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Collisional production of fast metastable hydrogen atoms from cold H2: toward twin atoms

Identifieur interne : 000E79 ( Istex/Corpus ); précédent : 000E78; suivant : 000E80

Collisional production of fast metastable hydrogen atoms from cold H2: toward twin atoms

Auteurs : Aline Medina ; G. Rahmat ; C R De Carvalho ; Ginette Jalbert ; F. Zappa ; R F Nascimento ; R. Cireasa ; N. Vanhaecke ; Ioan F. Schneider ; N V De Castro Faria ; J. Robert

Source :

RBID : ISTEX:7C7C356D9834ED4CCD0B4E575DCD7B22D48FA8F7

Abstract

We have investigated the production of fast metastable H(22S) coming from the dissociation of cold H2 molecules produced in a Campargue nozzle beam after crossing with an electron beam emerging from a high intensity pulsed electron gun. We have achieved dissociation by electron impact in order to avoid limitations due to the selection rules governing radiative transitions. Two detectors, placed 230 and 254 mm away from the collision centre, have analysed the neutral fragments as a function of their time-of-flight through localized quenching of H(22S) in H(22P) and Lyman- detection. Performing coincidence experiments in order to ascertain the existence of the H(22S)H(22S) dissociation channel is appealing due to the anlysis of the spectra.

Url:
DOI: 10.1088/0953-4075/44/21/215203

Links to Exploration step

ISTEX:7C7C356D9834ED4CCD0B4E575DCD7B22D48FA8F7

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<div type="abstract">We have investigated the production of fast metastable H(22S) coming from the dissociation of cold H2 molecules produced in a Campargue nozzle beam after crossing with an electron beam emerging from a high intensity pulsed electron gun. We have achieved dissociation by electron impact in order to avoid limitations due to the selection rules governing radiative transitions. Two detectors, placed 230 and 254 mm away from the collision centre, have analysed the neutral fragments as a function of their time-of-flight through localized quenching of H(22S) in H(22P) and Lyman- detection. Performing coincidence experiments in order to ascertain the existence of the H(22S)H(22S) dissociation channel is appealing due to the anlysis of the spectra.</div>
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<affiliation>Laboratoire Collisions Agrgats Ractivit, IRSAMC, Univ Paul Sabatier, 31062 Toulouse Cedex 09, France</affiliation>
</author>
<author xml:id="author-8">
<persName>
<forename type="first">N</forename>
<surname>Vanhaecke</surname>
</persName>
<affiliation>Laboratoire Aim Cotton CNRS, Univ Paris Sud 11, 91405 Orsay Cedex, France</affiliation>
</author>
<author xml:id="author-9">
<persName>
<forename type="first">Ioan F</forename>
<surname>Schneider</surname>
</persName>
<affiliation>LOMC-FRE 3102-CNRS, Univ du Havre, 25 rue Philippe Lebon, BP 540, 76058, Le Havre, France</affiliation>
</author>
<author xml:id="author-10">
<persName>
<forename type="first">N V</forename>
<surname>de Castro Faria</surname>
</persName>
<affiliation>Laboratoire Aim Cotton CNRS, Univ Paris Sud 11, 91405 Orsay Cedex, France</affiliation>
<affiliation>Instituto de Fsica, UFRJ, Cx. Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil</affiliation>
</author>
<author xml:id="author-11">
<persName>
<forename type="first">J</forename>
<surname>Robert</surname>
</persName>
<affiliation>Laboratoire Aim Cotton CNRS, Univ Paris Sud 11, 91405 Orsay Cedex, France</affiliation>
</author>
</analytic>
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<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>
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<p>We have investigated the production of fast metastable H(22S) coming from the dissociation of cold H2 molecules produced in a Campargue nozzle beam after crossing with an electron beam emerging from a high intensity pulsed electron gun. We have achieved dissociation by electron impact in order to avoid limitations due to the selection rules governing radiative transitions. Two detectors, placed 230 and 254 mm away from the collision centre, have analysed the neutral fragments as a function of their time-of-flight through localized quenching of H(22S) in H(22P) and Lyman- detection. Performing coincidence experiments in order to ascertain the existence of the H(22S)H(22S) dissociation channel is appealing due to the anlysis of the spectra.</p>
</abstract>
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<head>keywords</head>
<item>
<term>metastable hydrogen atoms</term>
</item>
<item>
<term>dissociation of molecular hydrogen</term>
</item>
<item>
<term>twin atoms</term>
</item>
</list>
</keywords>
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<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>
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<year-publication>2011</year-publication>
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<issue-number>21</issue-number>
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<type-number type="paper" numbering="article" artnum="215203">215203</type-number>
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<last-page>12</last-page>
<length>12</length>
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<doi>10.1088/0953-4075/44/21/215203</doi>
<copyright>2011 IOP Publishing Ltd</copyright>
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<header>
<title-group>
<title>Collisional production of fast metastable hydrogen atoms from cold H
<sub>2</sub>
: toward twin atoms</title>
<short-title>Collisional production of fast metastable hydrogen atoms from cold H
<sub>2</sub>
</short-title>
<ej-title>Collisional production of fast metastable hydrogen atoms from cold H2</ej-title>
</title-group>
<author-group>
<author address="jpb399600ad1 jpb399600ad2">
<first-names>Aline</first-names>
<second-name>Medina</second-name>
</author>
<author address="jpb399600ad1">
<first-names>G</first-names>
<second-name>Rahmat</second-name>
</author>
<author address="jpb399600ad1 jpb399600ad2" email="jpb399600ea1">
<first-names>C R</first-names>
<second-name>de Carvalho</second-name>
</author>
<author address="jpb399600ad1 jpb399600ad2">
<first-names>Ginette</first-names>
<second-name>Jalbert</second-name>
</author>
<author address="jpb399600ad3">
<first-names>F</first-names>
<second-name>Zappa</second-name>
</author>
<author address="jpb399600ad2 jpb399600ad4">
<first-names>R F</first-names>
<second-name>Nascimento</second-name>
</author>
<author address="jpb399600ad1 jpb399600ad5">
<first-names>R</first-names>
<second-name>Cireasa</second-name>
</author>
<author address="jpb399600ad1">
<first-names>N</first-names>
<second-name>Vanhaecke</second-name>
</author>
<author address="jpb399600ad6">
<first-names>Ioan F</first-names>
<second-name>Schneider</second-name>
</author>
<author address="jpb399600ad1 jpb399600ad2">
<first-names>N V</first-names>
<second-name>de Castro Faria</second-name>
</author>
<author address="jpb399600ad1">
<first-names>J</first-names>
<second-name>Robert</second-name>
</author>
</author-group>
<address-group>
<address id="jpb399600ad1">
<orgname>Laboratoire Aimé Cotton CNRS</orgname>
, Univ Paris Sud 11, 91405 Orsay Cedex,
<country>France</country>
</address>
<address id="jpb399600ad2">
<orgname>Instituto de Física, UFRJ</orgname>
, Cx. Postal 68528, Rio de Janeiro, RJ 21941-972,
<country>Brazil</country>
</address>
<address id="jpb399600ad3">
<orgname>Departamento de Física, UFJF</orgname>
, Juíz de Fora, MG 36036-330,
<country>Brazil</country>
</address>
<address id="jpb399600ad4">
<orgname>CEFET/RJ, UnED Petrópolis</orgname>
, RJ 25620-003,
<country>Brazil</country>
</address>
<address id="jpb399600ad5">
<orgname>Laboratoire Collisions Agrégats Réactivité, IRSAMC</orgname>
, Univ Paul Sabatier, 31062 Toulouse Cedex 09,
<country>France</country>
</address>
<address id="jpb399600ad6">
<orgname>LOMC-FRE 3102-CNRS, Univ du Havre, 25 rue Philippe Lebon</orgname>
, BP 540, 76058, Le Havre,
<country>France</country>
</address>
<e-address id="jpb399600ea1">
<email mailto="crenato@if.ufrj.br">crenato@if.ufrj.br</email>
</e-address>
</address-group>
<history received="8 July 2011" finalform="9 September 2011" online="20 October 2011"></history>
<abstract-group>
<abstract>
<heading>Abstract</heading>
