Reactive collisions between electrons and NO ions: rate coefficient computations and relevance for the air plasma kinetics
Identifieur interne : 000809 ( Istex/Corpus ); précédent : 000808; suivant : 000810Reactive collisions between electrons and NO ions: rate coefficient computations and relevance for the air plasma kinetics
Auteurs : O. Motapon ; M. Fifirig ; A. Florescu ; F O Waffeu Tamo ; O. Crumeyrolle ; G. Varin-Brant ; A. Bultel ; P. Vervisch ; J. Tennyson ; I F SchneiderSource :
- Plasma Sources Science and Technology [ 0963-0252 ] ; 2006.
Abstract
Extensive calculations of the rate coefficients for dissociative recombination (DR), elastic collisions, inelastic collisions (ICs) and superelastic collisions of NO ions on initial vibrational levels, , with electrons of energy between 105 and 10eV have been performed, with a method based on multichannel quantum defect theory. Comparisons of the DR rate coefficients with the plasma experimental results give a good agreement, confirming that the vibrationally excited NO ions recombine more slowly than those in the ground state. Also, our ground state IC rate coefficients are very similar to previously computed R-matrix data. The rate coefficients have been fitted to a modified Arrhenius law, and the corresponding parameters are given, in order to facilitate the use of the reaction data in kinetical plasma modelling.
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DOI: 10.1088/0963-0252/15/1/004
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Motapon</name><affiliation><mods:affiliation>Centre for Atomic, Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala, PO Box 8580, Douala, Cameroon</mods:affiliation></affiliation><affiliation><mods:affiliation>Junior associate of the Abdus Salam ICTP, Strada Costiera 11, 34014 Trieste, Italy.</mods:affiliation></affiliation></author><author><name sortKey="Fifirig, M" sort="Fifirig, M" uniqKey="Fifirig M" first="M" last="Fifirig">M. Fifirig</name><affiliation><mods:affiliation>Department of Chemistry, University of Bucharest, R-70900 Bucharest, Romania</mods:affiliation></affiliation></author><author><name sortKey="Florescu, A" sort="Florescu, A" uniqKey="Florescu A" first="A" last="Florescu">A. Florescu</name><affiliation><mods:affiliation>Laboratoire de Photophysique Molculaire, Universit Paris-Sud, F-91405 Orsay, France</mods:affiliation></affiliation><affiliation><mods:affiliation>Laboratoire de Physique des Atomes, Lasers, Molcules et Surfaces, Universit de Rennes I, France.</mods:affiliation></affiliation></author><author><name sortKey="Waffeu Tamo, F O" sort="Waffeu Tamo, F O" uniqKey="Waffeu Tamo F" first="F O" last="Waffeu Tamo">F O Waffeu Tamo</name><affiliation><mods:affiliation>Centre for Atomic, Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala, PO Box 8580, Douala, Cameroon</mods:affiliation></affiliation><affiliation><mods:affiliation>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</mods:affiliation></affiliation></author><author><name sortKey="Crumeyrolle, O" sort="Crumeyrolle, O" uniqKey="Crumeyrolle O" first="O" last="Crumeyrolle">O. 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Comparisons of the DR rate coefficients with the plasma experimental results give a good agreement, confirming that the vibrationally excited NO ions recombine more slowly than those in the ground state. Also, our ground state IC rate coefficients are very similar to previously computed R-matrix data. The rate coefficients have been fitted to a modified Arrhenius law, and the corresponding parameters are given, in order to facilitate the use of the reaction data in kinetical plasma modelling.</div></front></TEI><istex><corpusName>iop</corpusName><author><json:item><name>O Motapon</name><affiliations><json:string>Centre for Atomic, Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala, PO Box 8580, Douala, Cameroon</json:string><json:string>Junior associate of the Abdus Salam ICTP, Strada Costiera 11, 34014 Trieste, Italy.