer 4s-electrons in a Ca atom into the next higher 4p shell. In a similar way, many investigations, well known in optical laser spectroscopy, can be transferred to studies of the photoionization mechanism and its dynamics.</p></sec-level2><sec-level2 id="jpb205870s6-3" label="6.3"><heading>Short pulse sources</heading><p indent="no">Starting with the operation of the new Free Electron Laser facilities providing intense femtosecond pulses in the VUV and XUV regime [<cite linkend="jpb205870bib183">183</cite>, <cite linkend="jpb205870bib184">184</cite>], new phenomena can be studied, which were not accessible by the ‘classical’ synchrotron radiation sources. The extremely high number of photons (10<sup>13</sup>–10<sup>14</sup> photons per pulse) delivered in a very short time interval (pulse width of 30–100 fs) will make it possible to investigate very dilute species (such as ions, dissociation fragments and mass selected clusters), nonlinear effects (such as two- or multi-photon processes and direct two- or multi-electron ionization) as well as time-resolved phenomena on the femtosecond time scale. Pump–probe experiments will make use of the high-intensity sub-picosecond regime for particular applications, selecting, e.g., different excited states or different intermediate states of an Auger cascade. However, in order to follow directly the Auger decay on a sub-femtosecond scale, sources based on the production of attosecond pulses from an intense optical laser seems to be the only solution at present [<cite linkend="jpb205870bib185">185</cite>, <cite linkend="jpb205870bib186">186</cite>].</p><p>First two-colour experiments have been started at the FLASH facility (the Free Electron LASer in Hamburg) using XUV pulses from the FEL in combination with a synchronized optical laser. These studies have, up to now, concentrated on the investigation of above threshold ionization (ATI) through the observation of sidebands in the photoelectron spectra [<cite linkend="jpb205870bib187">187</cite>, <cite linkend="jpb205870bib188">188</cite>], as shown in figure <figref linkend="jpb205870fig39">39</figref>. The experiments were mainly used to characterize the new source of XUV radiation, but show, in particular by its single-shot capability, the huge potential of this intense and tunable femtosecond photon source. Using the high intensities it becomes possible to manipulate not only the electrons bound in the electronic cloud of the atom, as it has been done and discussed in this pump–probe review, but also free electrons after ejection from the atom by the photoionization process.
<figure id="jpb205870fig39"><graphic><graphic-file version="print" format="EPS" filename="images/jpb205870fig39.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/jpb205870fig39.jpg"></graphic-file></graphic><caption id="jpb205870fc39" label="Figure 39"><p indent="no">Photoelectron spectra of atomic He (left) and Xe (right) recorded after photoionization with XUV-FEL radiation at 25 nm and 13.7 nm, respectively in the presence of a strong infrared laser (800 nm). Besides the main one-photon lines, the additional sidebands (SB) arising from above threshold ionization (ATI) are indicated (from [<cite linkend="jpb205870bib188">188</cite>]).</p></caption></figure></p><p>Future studies will take advantage of the wavelength tunability of the FEL, bringing it then closer to the synchrotron radiation sources. This will allow the excitation of a particular highly excited short-lived resonance and, through a pump–probe excitation scheme, the subsequent excitation of this autoionization state by a second laser. Due to the high number of photons available in a short femtosecond pulse, the two autoionizing states will be coupled by the optical laser giving rise to particular dynamical phenomena. First theoretical studies of the underlying processes have already been performed for the case of atomic He, coupling the doubly excited He* 2s3p and He* 2s3d states [<cite linkend="jpb205870bib189">189</cite>], as well as for atomic Na, in particular for the Na* 2p<sup>5</sup>3s3p and Na* 2p<sup>5</sup>3s3d resonances [<cite linkend="jpb205870bib174">174</cite>]. The calculated Fano profiles of these resonances show a strong dependence on the laser intensity, on the relative temporal delay between the XUV and the optical laser pulse as well as on wavelength detuning of one of the two photon sources. These studies allow probing the autoionization states in a different way than the pioneer studies, since the sensitivity of electron correlations to the coupling with another state of opposite parity and, thereby, with different continua of other parity, is investigated.