<p indent="no">We have investigated the production of fast metastable H(2
<sup>2</sup>
S) coming from the dissociation of cold H
<sub>2</sub>
molecules produced in a Campargue nozzle beam after crossing with an electron beam emerging from a high intensity pulsed electron gun. We have achieved dissociation by electron impact in order to avoid limitations due to the selection rules governing radiative transitions. Two detectors, placed 230 and 254 mm away from the collision centre, have analysed the neutral fragments as a function of their time-of-flight through localized quenching of H(2
<sup>2</sup>
S) in H(2
<sup>2</sup>
P) and Lyman-α detection. Performing coincidence experiments in order to ascertain the existence of the H(2
<sup>2</sup>
S)–H(2
<sup>2</sup>
S) dissociation channel is appealing due to the anlysis of the spectra.</p>
</abstract>
</abstract-group>
<classifications>
<class-codes scheme="pacs">
<code>34.50.Gb</code>
<code>34.80.Gs</code>
<code>34.20.−b</code>
<code>34.80.Ht</code>
</class-codes>
<keywords>
<keyword>metastable hydrogen atoms</keyword>
<keyword>dissociation of molecular hydrogen</keyword>
<keyword>twin atoms</keyword>
</keywords>
</classifications>
</header>
<body numbering="bysection">
<sec-level1 id="jpb399600s1" label="1">
<heading>Introduction</heading>
<p indent="no">The dissociation of a diatomic molecule in a pair of atoms is a well-known problem, and it is also established that the two fragments, say twin atoms for a homonuclear diatomic molecule, will share some coherence between them because they are linked to the same molecular state. The signature of the coherence between the fragments is revealed in coincidence experiments, for the centre of mass (CM) and relative motions, but a finer analysis also requires the spin coherence between the atoms to be detected, in the same way as performed for twin photons [
<cite linkend="jpb399600bib01">1</cite>
].</p>
<p>The superexcited states of the H
<sub>2</sub>
molecules have been shown to be good candidates for performing twin photons experiments, using the dissociation in twin H(2
<sup>2</sup>
P) atoms that disintegrate in twin Lymann-α photons [
<cite linkend="jpb399600bib02">2</cite>
]. As the spin analysis of the H(2
<sup>2</sup>
S) atom has been achieved through the use of Stern–Gerlach interferometry [
<cite linkend="jpb399600bib03">3</cite>
], it is legitimate to investigate the dissociation of superexcited states of the H
<sub>2</sub>
molecule in pairs of twin H(2
<sup>2</sup>
S) atoms. Other systems are, or have been, in focus such as Hg
<sub>2</sub>
, the first system that has been extensively studied [
<cite linkend="jpb399600bib04">4</cite>
], and there is current work in progress in cold or ultracold conditions [
<cite linkend="jpb399600bib05">5</cite>
].</p>
<p>This paper presents the first step of this study where we have revisited the dissociation of H
<sub>2</sub>
molecules excited by electron impact, using a molecular nozzle beam in order to use molecules with cold internal degrees of freedom and high intensity flux. We have sought the optimal experimental conditions for the largest possible production of H(2
<sup>2</sup>
S) atoms.</p>
<p>The paper is organized as follows: in section
<secref linkend="jpb399600s2">2</secref>
, we present a small survey of the studies concerning superexcited states of the H
<sub>2</sub>
molecule; in section
<secref linkend="jpb399600s3">3</secref>
, we discuss our experimental conditions. In section
<secref linkend="jpb399600s4">4</secref>
, the inversion of the time-of-flight (TOF) spectra in the laboratory frame to the energy spectra in the molecular frame is described in detail and the precision of the overall process is discussed including the behaviour of the cross section for H(2
<sup>2</sup>
S) production with respect to the electron excitation energy. Section
<secref linkend="jpb399600s5">5</secref>
is devoted to the analysis of the energy spectra using both a direct fitting procedure and a reconstruction of the spectra with the available theoretical potential energy curves (PECs). A tentative assignment of the relevant PECs is given and in the conclusion we discuss the optimal experimental conditions to get twin H(2
<sup>2</sup>
S) atoms.</p>
</sec-level1>
<sec-level1 id="jpb399600s2" label="2">
<heading>Dissociation of H
<sub>2</sub>
molecules in fast H(2
<sup>2</sup>
S) atoms</heading>
<p indent="no">In order to produce a pair of fast H(2
<sup>2</sup>
S) atoms, one has to reach a
<italic>doubly</italic>
excited molecular electronic state. For the sake of clarity, we give a brief summary of the characterization of the electronic states of molecular hydrogen. These states are often designated with respect to their dominant configurations in a Rydberg series built on the H
<sup>+</sup>
<sub valign="yes">2</sub>
ionic core, and as these states are in fact resonances, because they are embedded in the ionization continuum of H
<sub>2</sub>
→ H
<sup>+</sup>
<sub valign="yes">2</sub>
+
<italic>e</italic>
, they also possess a resonance width, as shown in figure
<figref linkend="jpb399600fig01">1</figref>
. Their names are commonly given in the form Q
<sub>
<italic>i</italic>
</sub>
<sup>2S + 1</sup>
Λ
<sub>
<italic>u</italic>
,
<italic>g</italic>
</sub>
(
<italic>j</italic>
), where
<italic>j</italic>
stands for the number of the state, numbered by increasing energy, of the Q
<sub>
<italic>i</italic>
</sub>
group.
<figure id="jpb399600fig01" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig01.eps" width="31pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig01.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc01" label="Figure 1">
<p indent="no">PECs as a function of the inter-atomic distance for H
<sub>2</sub>
below and above ionization threshold. The relevant Q
<sub>1</sub>
and Q
<sub>2</sub>
relevant family of states are represented. Reproduced from [
<cite linkend="jpb399600bib06">6</cite>
]. Copyright 2011 by IOP publishing.</p>
</caption>
</figure>
</p>
<p>The ground state, correlating to H(1
<italic>s</italic>
) + H(1
<italic>s</italic>
), together with all of the excited states which correlate to H(1
<italic>s</italic>
) + H(
<italic>n</italic>
ℓ), belongs to the Rydberg series of
<italic>mono</italic>
-excited states having the dominant configuration H
<sub>2</sub>
(1
<italic>s</italic>
σ
<sub>
<italic>g</italic>
</sub>
,
<italic>n</italic>
ℓλ
<sub>
<italic>g</italic>
/
<italic>u</italic>
</sub>
). Their PECs are situated
<italic>below</italic>
that of the X
<sup>2</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>g</italic>
</sub>
(1
<italic>s</italic>
σ
<sub>
<italic>g</italic>
</sub>
) ground-state PEC of the ion. The states situated between the ground and the first excited state of H
<sup>+</sup>
<sub valign="yes">2</sub>
,
<sup>2</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>u</italic>
</sub>
(2
<italic>p</italic>
σ
<sub>
<italic>u</italic>
</sub>
), correlate to H(1
<italic>s</italic>
) + H(
<italic>n</italic>
⩾ 2) and form the so-called Q
<sub>1</sub>
group. It consists in a Rydberg series of configuration (2
<italic>p</italic>
σ
<sub>
<italic>u</italic>
</sub>
,
<italic>n</italic>
ℓλ
<sub>
<italic>g</italic>
/
<italic>u</italic>
</sub>
,
<italic>n</italic>
⩾ 2). As for the states correlating to the H(2
<italic>s</italic>
) + H(2
<italic>s</italic>
) limit, they belong to the Q
<sub>2</sub>
group, built on the second excited state of H
<sup>+</sup>
<sub valign="yes">2</sub>
,
<sup>2</sup>
Π
<sub>
<italic>u</italic>
</sub>
(2
<italic>p</italic>
π
<sub>
<italic>u</italic>
</sub>
).</p>
<p>Several theoretical groups carry out these molecular dynamics studies by computing and exploring all of these doubly excited states. Extensive calculations, mainly in the range of internuclear distances
<italic>R</italic>
= 0–6 au, of the Q
<sub>1</sub>
and Q
<sub>2</sub>
doubly excited states were performed in the framework of the Born–Oppenheimer approximation using quantum chemistry [
<cite linkend="jpb399600bib07">7</cite>
], an
<italic>R</italic>
-matrix approach [
<cite linkend="jpb399600bib08">8</cite>
], a quantum defect method [
<cite linkend="jpb399600bib09">9</cite>
] and Feshbach-operator techniques [
<cite linkend="jpb399600bib10">10</cite>
,
<cite linkend="jpb399600bib11">11</cite>
]. The long-range interactions were addressed by Jonsell