</json:string></affiliations></json:item><json:item><name>M Fifirig</name><affiliations><json:string>Department of Chemistry, University of Bucharest, R-70900 Bucharest, Romania</json:string></affiliations></json:item><json:item><name>A Florescu</name><affiliations><json:string>Laboratoire de Photophysique Molculaire, Universit Paris-Sud, F-91405 Orsay, France</json:string><json:string>Laboratoire de Physique des Atomes, Lasers, Molcules et Surfaces, Universit de Rennes I, France.</json:string></affiliations></json:item><json:item><name>F O Waffeu Tamo</name><affiliations><json:string>Centre for Atomic, Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala, PO Box 8580, Douala, Cameroon</json:string><json:string>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</json:string></affiliations></json:item><json:item><name>O Crumeyrolle</name><affiliations><json:string>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</json:string></affiliations></json:item><json:item><name>G Varin-Brant</name><affiliations><json:string>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</json:string></affiliations></json:item><json:item><name>A Bultel</name><affiliations><json:string>CORIA, Universit de Rouen, Avenue de l'Universit, 76800 Saint-Etienne du Rouvray, France</json:string></affiliations></json:item><json:item><name>P Vervisch</name><affiliations><json:string>CORIA, Universit de Rouen, Avenue de l'Universit, 76800 Saint-Etienne du Rouvray, France</json:string></affiliations></json:item><json:item><name>J Tennyson</name><affiliations><json:string>Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK</json:string></affiliations></json:item><json:item><name>I F Schneider</name><affiliations><json:string>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>paper</json:string></originalGenre><abstract>Extensive calculations of the rate coefficients for dissociative recombination (DR), elastic collisions, inelastic collisions (ICs) and superelastic collisions of NO ions on initial vibrational levels, , with electrons of energy between 105 and 10eV have been performed, with a method based on multichannel quantum defect theory. Comparisons of the DR rate coefficients with the plasma experimental results give a good agreement, confirming that the vibrationally excited NO ions recombine more slowly than those in the ground state. Also, our ground state IC rate coefficients are very similar to previously computed R-matrix data. 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Comparisons of the DR rate coefficients with the plasma experimental results give a good agreement, confirming that the vibrationally excited NO ions recombine more slowly than those in the ground state. Also, our ground state IC rate coefficients are very similar to previously computed R-matrix data. The rate coefficients have been fitted to a modified Arrhenius law, and the corresponding parameters are given, in order to facilitate the use of the reaction data in kinetical plasma modelling.</p></abstract><textClass><classCode scheme="">34.80</classCode><classCode scheme="">52.20</classCode><classCode scheme="">25</classCode><classCode scheme="">72</classCode></textClass></profileDesc><revisionDesc><change when="2006">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/C898871B5008A5E711FD46362558AD8E0900283A/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_4_7a.dtd" name="istex:docType"></istex:docType><istex:document><article artid="psst205242"><article-metadata><jnl-data jnlid="psst"><jnl-fullname>Plasma Sources Science and Technology</jnl-fullname><jnl-abbreviation>Plasma Sources Sci. Technol.</jnl-abbreviation><jnl-shortname>PSST</jnl-shortname><jnl-issn>0963-0252</jnl-issn><jnl-coden>PSTEEU</jnl-coden><jnl-imprint>Institute of Physics Publishing</jnl-imprint><jnl-web-address>stacks.iop.org/PSST</jnl-web-address></jnl-data><volume-data><year-publication>2006</year-publication><volume-number>15</volume-number></volume-data><issue-data><issue-number>1</issue-number><coverdate>February 2006</coverdate></issue-data><article-data><article-type type="paper" sort="regular"></article-type><type-number type="paper" artnum="004">4</type-number><article-number>205242</article-number><first-page>23</first-page><last-page>32</last-page><length>10</length><pii>S0963-0252(06)05242-X</pii><doi>10.1088/0963-0252/15/1/004</doi><copyright>2006 