</p><p>Moreover, in the two-colour excitation processes, resonances of the same parity as the ground state are accessible and their subsequent Auger decay can be investigated. A simple, but interesting, example is given by the study of even parity 4d → <italic>n</italic>s, <italic>m</italic>d resonances in atomic Xe, e.g., the Xe* 4d<sup>9</sup>5s<sup>2</sup>5p<sup>6</sup>6d resonance. These resonances can be excited either by a two-photon excitation using only the strong FEL pulse at half the energy of the resonance or by a two-photon two-colour excitation using the FEL and the optical laser. For the later, depending on the wavelength of the optical laser, the final resonance energy is obtained by selecting with the FEL a virtual intermediate continuum state or, e.g., the strong Xe 4d<sup>9</sup>5s<sup>2</sup>5p<sup>6</sup>6p resonance. The relaxation of the core-excited state is then observed via the resonant Auger effect, leading to final Xe<sup>+</sup> 5p<sup>4</sup>6d states. Auger transitions to these final states have not been studied yet and the comparison of spectra obtained by the various ways of excitation provides information on the relaxation dynamics. Many similar studies will become possible and many phenomena, e.g., the formation of Rydberg state wavepackets and quantum interferences of coherently excited states [<cite linkend="jpb205870bib190" range="jpb205870bib190,jpb205870bib191,jpb205870bib192">190–192</cite>], can now be studied in the XUV regime by making use of the strong and short FEL radiation. The coherent excitation of many highly excited states and the observation of its temporal (and spatial) distribution by the pump–probe technique will open a different view to the dynamics of underlying relaxation processes. A further, large research field (exceeding the scope of this review) is given by the studies of molecular ionization and dissociation phenomena by time-resolved pump–probe spectroscopy [<cite linkend="jpb205870bib193">193</cite>, <cite linkend="jpb205870bib194">194</cite>]. Atomic fragments will act here as well-identified and characterized products, which enable the investigation of the complex interplay between electronic and nuclear relaxation, i.e., between electronic and nuclear motion.</p></sec-level2></sec-level1><acknowledgment><heading>Acknowledgments</heading><p indent="no">The authors acknowledge the financial support of NATO under PST Collaborative Research Grant 980080 for part of the pump–probe experiments they have performed at the Advanced Light Source. They would also like to express their thanks to some of their direct collaborators, in particular D Cubaynes, J-M Bizau, S Aloïse, J Bozek, S Diehl, M Gisselbrecht, J Lacoursière and P O'Keeffe, for their constant help in obtaining a large number of the experimental results discussed in this review. They want to extend their gratitude to L Voky, A Grum-Grzhimailo, S T Manson and V Sukhorukov for their constant assistance in providing the theoretical input necessary for the interpretation of many experiments. 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The strong potential of these pumpprobe experiments to gain information on excited atomic states is illustrated through some exemplary studies. The first series of experiments carried out with the early synchrotron sources, from 1960 to about 1995, are reviewed, including photoionization of unpolarized and polarized excited atoms, and time-resolved lasersynchrotron studies. With the most advanced generation of synchrotron sources, a whole new class of pumpprobe experiments benefiting from the high brightness of the new synchrotron beams has been developed since 1996. A detailed review of these studies as well as possible future applications of pumpprobe experiments using third generation synchrotron sources and free electron lasers is presented.</abstract><relatedItem type="host"><titleInfo><title>Journal of Physics B: Atomic, Molecular and Optical Physics</title></titleInfo><titleInfo type="abbreviated"><title>J. Phys. B: At. Mol. Opt. Phys.</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0953-4075</identifier><identifier type="eISSN">1361-6455</identifier><identifier type="PublisherID">jpb</identifier><identifier type="CODEN">JPAPEH</identifier><identifier type="URL">stacks.iop.org/JPhysB</identifier><part><date>2006</date><detail type="volume"><caption>vol.</caption><number>39</number></detail><detail type="issue"><caption>no.</caption><number>23</number></detail><extent unit="pages"><start>R425</start><end>R477</end><total>53</total></extent></part></relatedItem><identifier type="istex">180A52073CAE3E69752AADCB5FE46B867C54C592</identifier><identifier type="DOI">10.1088/0953-4075/39/23/R01</identifier><identifier type="PII">S0953-4075(06)05870-6</identifier><identifier type="articleID">205870</identifier><identifier type="articleNumber">R01</identifier><accessCondition type="use and reproduction" contentType="copyright">2006 IOP Publishing Ltd</accessCondition><recordInfo><recordContentSource>IOP</recordContentSource><recordOrigin>2006 IOP Publishing Ltd</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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