<italic>et al</italic>
[
<cite linkend="jpb399600bib12">12</cite>
], who focused on the study of the relevant Q
<sub>2</sub>
doubly excited states of H
<sub>2</sub>
dissociating into H(2ℓ) + H(2ℓ′). Their numerical calculations extended the previously available data from the internuclear distance
<italic>R</italic>
= 6 au to
<italic>R</italic>
= 22 au, although the method employed cannot accurately determine the PEC at short internuclear distances. The photodissociation path toward the fast H(2
<italic>s</italic>
) production has been explored by Sanz-Vicario
<italic>et al</italic>
[
<cite linkend="jpb399600bib13">13</cite>
] with a nonperturbative time-dependent method which describes autoionization of H
<sub>2</sub>
doubly excited states and its manifestation in dissociative and nondissociative ionization, when the molecule interacts with femtosecond XUV laser pulses. They found that the states which photodissociate into H(2
<italic>s</italic>
)+H(
<italic>nl</italic>
) are Q
<sub>1</sub>
<sup>1</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>u</italic>
</sub>
(1) and Q
<sub>2</sub>
<sup>1</sup>
Π
<sub>
<italic>u</italic>
</sub>
(1).</p>
<p>On the experimental side, three decades ago, Spezeski
<italic>et al</italic>
[
<cite linkend="jpb399600bib14">14</cite>
] produced the TOF spectra of H(2
<sup>2</sup>
S) in electron-impact dissociation experiments on H
<sub>2</sub>
. In spite of low resolution, they concluded that the major H
<sub>2</sub>
dissociation channels were Q
<sub>2</sub>
<sup>1</sup>
Π
<sub>
<italic>u</italic>
</sub>
(1π
<sub>
<italic>u</italic>
</sub>
<sub>
<italic>g</italic>
</sub>
) and Q
<sub>1</sub>
<sup>1</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>g</italic>
</sub>
(1σ
<sub>
<italic>u</italic>
</sub>
<sup>2</sup>
). Glass-Maujean
<italic>et al</italic>
[
<cite linkend="jpb399600bib15">15</cite>
] modelled experimental photodissociation cross section data in order to quantify the competition between the various decay channels and to obtain information on the dynamics of the different doubly excited states. In order to evaluate the H(2
<sup>2</sup>
S) production cross section, they monitored the contributions of the Q
<sub>1</sub>
<sup>1</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>u</italic>
</sub>
(2), Q
<sub>2</sub>
<sup>1</sup>
Π
<sub>
<italic>u</italic>
</sub>
(1, 4, 5), Q
<sub>3</sub>
<sup>1</sup>
Π
<sub>
<italic>u</italic>
</sub>
(2) H
<sub>2</sub>
states and of the (2
<italic>s</italic>
σ
<sub>
<italic>g</italic>
</sub>
) H
<sup>+</sup>
<sub valign="yes">2</sub>
state. Their study resulted in the conclusion that the Q
<sub>2</sub>
<sup>1</sup>
Π
<sub>
<italic>u</italic>
</sub>
(4, 5) states give a major contribution to the cross section. Other studies [
<cite linkend="jpb399600bib16">16</cite>
] showed evidence of the contribution of states belonging to the Q
<sub>3</sub>
and Q
<sub>4</sub>
groups.</p>
<p>Attempts to quantitatively relate the PECs of the doubly excited molecular states to the experimental detection of atoms were performed by Odagiri
<italic>et al</italic>
[
<cite linkend="jpb399600bib06">6</cite>
,
<cite linkend="jpb399600bib17">17</cite>
]. They used electron-energy-loss spectroscopy in coincidence to monitor the formation of H(2
<sup>2</sup>
P) at 80 eV incident energy and several scattering angles.</p>
</sec-level1>
<sec-level1 id="jpb399600s3" label="3">
<heading>Experimental method</heading>
<p indent="no">The basic layout of the experimental setup (figure
<figref linkend="jpb399600fig02">2</figref>
) is equivalent to the classical one [
<cite linkend="jpb399600bib18">18</cite>
] for TOF studies of H(2
<sup>2</sup>
S
<sub>1/2</sub>
) produced by electron impact on H
<sub>2</sub>
, i.e. a hydrogen jet crossing an electron beam at a right angle. In order to reduce the spread of the velocity distribution of the hydrogen molecules, as well as to use well-defined initial molecular states and to have sufficient target density, the hydrogen beam is produced by a Campargue-type supersonic jet source [
<cite linkend="jpb399600bib19">19</cite>
]. In the chamber where the collisions with the electrons take place, the pressure is maintained in the range of 5 × 10
<sup>−7</sup>
Torr, without the supersonic beam, to 1.2 × 10
<sup>−6</sup>
Torr, with the supersonic beam in operation, by a 2000 l s
<sup>−1</sup>
diffusion pump. The measured mean velocity of the hydrogen molecules in the supersonic jet is 2.7 km s
<sup>−1</sup>
with Δ
<italic>v</italic>
/
<italic>v</italic>
∼ 1%. The jet has a rotational temperature of about 1 K and a vibrational temperature of about 10 K. Because of the expansion, essentially all hydrogen molecules are in the vibrational level
<italic>v</italic>
= 0, with relative rotational populations that depend drastically on the detail of the expansion dynamics, but are mainly restricted to the states
<italic>J</italic>
= 0, para hydrogen or
<italic>J</italic>
= 1, ortho hydrogen [
<cite linkend="jpb399600bib20" range="jpb399600bib20,jpb399600bib21,jpb399600bib22">20–22</cite>
]. In the region where the molecular jet crosses the electron beam, its diameter is approximately 3 mm, and the flow is estimated to be about 10
<sup>22</sup>
molecules per steradian per second, which corresponds to (2.3 ± 0.2) × 10
<sup>3</sup>
molecules per microsecond per cubic millimetre in the collision volume.
<figure id="jpb399600fig02" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig02.eps" width="30pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig02.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc02" label="Figure 2">
<p indent="no">Schematic view of the experimental setup (see the text for details).</p>
</caption>
</figure>
</p>
<p>The pulsed electron gun consists of a 150 µm diameter thoriated-tungsten filament, a grid and a collimator with a circular aperture of 2 mm radius, and it produces an electron beam with an angular spread FWHM of 5°, which is detected by a Faraday cup and produced a typical average current of 2 mA in continuous operation, for 120 V acceleration. The electron beam can be pulsed by applying a negative step voltage, whose duration can be chosen in the range of 0.2–2 µs, to the filament's dc circuit, which is otherwise maintained positive in order to reduce the electron background. The typical pulse rate is 10 kHz. The electron energy is given by the difference between the potential of the filament and that of the interaction region, which has to be grounded in order to avoid the disappearance of H(2
<sup>2</sup>
S
<sub>1/2</sub>
) atoms through the coupling with radiative H(2
<sup>2</sup>
P
<sub>1/2</sub>
) states. The energy spread of the electron beam is estimated to be of about 6 eV, taking into account the voltage drop in the directly heated filament. This low resolution has no significant effect at high electron energies, as we do not intend to perform precise cross section measurements near threshold. One may also note that the coherent energy width corresponding to Δ
<italic>E</italic>
= ℏ/Δ
<italic>t</italic>
is of the order of 10 eV for electron energies of 100 eV, assuming a size of the hydrogen molecules of a few
<italic>a</italic>
<sub>0</sub>
.</p>
<p>The detection of the metastable H(2
<sup>2</sup>
S
<sub>1/2</sub>
) atoms is performed by a specially devised detection system (figure
<figref linkend="jpb399600fig03">3</figref>
). A pair of these devices is placed symmetrically with respect to the plane defined by the electron beam and the H
<sub>2</sub>
beam, their detection zone being chosen at distances 230 and 254 mm away from the collision zone, in order to keep a good compromise between the counting rate and the TOF resolution and also to avoid systematic experimental errors in the measurement of the flight distances. This distance range precludes the arrival of excited H(2
<sup>2</sup>
P
<sub>1/2</sub>
) atoms since, because of their lifetime of 1.7 ns, they all decay after travelling only a few millimetres, even in the case of the fastest fragments. As these experiments were preliminaries to the search of coincidence events, care is taken to place the detectors in positions consistent with the expected recoil of the superexcited H
<sub>2</sub>
molecules after collision with the electrons, before dissociation, as described in section
<secref linkend="jpb399600s4">4</secref>
.