IOP Publishing Ltd</copyright><ccc>0963-0252/06/010023+10$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>Reactive collisions between electrons and NO<sup>+</sup> ions: rate coefficient computations and relevance for the air plasma kinetics</title><short-title>Reactive collisions of NO<sup>+</sup> ions</short-title><ej-title>Reactive collisions of NO+ ions</ej-title></title-group><author-group><author address="psst205242ad1" alt-address="psst205242ad7"><first-names>O</first-names><second-name>Motapon</second-name></author><author address="psst205242ad2"><first-names>M</first-names><second-name>Fifirig</second-name></author><author address="psst205242ad3" alt-address="psst205242ad8"><first-names>A</first-names><second-name>Florescu</second-name></author><author address="psst205242ad1 psst205242ad4"><first-names>F O</first-names><second-name>Waffeu Tamo</second-name></author><author address="psst205242ad4"><first-names>O</first-names><second-name>Crumeyrolle</second-name></author><author address="psst205242ad4"><first-names>G</first-names><second-name>Varin-Bréant</second-name></author><author address="psst205242ad5"><first-names>A</first-names><second-name>Bultel</second-name></author><author address="psst205242ad5"><first-names>P</first-names><second-name>Vervisch</second-name></author><author address="psst205242ad6"><first-names>J</first-names><second-name>Tennyson</second-name></author><author address="psst205242ad4"><first-names>I F</first-names><second-name>Schneider</second-name></author></author-group><address-group><address id="psst205242ad1"><orgname>Centre for Atomic, Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala</orgname>, PO Box 8580, Douala, <country>Cameroon</country></address><address id="psst205242ad2"><orgname>Department of Chemistry, University of Bucharest</orgname>, R-70900 Bucharest, <country>Romania</country></address><address id="psst205242ad3"><orgname>Laboratoire de Photophysique Moléculaire, Université Paris-Sud</orgname>, F-91405 Orsay, <country>France</country></address><address id="psst205242ad4"><orgname>Laboratoire de Mécanique, Physique et Géosciences, UFR Sciences et Techniques, Université du Havre</orgname>, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, <country>France</country></address><address id="psst205242ad5"><orgname>CORIA, Université de Rouen, Avenue de l'Université</orgname>, 76800 Saint-Etienne du Rouvray, <country>France</country></address><address id="psst205242ad6"><orgname>Department of Physics and Astronomy, University College London</orgname>, Gower Street, London WC1E 6BT, <country>UK</country></address><address id="psst205242ad7" alt="yes"><orgname>Junior associate of the Abdus Salam ICTP</orgname>, Strada Costiera 11, 34014 Trieste, <country>Italy</country>.</address><address id="psst205242ad8" alt="yes"><orgname>Laboratoire de Physique des Atomes, Lasers, Molécules et Surfaces, Université de Rennes I</orgname>, <country>France</country>.</address></address-group><history received="3 August 2005" finalform="31 October 2005" online="25 November 2005"></history><abstract-group><abstract><heading>Abstract</heading><p indent="no">Extensive calculations of the rate coefficients for dissociative recombination (DR), elastic collisions, inelastic collisions (ICs) and superelastic collisions of NO<sup>+</sup> ions on initial vibrational levels,
<inline-eqn></inline-eqn>, with electrons of energy between 10<sup>−5</sup> and 10 eV have been performed, with a method based on multichannel quantum defect theory. Comparisons of the DR rate coefficients with the plasma experimental results give a good agreement, confirming that the vibrationally excited NO<sup>+</sup> ions recombine more slowly than those in the ground state. Also, our ground state IC rate coefficients are very similar to previously computed R-matrix data. The rate coefficients have been fitted to a modified Arrhenius law, and the corresponding parameters are given, in order to facilitate the use of the reaction data in kinetical plasma modelling.