<figure id="jpb399600fig03" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig03.eps" width="31pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig03.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc03" label="Figure 3">
<p indent="no">(a) A detailed picture of our detection system. (b) A schematic picture of the detection system. The small spot between the needles represents the region where the atoms emit the Lyman-α radiation. This atomic emission region is not displayed full scale; its real size is much smaller than shown, as discussed in the text.</p>
</caption>
</figure>
</p>
<p>The entrance into each detection system takes place through a collimator of 2 mm diameter, followed by a pair of needles normal to the direction of H(2
<sup>2</sup>
S
<sub>1/2</sub>
) atoms. The potential difference applied to these needles was chosen to be 200 V and produces an electrostatic field of maximum value 4 × 10
<sup>4</sup>
V m
<sup>−1</sup>
that mixes the 2
<sup>2</sup>
S
<sub>1/2</sub>
and 2
<sup>2</sup>
P
<sub>1/2</sub>
states of the atoms, quenching them, i.e. allowing them to decay to the 1
<sup>2</sup>
S
<sub>1/2</sub>
state and consequently producing Lyman-α radiation (1216 Å). In order to avoid counting photons originating from the de-excitation of short-lived states and of radiative molecular states, a channel electron multiplier detector of 10 mm aperture is oriented at right angles with respect to the atom trajectories and to the needles, and is located 4 mm away from the needles. Before being detected, the Lyman-α radiation passes through a grid and a MgF
<sub>2</sub>
plate that shields the channeltron against massive species such as electrons and ions. The efficiency of the detection system is of the order of 0.3%, including the intrinsic detector efficiency, the effective solid angle seen by the Lyman-α radiation, the plate transparency and the grid transmission.</p>
<p>Pulses from the detectors are separately pre-amplified and amplified by standard NIM electronics. After discrimination from electronic noise, the signals are fed as stop pulses of a ‘FAST ComTec’ multi-stop time analyser card. The detector pulses are also analysed in parallel, after pre-amplification, by a fast oscilloscope. Care was taken that the average pulse heights had a uniform non-saturated value over all of the observation range. This allowed us to avoid any saturation effects, such as bleaching, that can arise because of the huge peak associated with the electron pulse itself. As a consequence, all experimental spectra appear on a very small and uniform background.</p>
</sec-level1>
<sec-level1 id="jpb399600s4" label="4">
<heading>Experimental TOF spectra and collision kinematics</heading>
<p indent="no">The experimental TOF spectrum obtained for an electron collision energy of 126 eV, that we have used for the calibration of our data, is presented in figure
<figref linkend="jpb399600fig04">4</figref>
for the detector at 254 mm from the collision centre. In this spectrum, one can distinguish three main regions corresponding to increasing TOFs: (i) a very bright peak related to the electron gun pulse, in width and intensity, (ii) a contribution of fast atoms, not resolved, and (iii) a contribution of slow atoms at a larger TOF, which is not quite as well resolved as the spectra obtained by photoabsorption [
<cite linkend="jpb399600bib23">23</cite>
] and whose structures will be analysed elsewhere [
<cite linkend="jpb399600bib24">24</cite>
].
<figure id="jpb399600fig04" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig04.eps" width="26pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig04.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc04" label="Figure 4">
<p indent="no">TOF spectrum—see the text for details.</p>
</caption>
</figure>
</p>
<p>The quenching electric field profile inside the detection system acts in a very localized region that is of the order of 10 µm and located about 10 µm in front of the needle axis for atoms with velocities in the range of a few dozens of km s
<sup>−1</sup>
and needle voltages in the 10–500 V range. This value is obtained through the analysis of spectra taken with different values of the needle voltage, where the intensities of the peaks for slow and fast atoms saturate for different field values. The lifetime τ
<sub>Stark</sub>
of an atom initially in a 2
<sup>2</sup>
S level in an electric field is given by [
<cite linkend="jpb399600bib25">25</cite>
]
<display-eqn id="jpb399600eqn01" eqnnum="1"></display-eqn>
τ
<sub>2P</sub>
= 1.7 ns is the lifetime of the 2P level, Ω = 1.06 GHz is the Lamb shift,
<italic>e</italic>
the electron charge,
<italic>a</italic>
<sub>0</sub>
the Bohr radius so that
<italic>A</italic>
= 3.5 × 10
<sup>−2</sup>
s V
<sup>2</sup>
m
<sup>−2</sup>
and
<italic>F</italic>
the electric field intensity in V m
<sup>−1</sup>
. Building a model where we assume a Gaussian distribution for the electric field intensity
<italic>F</italic>
(
<italic>z</italic>
), centred at the location of the needles
<italic>z</italic>
<sub>0</sub>
and localized in a domain of size
<italic>b</italic>
, for a flight distance
<italic>z</italic>
, corresponding to an applied value
<italic>F</italic>
<sub>0</sub>
, such that
<display-eqn id="jpb399600eqn02" eqnnum="2"></display-eqn>
one obtains for the intensity
<italic>N</italic>
(
<italic>z</italic>
,
<italic>v</italic>
) of the emitted photons for atoms of velocity
<italic>v</italic>
at position
<italic>z</italic>
, received by the channeltron:
<display-eqn id="jpb399600eqn03" lines="multiline" eqnnum="3" eqnalign="left"></display-eqn>
where
<italic>r</italic>
is the radius of the channeltron cone,
<italic>h</italic>
is the distance from the needles to the entrance of the cone, α is the loss due to the grids and the
<italic>MgF</italic>
<sub>2</sub>
window,
<italic>F</italic>
<sub>0</sub>
is the value imposed on the electric field and
<italic>N</italic>
<sub>0</sub>
(
<italic>v</italic>
) is the atom velocity distribution. One can note that the detection occurs at a distance differing from
<italic>z</italic>
<sub>0</sub>
by the value
<inline-eqn></inline-eqn>
.
<fnref linkend="jpb399600fn01"></fnref>
</p>
<p>Thus, the uncertainty on the total flight length is given by the size of the interaction zone between the electron and the molecular beams, i.e. 2 mm, and consequently the main uncertainty in the TOF is due to the electron pulse duration: our best resolved peak involves an electron pulse of 0.25 µs duration with a flight length distance of 254 mm, which leads to a peak with a maximum around 8.0 µs and consequently to a TOF uncertainty of 0.125 µs/8.0 µs ≈ 1.7%.</p>
<p>The experimental TOF spectra obtained for electron collision energies between 10 and 126 eV are presented in figure
<figref linkend="jpb399600fig05">5</figref>
. They correspond to the measurements of one detector, normalized both to electron beam current and acquisition time, for the detector at 230 mm from the collision centre.
<figure id="jpb399600fig05">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig05.eps" width="20.5pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig05.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc05" label="Figure 5">
<p indent="no">TOF spectra of H(2
<sup>2</sup>
S) atoms dissociated from H
<sub>2</sub>
.</p>
</caption>
</figure>
</p>
<p>As mentioned previously, the very high peak close to zero is related to the electron gun pulse, as seen by the channel electron multiplier detectors through the holes which allow pumping in the channeltron. Its width is related to the width of the triggering pulse. It is used for setting the correct zero time for the TOF measurements. In these spectra the traditional classification of the metastable H(2
<sup>2</sup>
S) atoms into ‘slow’ (velocities of about 10 km s
<sup>−1</sup>
) and ‘fast’ (velocities of about 35 km s
<sup>−1</sup>
) is evident, as well as their energetic thresholds: while the slow atoms coming from the simply excited states are visible in our entire energy range, the fast atoms, originating from the doubly excited states, require electron energies greater than 30 eV.</p>
<p>In order to express the data of figure
<figref linkend="jpb399600fig05">5</figref>
as a function of
<italic>E</italic>
<sub>H</sub>
, the kinetic energy of the H(2
<sup>2</sup>
S) atoms in the CM reference frame, we need to describe the kinematics of the dissociation. Frame transformation for the velocity vectors is written as
<display-eqn id="jpb399600eqn04" eqnnum="4"></display-eqn>
where
<inline-eqn></inline-eqn>
is the velocity of the excited H
<sub>2</sub>
molecule after electron impact in the laboratory reference frame (LAB),
<inline-eqn></inline-eqn>
is the velocity of one of the H atoms in the molecular CM reference frame (CM
<inline-eqn></inline-eqn>
),
<inline-eqn></inline-eqn>
is the velocity of the same fragment in the laboratory reference frame,
<inline-eqn></inline-eqn>
is the distance vector between the collision zone and the detector and τ is the TOF. Starting from
<inline-eqn></inline-eqn>
,
<italic>E</italic>
<sub>H</sub>
is expressed as
<display-eqn id="jpb399600eqn05" eqnnum="5"></display-eqn>
where
<inline-eqn></inline-eqn>
is written as
<display-eqn id="jpb399600eqn06" eqnnum="6"></display-eqn>
<inline-eqn></inline-eqn>
being the velocity of the H
<sub>2</sub>
-electron CM and
<inline-eqn></inline-eqn>
the velocity of the excited molecule in the CM frame, see figure
<figref linkend="jpb399600fig06" override="yes">6(a)</figref>
. This velocity has the magnitude
<display-eqn id="jpb399600eqn07" eqnnum="7"></display-eqn>
where μ is the reduced mass of the system and
<italic>E
<sub>a</sub>
</italic>
is the total energy in the CM reference frame, i.e. the available energy corresponding to the initial energies
<italic>E
<sub>e</sub>
</italic>
and
<inline-eqn></inline-eqn>
of the electron and molecule:
<display-eqn id="jpb399600eqn08" eqnnum="8"></display-eqn>
Δ
<italic>E</italic>
is the energy transferred to the molecule by the impact of the electron. This latter quantity is involved in the energy conservation law
<display-eqn id="jpb399600eqn09" eqnnum="9"></display-eqn>
where
<italic>E</italic>
<sub>0</sub>
and
<italic>E
<sub>d</sub>
</italic>
are the ground state and the dissociation energy, respectively.