</p></abstract></abstract-group><classifications><class-codes scheme="pacs" print="no"><code>34.80</code><code>52.20</code><code>25</code><code>72</code></class-codes></classifications></header><body numbering="bysection"><sec-level1 id="psst205242s1" label="1"><heading>Introduction</heading><p indent="no">Cold plasmas containing a large number of molecules and molecular ions constitute a subject of rising scientific interest, involving more and more technological applications. NO<sup>+</sup> has been proved to be one of the most important of such molecular ionic species, since it occurs in practically all air-assisted processes.</p><p>During the re-entry of a spatial vehicle in the high shells of the terrestrial atmosphere, the air interacting with the vehicle's surface is compressed. This leads to a subsequent increase of its temperature and its transition to a plasma state. A detailed study of this plasma and of its interaction with the exterior wall of the spacecraft is absolutely necessary, since the corresponding material must be able to support outstanding high energy fluxes. Its kinetic description needs a good knowledge of the rate coefficients of the dominant reactions, including those between electrons and molecular ions. As for the NO<sup>+</sup> ions, which are probably the dominant ionic species in this region, their concentration is strongly affected not only by the <italic>dissociative recombination</italic> (DR):
<display-eqn id="psst205242eq001" eqnnum="1.1"></display-eqn>
but also by other related competitive processes, mainly <italic>inelastic</italic> (IC) (
<inline-eqn></inline-eqn>) and <italic>superelastic</italic> (
<inline-eqn></inline-eqn>) <italic>collisions</italic> (SEC) with electrons:
<display-eqn id="psst205242eq002" eqnnum="1.2"></display-eqn>
At high energy (above 10 eV), <italic>dissociative excitation</italic>,
<display-eqn id="psst205242eq003" eqnnum="1.3"></display-eqn>
plays an important role, and at high pressure so does <italic>associative ionization</italic>:
<display-eqn id="psst205242eq004" eqnnum="1.4"></display-eqn>
In the preceding equations,
<inline-eqn></inline-eqn> and
<inline-eqn></inline-eqn> stand for the initial and final vibrational quantum numbers of the target ion, and rotational structure is neglected.</p><p>The same elementary processes contribute to the chemistry of other discharges in N<sub>2</sub> and O<sub>2</sub> mixtures such as those involved in the synthesis of nitrogen oxides, cleaning of exhaust gases resulting from combustion, plasma assisted combustion and streamer propagation.</p><p>Finally, the rate coefficients of DR can help in the accurate estimation of the temperature seasonal variations in the lower thermosphere from ionospheric data (<cite linkend="psst205242bib11">Givishvili and Leshchenko 2003</cite>).</p><p>After the pioneering theoretical estimation of the DR rate coefficient by <cite linkend="psst205242bib02">Bardsley (1968a</cite>, <cite linkend="psst205242bib03">1968b</cite>), several measurements, using various techniques, were carried out: stationary afterglow (<cite linkend="psst205242bib44">Weller and Biondi 1968</cite>), trapped ion technique (<cite linkend="psst205242bib43">Walls and Dunn 1974</cite>), merged electron–ion beam technique (<cite linkend="psst205242bib21">Mul and McGowan 1979</cite>) and shock tube (<cite linkend="psst205242bib05">Davidson and Hobson 1987</cite>).</p><p>The first elaborate DR calculations were carried out by <cite linkend="psst205242bib19">Lee (1977)</cite>. They were followed much later by those of <cite linkend="psst205242bib37">Sun and Nakamura (1990)</cite> and <cite linkend="psst205242bib41">Vâlcu <italic>et al</italic> (1998)</cite>. In the former study, based on quantum chemistry computations (<cite linkend="psst205242bib22">Nakashima <italic>et al</italic> 1989</cite>) and other studies (see [24–30] of <cite linkend="psst205242bib37">Sun and Nakamura (1990)</cite>), five dissociative states were considered: <italic>A</italic>′<sup>2</sup>Σ<sup>+</sup>, <italic>I</italic><sup>2</sup>Σ<sup>+</sup>, <italic>B</italic><sup>2</sup>Π, <italic>L</italic><sup>2</sup>Π and <italic>B</italic>′<sup>2</sup>Δ. The reaction matrix
<inline-eqn></inline-eqn> was calculated within the first order approximation, and only the 10 lowest vibrational levels (
<inline-eqn></inline-eqn>) were considered. This led to significantly smaller thermal rates as compared with the most recent experimental values (<cite linkend="psst205242bib42">Vejby-Christensen <italic>et al</italic> 1998</cite>, <cite linkend="psst205242bib20">Mostefaoui <italic>et al</italic> 1999</cite>).</p><p>In the same way, the work by Vâlcu <italic>et al</italic>, which was aimed at showing the role played by rotations in the indirect recombination process through bound Rydberg states, and which used data from <cite linkend="psst205242bib10">Giusti-Suzor and Jungen (1984)</cite> and <cite linkend="psst205242bib30">Raoult (1987)</cite> for NO<sup>+</sup> ions, yielded smaller thermal rates than experiment. In a previous paper (<cite linkend="psst205242bib33">Schneider <italic>et al</italic> 2000a</cite>), hereafter referred to as Paper I, <italic>ab initio</italic> potential curves were calibrated from <cite linkend="psst205242bib30">Raoult (1987)</cite>, and couplings were derived from the autoionization widths of <cite linkend="psst205242bib27">Rabadán and Tennyson (1997)</cite> to perform a series of multichannel quantum defect theory (MQDT) calculations of the DR cross section of NO<sup>+</sup>, assuming the molecular ion to be in its ground state (<italic>X</italic><sup>1</sup>Σ<sup>+</sup>,
<inline-eqn></inline-eqn>). In addition to the five dissociative states used by Sun and Nakamura, the highly excited 3<sup>2</sup>Π was taken into account. All the 57 vibrational levels of the ion were considered: although many of them correspond to <italic>closed</italic> channels, they do contribute through the <italic>indirect</italic> mechanism. The results obtained were in good agreement with the low-energy experimental data, up to 3 eV, and validated the reliability of the calibrated data. Nevertheless, that work was limited to the ground vibrational state of the target ion.</p><p>Recently, one of us and his co-worker (<cite linkend="psst205242bib29">Rabadán and Tennyson 1999</cite>) addressed the problem of the NO<sup>+</sup> vibrational excitation (i.e. vibrational IC, equation (<eqnref linkend="psst205242eq002">1.2</eqnref>),
<inline-eqn></inline-eqn>) and, later (<cite linkend="psst205242bib07">Faure and Tennyson 2001</cite>), that of its rotational excitation.</p><p>The purpose of the present work is to use the above described data set (<cite linkend="psst205242bib33">Schneider <italic>et al</italic> 2000a</cite>) to provide a wide range of rate coefficients for reactive collisions between NO<sup>+</sup> ions and low-energy electrons, involving not only DR and ICs, but also elastic (EC) and SECs which, to our knowledge, have not been the object of theoretical investigations for this molecular ion. This study aims to investigate the dependence of the rate coefficients on the initial vibrational level of the target and, as well, to provide data necessary to develop a kinetic model of air plasmas (<cite linkend="psst205242bib04">Bultel <italic>et al</italic> 2006</cite>). The vibrational states considered are
<inline-eqn></inline-eqn> to
<inline-eqn></inline-eqn> for all the processes.</p><p>The present paper is organized as follows. Section <secref linkend="psst205242s2">2</secref> is concerned with a brief reminder of the theory. Section <secref linkend="psst205242s3">3</secref> presents the molecular data and the calculations. In section <secref linkend="psst205242s4">4</secref>, the results are presented, discussed and compared with previously reported experimental and theoretical data. The rate coefficients of the different reactions of interest are fitted with a modified Arrhenius law in section <secref linkend="psst205242s5">5</secref>, which is followed by the conclusion.</p></sec-level1><sec-level1 id="psst205242s2" label="2"><heading>Theory</heading><p indent="no">The MQDT approach (<cite linkend="psst205242bib35">Seaton 1983</cite>, <cite linkend="psst205242bib12">Greene and Jungen 1985</cite>, <cite linkend="psst205242bib15">Jungen 1996</cite>, <cite linkend="psst205242bib19">Lee 1977</cite>, <cite linkend="psst205242bib08">Giusti-Suzor 1980</cite> has been shown to be a powerful method for the evaluation of the cross sections of the DR process. Although it was applied with great success to several diatomics like