<figure id="jpb399600fig06" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig06.eps" width="36pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig06.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc06" label="Figure 6">
<p indent="no">(a) The Newton diagram representing the electron–molecule collision as follows:
<inline-eqn></inline-eqn>
and
<inline-eqn></inline-eqn>
are the velocities of H
<sub>2</sub>
and electron, respectively, before the collision in the LAB frame. For the sake of clarity the vectors are not to scale. In fact,
<inline-eqn></inline-eqn>
;
<inline-eqn></inline-eqn>
is the H
<sub>2</sub>
-electron CM velocity in the LAB frame;
<inline-eqn></inline-eqn>
and
<inline-eqn></inline-eqn>
are the velocities of H
<sub>2</sub>
and electron, respectively, before the collision in the H
<sub>2</sub>
-electron CM frame (CM);
<inline-eqn></inline-eqn>
is the velocity of H
<sub>2</sub>
after the collision in the LAB frame; and
<inline-eqn></inline-eqn>
is the velocity of H
<sub>2</sub>
after the collision in the CM frame. (b) Three-dimensional diagram representing the H
<sub>2</sub>
dissociation corresponding to the collision sketched in panel (a):
<inline-eqn></inline-eqn>
and
<inline-eqn></inline-eqn>
are the velocities of one of the two H atoms in the CM
<inline-eqn></inline-eqn>
frame and in the LAB frame, respectively. This figure is also not to scale;
<inline-eqn></inline-eqn>
,
<inline-eqn></inline-eqn>
. This inequality guarantees the approximation used to transform the TOF spectrum into the energy spectrum.</p>
</caption>
</figure>
</p>
<p>In order to obtain
<inline-eqn></inline-eqn>
, the recoil of the H
<sub>2</sub>
molecules due to the impact of the electrons has to be known. For example, a completely inelastic frontal collision with a 120 eV electron could contribute to the molecule's final velocity as much as 2/3 of its initial velocity in the supersonic beam. In order to evaluate recoil possibilities one has to take care of the angular differential cross sections for electronic excitation by electron scattering in the specific case of the states that contribute to our signal. This kind of information is available for H
<sub>2</sub>
for a variety of low lying electronic states [
<cite linkend="jpb399600bib26">26</cite>
], but not for those involved in the metastable H(2
<sup>2</sup>
S) pair production.</p>
<p>The graphic representation of the collision kinematics, in which energy and momentum conservation are taken into account, the so-called Newton diagram, is displayed in figure
<figref linkend="jpb399600fig06">6</figref>
in the case of 120 eV electrons colliding at a right angle with the H
<sub>2</sub>
supersonic beam. In the general case, if any scattering angle is possible, the final recoil velocity vector of the target can sweep the whole surface of a sphere centred at the top of the CM velocity vector (
<inline-eqn></inline-eqn>
). For elastic scattering, the radius of the sphere stands for the magnitude of the electron momentum in the CM reference frame, after the collision, divided by the target mass. If the momentum vector is reduced due to inelasticity of the collision, the radius of the sphere becomes proportionally smaller.</p>
<p>The position of the detectors can be chosen so that
<inline-eqn></inline-eqn>
is orthogonal to the plane defined by
<inline-eqn></inline-eqn>
and
<inline-eqn></inline-eqn>
, which evidently includes
<inline-eqn></inline-eqn>
. Therefore, we can write
<display-eqn id="jpb399600eqn10" eqnnum="10"></display-eqn>
where we have used
<inline-eqn></inline-eqn>
. In fact this approximation is supported by numerical simulations to estimate
<italic>E</italic>
<sub>H</sub>
from τ, for a definite distance of flight
<inline-eqn></inline-eqn>
, for several dissociation processes (different Δ
<italic>E</italic>
) and for all possible recoil angles of the excited molecule. These simulations show that in the domain of the initial energies
<italic>E
<sub>e</sub>
</italic>
and
<inline-eqn></inline-eqn>
, the error produced by the inversion process from τ to
<italic>E</italic>
<sub>H</sub>
is less than 1% when we replace any possible value of
<inline-eqn></inline-eqn>
by
<inline-eqn></inline-eqn>
. This can be understood from a simple geometrical argument based on figure
<figref linkend="jpb399600fig06">6</figref>
, as long as
<inline-eqn></inline-eqn>
for the different Δ
<italic>E</italic>
of interest: we consider that the top of the vector
<inline-eqn></inline-eqn>
is fixed on the detector position and that its bottom can cover the possible surface described by the top of
<inline-eqn></inline-eqn>
. Hence, the error in the replacement of
<inline-eqn></inline-eqn>
by
<inline-eqn></inline-eqn>
is of the order of
<inline-eqn></inline-eqn>
.</p>
<p>To deduce the distribution of the CM energy of each fragment, ρ′(
<italic>E</italic>
<sub>H</sub>
), from the TOF distribution, ρ(τ), one has to remark that
<inline-eqn></inline-eqn>
and then
<display-eqn id="jpb399600eqn11" eqnnum="11"></display-eqn>
This equation establishes how to transform the TOF spectrum into the energy spectrum in the molecular CM
<inline-eqn></inline-eqn>
frame. The resulting spectra for the fast peak contributions are presented in arbitrary units in figure
<figref linkend="jpb399600fig07">7</figref>
, as well as the dependence of the cross section of the H(2
<sup>2</sup>
S) production on the incident electron energy.