<inline-eqn></inline-eqn> and its isotopomers (<cite linkend="psst205242bib09">Giusti-Suzor <italic>et al</italic> 1983</cite>, <cite linkend="psst205242bib31">Schneider <italic>et al</italic> 1991</cite>, <cite linkend="psst205242bib34">1997</cite>, <cite linkend="psst205242bib38">Takagi 1993</cite>, <cite linkend="psst205242bib39">Tanabe <italic>et al</italic> 1995</cite>, <cite linkend="psst205242bib01">Amitay <italic>et al</italic> 1999</cite>),
<inline-eqn></inline-eqn> (<cite linkend="psst205242bib14">Guberman and Giusti-Suzor 1991</cite>, <cite linkend="psst205242bib13">Guberman 2000</cite>), NO<sup>+</sup> (<cite linkend="psst205242bib19">Lee 1977</cite>, <cite linkend="psst205242bib37">Sun and Nakamura 1990</cite>, <cite linkend="psst205242bib41">Vâlcu <italic>et al</italic> 1998</cite>) and triatomics like
<inline-eqn></inline-eqn> (<cite linkend="psst205242bib32">Schneider <italic>et al</italic> 2000b</cite>, <cite linkend="psst205242bib18">Kokoouline <italic>et al</italic> 2001</cite>, <cite linkend="psst205242bib17">Kokoouline and Greene 2003</cite>), its application to vibrational transitions, mainly to SECs, is very recent (<cite linkend="psst205242bib25">Ngassam <italic>et al</italic> 2003a</cite>).</p><p>If we aim to describe the sensitivity of the reactive electron–cation collisions on the <italic>vibrational</italic> levels involved, the rotational effects are known to be negligible for NO<sup>+</sup> (<cite linkend="psst205242bib41">Vâlcu <italic>et al</italic> 1998</cite>), at least to first approximation. One reason for this is the weakness of the indirect process with respect to the direct one in the case of the NO<sup>+</sup>/NO system. Since rotational structure and interactions play their role especially within the indirect mechanism—due to its resonant character—the weakness of this latter process implies that the rotational effects—if of any relevance—can be roughly restricted to the existence of the centrifugual barrier, due to the rotational excitation. But even in this latter context, rotation does not matter very much, since the target ion and the neutral are <italic>equally</italic> excited and, consequently, the Franck–Condon overlaps do not change in a significant way with respect to those occurring for the case of rotationally ground states.</p><p>However, this does not mean at all (<cite linkend="psst205242bib07">Faure and Tennyson 2001</cite>) that rotational transitions are negligible. Although the theoretical reminder given below—limited here to the account of the <italic>vibrational</italic> structure and couplings—will illustrate mainly the DR, the reader should keep in mind that the other competitive reactions—SEC, EC and IC—display quite similar features.</p><p>The DR can take place by the following two mechanisms/processes:
<ordered-list id="psst205242ol1" type="roman" pattern="2"><list-item id="psst205242ol1.1"><p>the direct process where the capture takes place into a dissociative state (NO<sup>**</sup>),
<display-eqn id="psst205242eq005" eqnnum="2.1"></display-eqn></p></list-item><list-item id="psst205242ol1.2"><p>the indirect process where the capture occurs <italic>via</italic> a Rydberg state NO<sup>*</sup> which is predissociated by the NO<sup>**</sup> state,
<display-eqn id="psst205242eq006" eqnnum="2.2"></display-eqn></p></list-item></ordered-list></p><p>In both cases, the autoionization is competitive with the predissociation and leads, through the reaction (<eqnref linkend="psst205242eq002">1.2</eqnref>), to SEC, EC or ICs. In this work NO<sup>**</sup> and NO<sup>*</sup> represent the doubly excited and singly excited states of NO, respectively.</p><p>The MQDT treatment of DR involves ionization channels (describing the electron–ion scattering) and dissociation channels (describing the atom–atom scattering). Each ionization channel consists of a Rydberg series of excited states, extrapolated above the continuum threshold—a vibrational level, <italic>v</italic><sup>+</sup>, of the molecular ion. It is <italic>open</italic> if its corresponding threshold is situated <italic>below</italic> the total energy of the system and <italic>closed</italic> in the opposite case. As for the dissociative channels, only open channels are used in the present work.