<figure id="jpb399600fig07" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig07.eps" width="26pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig07.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc07" label="Figure 7">
<p indent="no">(a) Energy spectra for the fast atoms with the same counting time intervals for different electron collision energy. From bottom to top: 26, 36, 46, 66, 86, 106 and 126 eV. (b) We display (vertical axis in arbitrary units)
<italic>I</italic>
× E
<sub>
<italic>e</italic>
</sub>
, where
<italic>I</italic>
= ∫
<sub>Fastpeak</sub>
<italic>N</italic>
(
<italic>E</italic>
)d
<italic>E</italic>
/
<italic>V</italic>
<sub>Faradaycup</sub>
, which is proportional to the H(2
<sup>2</sup>
S) production.</p>
</caption>
</figure>
</p>
<p>In these spectra, where the components of the peak are not resolved, one can guess a smooth evolution of the location of the maximum of the peak from low to higher energies as the electron energy increases, which saturates at energies higher than 60 eV (about twice the mean threshold energy). The TOF spectra are not sensitive to the temperature of the H
<sub>2</sub>
gas as one can see from previous works on these processes summarized with our contributions in table
<tabref linkend="jpb399600tab01">1</tabref>
.</p>
<table id="jpb399600tab01" frame="topbot" indent="no">
<caption id="jpb399600tc01" label="Table 1">
<p indent="no">Maximum location of the fast atoms peak.</p>
</caption>
<tgroup cols="5">
<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>
<thead>
<row>
<entry></entry>
<entry></entry>
<entry>Maximum</entry>
<entry>Peak width</entry>
<entry align="left">Electron</entry>
</row>
<row>
<entry>Date</entry>
<entry>Authors</entry>
<entry>position (eV)</entry>
<entry>(eV)</entry>
<entry align="left">energy (eV)</entry>
</row>
</thead>
<tbody>
<row>
<entry>1967</entry>
<entry>Leventhal, Robiscoe and Lea [
<cite linkend="jpb399600bib18">18</cite>
]</entry>
<entry>4.7±0.7</entry>
<entry>2.6</entry>
<entry> 60</entry>
</row>
<row>
<entry>1972</entry>
<entry>Misakian and Zorn [
<cite linkend="jpb399600bib28">28</cite>
]</entry>
<entry>4.5±0.5</entry>
<entry>2.8</entry>
<entry> 70</entry>
</row>
<row>
<entry>1977</entry>
<entry>Carnahan and Zipf [
<cite linkend="jpb399600bib29">29</cite>
]</entry>
<entry>5.1±0.4</entry>
<entry>3.1</entry>
<entry> 75</entry>
</row>
<row>
<entry>1977</entry>
<entry>Carnahan and Zipf [
<cite linkend="jpb399600bib29">29</cite>
]</entry>
<entry>5.3±0.4</entry>
<entry>3.4</entry>
<entry>100</entry>
</row>
<row>
<entry>1977</entry>
<entry>Hazi and Wiemers [
<cite linkend="jpb399600bib30">30</cite>
]</entry>
<entry>4.8±0.4</entry>
<entry>2.6</entry>
<entry>100</entry>
</row>
<row>
<entry>1980</entry>
<entry>Spezeski, Kalman and McIntyre Jr. [
<cite linkend="jpb399600bib14">14</cite>
]</entry>
<entry>5.6±0.4</entry>
<entry>3.7</entry>
<entry> 98</entry>
</row>
<row>
<entry></entry>
<entry>Present work</entry>
<entry>5.6±0.2</entry>
<entry>3.3</entry>
<entry>126</entry>
</row>
<row>
<entry></entry>
<entry>Present work</entry>
<entry>5.5±0.5</entry>
<entry>3.2</entry>
<entry>106</entry>
</row>
<row>
<entry></entry>
<entry>Present work</entry>
<entry>5.4±0.5</entry>
<entry>3.3</entry>
<entry> 86</entry>
</row>
<row>
<entry></entry>
<entry>Present work</entry>
<entry>5.4±0.5</entry>
<entry>3.4</entry>
<entry> 66</entry>
</row>
<row>
<entry></entry>
<entry>Present work</entry>
<entry>5.0±0.5</entry>
<entry>3.8</entry>
<entry> 46</entry>
</row>
<row>
<entry></entry>
<entry>Present work</entry>
<entry>4.9±0.5</entry>
<entry>3.1</entry>
<entry> 36</entry>
</row>
</tbody>
<tfoot>Experimental conditions: Reference [
<cite linkend="jpb399600bib18">18</cite>
]: &thetas; = 77° and 90°, τ
<sub>
<italic>e</italic>
</sub>
= 0.2 µs and
<italic>L</italic>
= 10 cm.</tfoot>
<tfoot>Reference [
<cite linkend="jpb399600bib28">28</cite>
]: &thetas; = 80°, τ
<sub>
<italic>e</italic>
</sub>
= 0.5 µs and
<italic>L</italic>
= 13.14 ± 0.24 cm.</tfoot>
<tfoot>Reference [
<cite linkend="jpb399600bib29">29</cite>
]: &thetas; = 90°, τ
<sub>
<italic>e</italic>
</sub>
= 0.4 µs and
<italic>L</italic>
= 28 cm.</tfoot>
<tfoot>Reference [
<cite linkend="jpb399600bib14">14</cite>
]: &thetas; = 90°, τ
<sub>
<italic>e</italic>
</sub>
= 0.1 µs and
<italic>L</italic>
= 18.3 ± 0.3 cm.</tfoot>
<tfoot>Present work: for
<italic>E
<sub>e</sub>
</italic>
= 126 eV; &thetas; = 90°, τ
<sub>
<italic>e</italic>
</sub>
= 0.25 µs and
<italic>L</italic>
= 25.4 ± 0.1 cm.</tfoot>
<tfoot>Present work: for
<italic>E
<sub>e</sub>
</italic>
= 106–36 eV; &thetas; = 90°, τ
<sub>
<italic>e</italic>
</sub>
= 0.5 µs and
<italic>L</italic>
= 23.0 ± 0.1 cm, with
<italic>E
<sub>e</sub>
</italic>
the electron energy of the electron beam, &thetas; the angle between the direction where the metastable atoms are detected and the electron-beam axis, τ
<sub>
<italic>e</italic>
</sub>
the time duration of the electron pulse and
<italic>L</italic>
the distance between the collision region and the quenching region or the detector itself (TOF distance). The uncertainties displayed above, in the maximum position (in eV), are a consequence of the uncertainties in these quantities and of the electron pulse width, and their values were extracted from [
<cite linkend="jpb399600bib14">14</cite>
]. The pressure used in all works was in the range of 10
<sup>−4</sup>
–10
<sup>−5</sup>
Torr.</tfoot>
</tgroup>
</table>
</sec-level1>
<sec-level1 id="jpb399600s5" label="5">
<heading>Analysis of the experimental results</heading>
<p indent="no">In order to analyse our results, we have used the calculations of Sánchez and Martín [
<cite linkend="jpb399600bib10">10</cite>
] for the Q
<sub>1</sub>
and Q
<sub>2</sub>
states, respectively. As mentioned in section
<secref linkend="jpb399600s3">3</secref>
, numerical estimations of the correlation between
<italic>E</italic>
<sub>H</sub>
and τ, for a definite distance of flight
<inline-eqn></inline-eqn>
, for several dissociation processes and for all possible recoil angles of the excited molecule, show that in the domain of the initial energies
<italic>E
<sub>e</sub>
</italic>
and
<inline-eqn></inline-eqn>
, the error produced by the inversion process from τ to
<italic>E</italic>
<sub>H</sub>
is less than 1%. Thus, the width of the fast peak mainly corresponds to the width of the energy distribution of the fragments obtained by reflection of the fundamental rovibrational wavefunction on the repulsive energy curves of the repulsive superexcited states.</p>
<p>At first consideration of the fast peaks, it appears difficult to separate different contributions, in which they can be resolved. We have used the available Q
<sub>1</sub>
and Q
<sub>2</sub>
PECs [
<cite linkend="jpb399600bib10">10</cite>
] and the method of reflection [
<cite linkend="jpb399600bib27">27</cite>
], in order to examine how we can reconstruct the experimental peaks from the theoretical data. In figures
<figref linkend="jpb399600fig08">8</figref>
<figref linkend="jpb399600fig11">11</figref>
, we display the 80 theoretical distributions of the energy peaks obtained by reflecting the ground-state vibrational wavefunction of H
<sub>2</sub>
on the PEC of the excited states correlating to H(2
<sup>2</sup>
S) [
<cite linkend="jpb399600bib10">10</cite>
]. These distributions are compared with the experimental peak at 126 eV, given in terms of the energy in the excited H
<sub>2</sub>
CM reference frame
<inline-eqn></inline-eqn>
. As repulsive potentials can be locally represented by exponential fits, the peaks obtained by projection can be fitted by a function of the form
<display-eqn id="jpb399600eqn12" eqnnum="12"></display-eqn>
<italic>Ec</italic>
is the energy of the peak's maximum. This function illustrates well the peaks' asymmetry, as compared to a Gaussian one, showing a larger tail toward larger energies. The theoretical peaks obtained by reflection do not take into account the relative probabilities of the different channels in the final peak. The subsequent evolution along the PECs is a challenging and complex problem to describe because the PECs are coupled with the other dissociative channels (ionization, etc) and to each other by static and dynamical couplings during the paths from the inner molecular range to the separated atom one. Nevertheless, this kind of analysis indicates the energy range spanned by the emerging atoms issuing from the different PECs and shows separated characteristics between the Q
<sub>1</sub>
and Q
<sub>2</sub>
group. It also puts limitations on the range of variation of the PECs in the inner region.
<figure id="jpb399600fig08" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig08.eps" width="36pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig08.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc08" label="Figure 8">
<p indent="no">The reflection method applied to the Q
<sub>1</sub>
and Q
<sub>2</sub>
doubly excited states. (a) PECs. The five lowest theoretical energy curves obtained by Sánchez and Martín [
<cite linkend="jpb399600bib10">10</cite>
] for the symmetry displayed on each panel are plotted as a function of the internuclear distance: energy (left vertical axis)
<italic>versus</italic>
internuclear distance (horizontal axis). The dot-dashed curves correspond to the Q
<sub>1</sub>
branch and the continuous ones to the Q
<sub>2</sub>
branch. (b), (c) Reflected peaks: (inverted horizontal axis in arbitrary units) the experimental distribution (□) is displayed with its corresponding energy uncertainty due to the electron pulse duration. The theoretical reflected peaks are displayed with arbitrary amplitudes for the sake of clarity. In the first vertical axis on the right (b), the theoretical reflected peaks for the Q
<sub>1</sub>
branch are shown. The position of the experimental peak is given in terms of the asymptotic energy limit (⧫–⧫). In the same manner, in (c) the reflected peaks for the Q
<sub>2</sub>
branch and the experimental peak in its corresponding position (◊–◊) are shown.</p>
</caption>
</figure>
<figure id="jpb399600fig09" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig09.eps" width="36pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig09.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc09" label="Figure 9">
<p indent="no">See the caption of figure
<figref linkend="jpb399600fig08">8</figref>
.</p>
</caption>
</figure>
<figure id="jpb399600fig10" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig10.eps" width="36pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig10.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc10" label="Figure 10">
<p indent="no">See the caption of figure
<figref linkend="jpb399600fig08">8</figref>
.</p>
</caption>
</figure>
<figure id="jpb399600fig11" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig11.eps" width="36pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig11.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc11" label="Figure 11">
<p indent="no">See the caption of figure
<figref linkend="jpb399600fig08">8</figref>
.</p>
</caption>
</figure>
</p>
<p>In a first approach, we have applied a guess for the fit with two Gaussian curves, labelled exp126(1) and exp126(2), that reproduces fairly well the experimental peak at 126 eV, the relative weights of the two contributions are 0.8 for the exp126(2) and 0.2 for the exp126(1). The resulting parameters are given in table
<tabref linkend="jpb399600tab02">2</tabref>
. The exp126(1) peak has characteristics in agreement with what can be expected from a pure statistical reconstruction of the peak with all 40 Q
<sub>1</sub>
contributions, taking into account the degeneracies for the position of the maximum in energy and for the width. The exp126(2) peak has a maximum position in agreement with the statistical reconstruction with the 40 Q
<sub>2</sub>
contributions, but a width which is much larger than the average one and it reflects more the dispersion in energy of the values of the peak positions, see table
<tabref linkend="jpb399600tab02">2</tabref>
. This rough analysis indicates that with our experimental conditions the weight of the Q
<sub>2</sub>
group contribution is more important than the one of the Q
<sub>1</sub>
group.
<table id="jpb399600tab02" frame="topbot">
<caption id="jpb399600tc02" label="Table 2">
<p indent="no">Summary of the preliminary analysis of the spectrum 126 eV.</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>Nature of</entry>
<entry>Maximum</entry>
<entry>Full width</entry>
<entry>Range of variation</entry>
</row>
<row>
<entry>the peak</entry>
<entry>
<italic>E</italic>
<sub>H</sub>
(eV)</entry>
<entry>(eV)</entry>
<entry>of the maxima</entry>
</row>
</thead>
<tbody>
<row>
<entry>Exp126 (1)</entry>
<entry>8.9</entry>
<entry>2.43</entry>
<entry>/</entry>
</row>
<row>
<entry>Theo mean Q1</entry>
<entry>8.69</entry>
<entry>2.16</entry>
<entry>2.59</entry>
</row>
<row>
<entry>Exp126 (2)</entry>
<entry>5.6</entry>
<entry>2.63</entry>
<entry>/</entry>
</row>
<row>
<entry>Theo mean Q2</entry>
<entry>5.67</entry>
<entry>1.44</entry>
<entry>2.28</entry>
</row>
</tbody>
<tfoot>Comparison between the two Gaussian curves, exp126(1) and exp126(2), and the two theoretical peaks (theo mean Q
<sub>1</sub>
and theo mean Q
<sub>2</sub>
) designed to reproduce them. The Gaussian exp126(1) and exp126(2) fit well the experimental 126 eV peak. The peak theo mean Q
<sub>1</sub>
is consisted of only Q
<sub>1</sub>
curves, while theo mean Q
<sub>2</sub>
just of Q
<sub>2</sub>
ones.</tfoot>
</tgroup>
</table>
</p>
<p>This indicates also that the population of the 40 Q
<sub>2</sub>
states achieved by electron impact in the molecular region does not lead to a statistical population in the exit H(2
<italic>s</italic>
) channels. This is due to the couplings of these states to other states in the intermediate region. In order to determine which combination of states is able to reproduce the experimental peaks we have performed a more refined analysis of the series of spectra corresponding to increasing electronic excitation energies. For our discussion, we have only retained the states that remain as a majority in the spectra from 66 eV to 126 eV, where the peak structure and position are stationary.</p>
<p>The resulting fits are shown in figure
<figref linkend="jpb399600fig12">12</figref>
and the states involved are listed in figure
<figref linkend="jpb399600fig13">13</figref>
. It is known that the deconvolution of spectra with so many curves can but give a guess on the real processes. Nevertheless, as these fits are related to the successive opening of dissociation channels with increasing excitation energy we may infer a possible mechanism for the predominant population of the dissociation states from the one in the molecular core where the excitation takes place. As a general result, five states are predominantly involved and the relative contributions Q
<sub>2</sub>
/Q
<sub>1</sub>
are 4/1. These values are in qualitative agreement with the results of table
<tabref linkend="jpb399600tab03">3</tabref>
where the survival probability of the Q
<sub>2</sub>
states is shown to be higher than that of the Q
<sub>1</sub>
states. We have computed these survival probabilities from the data of Tennyson [
<cite linkend="jpb399600bib08">8</cite>
].
<figure id="jpb399600fig12" width="page">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig12.eps" width="36pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig12.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc12" label="Figure 12">
<p indent="no">Fits of experimental spectra as a linear combination of the reflected peaks (dots: experiment, line: best fit).Top of each panel: corresponding electronic excitation energy.</p>
</caption>
</figure>
<figure id="jpb399600fig13">
<graphic>
<graphic-file version="print" format="EPS" filename="images/jpb399600fig13.eps" width="20.5pc"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/jpb399600fig13.jpg"></graphic-file>
</graphic>
<caption id="jpb399600fc13" label="Figure 13">
<p indent="no">The components of the fits of the experimental spectra. First column: electronic excitation energy. In the same line, the corresponding terms used in the fitting; line below: the corresponding weight.</p>
</caption>
</figure>
</p>
<table id="jpb399600tab03" frame="topbot">
<caption id="jpb399600tc03" label="Table 3">
<p indent="no">Lifetimes of superexcited states of H
<sub>2</sub>
calculated from the data of Tennyson [
<cite linkend="jpb399600bib08">8</cite>
].</p>
</caption>
<tgroup cols="5">
<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>
<thead>
<row>
<entry></entry>
<entry>Q
<sub>1</sub>
</entry>
<entry>Q
<sub>2</sub>
</entry>
<entry>Lifetime</entry>
<entry></entry>
</row>
<row>
<entry>Symmetry(state)</entry>
<entry>lifetime (fs)</entry>
<entry>lifetime (fs)</entry>
<entry>ratio Q
<sub>2</sub>
/Q
<sub>1</sub>
</entry>
<entry></entry>
</row>
</thead>
<tbody>
<row>
<entry>
<sup>1</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>g</italic>
</sub>
(1)</entry>
<entry> 0.189</entry>
<entry>  1.667</entry>
<entry> 8.820</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>1</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>g</italic>
</sub>
(2)</entry>
<entry> 1.619</entry>
<entry>  8.172</entry>
<entry> 5.048</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>3</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>g</italic>
</sub>
(1)</entry>
<entry>10.751</entry>
<entry> 86.389</entry>
<entry> 8.035</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>3</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>g</italic>
</sub>
(2)</entry>
<entry>22.192</entry>
<entry>254.621</entry>
<entry>11.474</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>1</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>u</italic>
</sub>
(1)</entry>
<entry> 0.374</entry>
<entry> 21.406</entry>
<entry>57.235</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>1</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>u</italic>
</sub>
(2)</entry>
<entry> 0.999</entry>
<entry> 27.488</entry>
<entry>27.516</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>3</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>u</italic>
</sub>
(1)</entry>
<entry> 2.682</entry>
<entry>  7.957</entry>
<entry> 2.969</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>3</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>u</italic>
</sub>
(2)</entry>
<entry> 0.772</entry>
<entry> 18.051</entry>
<entry>23.382</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>1</sup>
Π
<sub>
<italic>g</italic>
</sub>
(1)</entry>
<entry> 0.322</entry>
<entry>  1.281</entry>
<entry> 3.978</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>1</sup>
Π
<sub>
<italic>g</italic>
</sub>