</p><p>The MQDT approach is based on a description of molecular states in which only part of the electronic Hamiltonian is diagonalized, within subspaces of electronic states with similar nature. We use a quasi-diabatic representation of molecular states (<cite linkend="psst205242bib36">Sidis and Lefebvre-Brion 1971</cite>) to cope with problems due to the avoided crossings of the potential energy curves. The short-range electronic interactions between states of different subspaces are then found out in terms of an electronic coupling operator,
<inline-eqn></inline-eqn>, which couples the ionization channels to the dissociative channels. Starting from
<inline-eqn></inline-eqn>, one builds the short-range reaction matrix
<inline-eqn></inline-eqn>, solution of a Lippmann–Schwinger integro-differential equation,
<display-eqn id="psst205242eq007" eqnnum="2.3"></display-eqn><bold-italic>H</bold-italic><sub>0</sub> being the zero order Hamiltonian associated to the molecular system, i.e. the Hamiltonian operator excluding the interaction potential
<inline-eqn></inline-eqn>. The effects of short-range are valid in the region of small electron–ion and nuclei–nuclei distances, that is, the ‘A-region’ (<cite linkend="psst205242bib16">Jungen and Atabek 1977</cite> where the Born–Oppenheimer representation is appropriate for the description of the colliding system. There, the energy dependence of the electronic couplings can be neglected. In the case of weak coupling, a perturbative solution of equation (<eqnref linkend="psst205242eq007">2.3</eqnref>) can be obtained. This solution has been recently proved to be exact to second order, in the case of energy-independent electronic coupling (<cite linkend="psst205242bib24">Ngassam <italic>et al</italic> 2003b</cite>). In the external zone, the ‘B-region’ (<cite linkend="psst205242bib16">Jungen and Atabek 1977</cite>) represented by large electron–core distances, the Born–Oppenheimer model is no longer valid for the ionization channels and a close-coupling representation in terms of ‘molecular ion+electron’ is more appropriate. This corresponds to a frame transformation defined by the projection coefficients:
<display-eqn id="psst205242eq008" eqnnum="2.4"></display-eqn><display-eqn id="psst205242eq009" eqnnum="2.5"></display-eqn><display-eqn id="psst205242eq010" eqnnum="2.6"></display-eqn><display-eqn id="psst205242eq011" eqnnum="2.7"></display-eqn>
In the preceding formulae,
<inline-eqn></inline-eqn> is a vibrational wavefunction of the molecular ion and χ<sub>v</sub> is a vibrational wavefunction adapted to the interaction (A) region. The index α denotes the eigenchannels built through the <italic>diagonalization</italic> of the reaction matrix
<inline-eqn></inline-eqn>—equation (<eqnref linkend="psst205242eq007">2.3</eqnref>)—and <italic>U</italic><sub>lv,α</sub> and
<inline-eqn></inline-eqn> are related to the corresponding eigenvectors and eigenvalues. The projection coefficients shown in (<eqnref linkend="psst205242eq008">2.4</eqnref>) include the two types of couplings controlling the process: the <italic>electronic</italic> coupling, expressed by the elements of the matrices <bold-italic>U</bold-italic> and &b.eta;, and the <italic>non-adiabatic</italic> coupling between the ionization channels, expressed by the matrix elements involving the quantum defect
<inline-eqn></inline-eqn>. This latter interaction is favoured by the variation of the quantum defect with the internuclear distance <italic>R</italic>. The matrices
<inline-eqn></inline-eqn> and
<inline-eqn></inline-eqn> with elements (<eqnref linkend="psst205242eq008">2.4</eqnref>) and (<eqnref linkend="psst205242eq009">2.5</eqnref>) are the building blocks of the ‘generalized’ scattering matrix <bold-italic>X</bold-italic>:
<display-eqn id="psst205242eq012" eqnnum="2.8"></display-eqn>
whereas the ‘proper’ scattering matrix, restricted to the <italic>open</italic> channels, is given by (<cite linkend="psst205242bib35">Seaton 1983</cite>):