(2)</entry>
<entry> 0.605</entry>
<entry>  3.526</entry>
<entry> 5.828</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>3</sup>
Π
<sub>
<italic>g</italic>
</sub>
(1)</entry>
<entry> 0.565</entry>
<entry>  3.490</entry>
<entry> 6.177</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>3</sup>
Π
<sub>
<italic>g</italic>
</sub>
(2)</entry>
<entry> 1.834</entry>
<entry> 10.945</entry>
<entry> 5.968</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>1</sup>
Π
<sub>
<italic>u</italic>
</sub>
(1)</entry>
<entry> 1.923</entry>
<entry>  0.684</entry>
<entry> 0.356</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>1</sup>
Π
<sub>
<italic>u</italic>
</sub>
(2)</entry>
<entry> 4.192</entry>
<entry>  2.291</entry>
<entry> 0.547</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>3</sup>
Π
<sub>
<italic>u</italic>
</sub>
(1)</entry>
<entry> 1.606</entry>
<entry> 21.406</entry>
<entry>13.329</entry>
<entry></entry>
</row>
<row>
<entry>
<sup>3</sup>
Π
<sub>
<italic>u</italic>
</sub>
(2)</entry>
<entry> 4.011</entry>
<entry>  7.931</entry>
<entry> 1.977</entry>
<entry></entry>
</row>
</tbody>
</tgroup>
</table>
<p>For the Q
<sub>1</sub>
group, our data are consistent with the population of mostly Q
<sub>1</sub>
<sup>3</sup>
Π
<sub>
<italic>g</italic>
</sub>
(1) states, which can be adiabatically related to 1s2p states. For the Q
<sub>2</sub>
group, the Q
<sub>2</sub>
<sup>3</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>g</italic>
</sub>
(1) states, related to the 2s2p states, the Q
<sub>2</sub>
<sup>1</sup>
Σ
<sup>+</sup>
<sub valign="yes">
<italic>g</italic>
</sub>
(2) states, and Q
<sub>2</sub>
<sup>3</sup>
Π
<sub>
<italic>u</italic>
</sub>
(2) states both related to 2s2p states appear with approximately equal weight. The 2s state is strongly degenerated with the 2p one, the degeneracy being broken by the Lamb shift radiative correction at infinite separation. The calculations of the long-range part of the PECs by the group of Dalgarno [
<cite linkend="jpb399600bib12">12</cite>
] suggest that the states of this multiplicity are strongly coupled. As a conclusion, the dissociation in H(2
<sup>2</sup>
S
<sub>1/2</sub>
) + H(2
<sup>2</sup>
S
<sub>1/2</sub>
) remains as possible as the ones in H(2
<sup>2</sup>
S
<sub>1/2</sub>
) + H(2
<sup>2</sup>
P
<sub>1/2</sub>
) and H(2
<sup>2</sup>
P
<sub>1/2</sub>
) + H(2
<sup>2</sup>
P
<sub>1/2</sub>
) that have been investigated up to now.</p>
</sec-level1>
<sec-level1 id="jpb399600s6" label="6">
<heading>Conclusions</heading>
<p indent="no">Our measurements of the H(2
<sup>2</sup>
S) atoms produced by the dissociation of doubly excited states of the H
<sub>2</sub>
molecule with electron excitation energies in the range from 36 to 126 eV show that the so-called fast metastable peak is composed of a greater fraction of states from the Q
<sub>2</sub>
group (8/10) than from the Q
<sub>1</sub>
group (2/10) and that these contributions are distinguishable by using energy considerations. We have found that the structure of the peaks for the fast H(2
<sup>2</sup>
S) atoms is quasi-stationary when the electron excitation energy is higher than 60 eV. This study ascertains the fact that the width of the dissociation peaks is due to the slope of the potential energy curve (PECs) as we have operated with molecules in the lowest vibrational and rotational levels. The analysis of the experimental spectra was performed using the available molecular PECs, the reflection method, and the assumption that the dissociation paths ‘adiabatically’ connect the PECs from short to large distances with the weak assumption that the order of the level of the same symmetry is conserved from small to infinite internuclear distances. The scenario suggested by the fit is not the only one that is compatible with our data as it disregards the recoupling between states and the 2s 2p couplings that can either be in disfavour or in favour of the production of molecular twin H(2
<sup>2</sup>
S) atoms. Performing (i) molecular dynamics calculations in order to ascertain the role played by dynamical and electronic couplings and (ii) coincidence experiments in order to ascertain both the existence of the 2s 2s dissociation channel and its weight relative to the other processes is appealing due to these results.</p>
<p>In this paper, the production of the fast metastable hydrogen atoms has been studied as a function of the variation of the electron excitation energy. With uncorrelated detectors we have observed that the signal intensities are angle independent. This will no longer be the case for coincidence experiments with correlated detectors because this configuration corresponds to the selection of definite values for the direction of the inter-atomic vector in the CM frame. This angular dependence will reflect the angular momentum conservation rules of the electron–molecule excitation process. For instance it will allow us to determine the dependence of the production of the atom pairs with respect to the forward (small electron–molecule impact parameters) or backward (high electron–molecule impact parameters) processes.</p>
</sec-level1>
<acknowledgment>
<heading>Acknowledgments</heading>
<p indent="no">We thank Professor Christian Jungen, Pierre Pillet and Olivier Dulieu for enlightening discussions on the theory of superexcited states of H
<sub>2</sub>
, and Professor J Baudon for continuous interest in this work. One of us (CRC) would like to acknowledge the friendly hospitality at the Laboratoire Aim
<inline-eqn></inline-eqn>
Cotton CNRS. RC gratefully acknowledges CNRS for her postdoctoral fellowship for the project ‘Twin atoms’. IFS acknowledges financial support from the French ANR SUMOSTAI grant, as well as European Space Agency. This work is supported by CAPES, FAPERJ, CNPq and the Scientific Cooperation Agreement CAPES/COFECUB between France and Brazil, project number Ph 636/09.</p>
</acknowledgment>
</body>
<back>
<references>
<heading>References</heading>
<reference-list type="numeric">
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<footnote id="jpb399600fn01">
<p indent="no">ProductLog[z] gives the principal solution for
<italic>w</italic>
in
<italic>z</italic>
=
<italic>w</italic>
e
<sup>
<italic>w</italic>
</sup>
.</p>
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<title>Collisional production of fast metastable hydrogen atoms from cold H2: toward twin atoms</title>
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<title>Collisional production of fast metastable hydrogen atoms from cold H2</title>
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<title>Collisional production of fast metastable hydrogen atoms from cold H2: toward twin atoms</title>
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<name type="personal">
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<namePart type="family">Medina</namePart>
<affiliation>Laboratoire Aim Cotton CNRS, Univ Paris Sud 11, 91405 Orsay Cedex, France</affiliation>
<affiliation>Instituto de Fsica, UFRJ, Cx. Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil</affiliation>
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<namePart type="family">Rahmat</namePart>
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<affiliation>Instituto de Fsica, UFRJ, Cx. Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil</affiliation>
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<affiliation>Instituto de Fsica, UFRJ, Cx. Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil</affiliation>
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<name type="personal">
<namePart type="given">F</namePart>
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<affiliation>Departamento de Fsica, UFJF, Juz de Fora, MG 36036-330, Brazil</affiliation>
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<affiliation>Laboratoire Collisions Agrgats Ractivit, IRSAMC, Univ Paul Sabatier, 31062 Toulouse Cedex 09, France</affiliation>
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<namePart type="given">N</namePart>
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<affiliation>Instituto de Fsica, UFRJ, Cx. Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil</affiliation>
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<name type="personal">
<namePart type="given">J</namePart>
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<abstract>We have investigated the production of fast metastable H(22S) coming from the dissociation of cold H2 molecules produced in a Campargue nozzle beam after crossing with an electron beam emerging from a high intensity pulsed electron gun. We have achieved dissociation by electron impact in order to avoid limitations due to the selection rules governing radiative transitions. Two detectors, placed 230 and 254 mm away from the collision centre, have analysed the neutral fragments as a function of their time-of-flight through localized quenching of H(22S) in H(22P) and Lyman- detection. Performing coincidence experiments in order to ascertain the existence of the H(22S)H(22S) dissociation channel is appealing due to the anlysis of the spectra.</abstract>
<subject>
<genre>keywords</genre>
<topic>metastable hydrogen atoms</topic>
<topic>dissociation of molecular hydrogen</topic>
<topic>twin atoms</topic>
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<title>J. Phys. B: At. Mol. Opt. Phys.</title>
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<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>2011</date>
<detail type="volume">
<caption>vol.</caption>
<number>44</number>
</detail>
<detail type="issue">
<caption>no.</caption>
<number>21</number>
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<extent unit="pages">
<start>1</start>
<end>12</end>
<total>12</total>
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<identifier type="istex">7C7C356D9834ED4CCD0B4E575DCD7B22D48FA8F7</identifier>
<identifier type="DOI">10.1088/0953-4075/44/21/215203</identifier>
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<identifier type="articleID">399600</identifier>
<identifier type="articleNumber">215203</identifier>
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