<display-eqn id="psst205242eq013" eqnnum="2.9"></display-eqn>
It is obtained from the sub-matrices <bold-italic>X</bold-italic> involving the lines and columns associated with the open (o) and closed (c) channels, and a further diagonal matrix &b.nu; was formed with the effective quantum numbers
<inline-eqn></inline-eqn> (in atomic units) associated with each vibrational threshold
<inline-eqn></inline-eqn> of the ion situated <italic>above</italic> the current energy <italic>E</italic>. For a molecular ion initially in the level
<inline-eqn></inline-eqn> and recombining with an electron of energy ϵ, the cross section of capture into <italic>all</italic> the dissociative states <italic>d</italic><sub><italic>j</italic></sub> of the same symmetry Γ is given by
<display-eqn id="psst205242eq014" eqnnum="2.10"></display-eqn>
Here Γ refers to the electronic symmetry of the neutral species (<sup>2</sup>Σ<sup>+</sup>, <sup>2</sup>Π and <sup>2</sup>Δ in the present study) and ρ<sup>Γ</sup> is the ratio between the multiplicities of the neutral system and the ion. One has to perform the MQDT calculation for each group of dissociative states of symmetry Γ, and the sum over the resulting cross sections is the total DR cross section:
<display-eqn id="psst205242eq015" eqnnum="2.11"></display-eqn>
In a similar way, the cross section for a vibrational transition of a molecular ion from the initial level
<inline-eqn></inline-eqn> to the final level <italic>v</italic><sub>f</sub> is
<display-eqn id="psst205242eq016" eqnnum="2.12"></display-eqn>
and the total cross section for this vibrational transition is
<display-eqn id="psst205242eq017" eqnnum="2.13"></display-eqn></p></sec-level1><sec-level1 id="psst205242s3" label="3"><heading>Molecular data and calculations</heading><p indent="no">In Paper I, we had used the <italic>ab initio</italic> potential curves produced by MQDT interpretation of spectroscopic data (<cite linkend="psst205242bib30">Raoult 1987</cite>) from high-precision spectroscopic measurements (<cite linkend="psst205242bib06">Dressler and Miescher 1981</cite>) to build ‘calibrated’ curves. The calibration consisted of using all the data available to put the minima of the curves in coincidence with the spectroscopic data and then to derive the asymptotic limit. The data are plotted in figure <figref linkend="psst205242fig01">1</figref> for all the symmetries. Figure <figref linkend="psst205242fig01">1</figref> also displays the electronic couplings
<inline-eqn></inline-eqn>, derived from R-matrix calculations (<cite linkend="psst205242bib26">Rabadán and Tennyson 1996</cite>, <cite linkend="psst205242bib27">1997</cite>, <cite linkend="psst205242bib28">1998</cite>, <cite linkend="psst205242bib40">Tennyson 2000</cite>) of autoionization widths
<inline-eqn></inline-eqn> by
<display-eqn id="psst205242eq018" eqnnum="3.1"></display-eqn>
It can be seen that most of the interaction takes place at distances <italic>R</italic> ⩽ 3 a.u. Using the set of molecular data described above, we have performed a series of MQDT calculations of the cross sections of DR, EC, SEC and IC, with the molecular ion in different vibrational levels (
<inline-eqn></inline-eqn>) of its ground electronic state. This is aimed at evaluating the relative contributions of the vibrationally excited states of NO<sup>+</sup> on its DR and the role of autoionization (SEC, EC and IC) on the dynamics of NO<sup>+</sup> in interaction with low-energy electrons. The rotational structure, as stated above, is not considered, nor are spin–orbit effects. The cross sections are calculated separately for each symmetry (involving all the relevant dissociative states within the symmetry) and are summed to give the total cross section. The energy range of the incident electron is 0.01 meV–10 eV, in steps of 0.01 meV. As in Paper I, for each dissociative channel available, we have considered its interaction with only one Rydberg series: <italic>p</italic>π for the <sup>2</sup>Π states, <italic>p</italic>σ for the <italic>A</italic>′<sup>2</sup>Σ<sup>+</sup>, <italic>s</italic>σ for the <italic>I</italic>′<sup>2</sup>Σ<sup>+</sup> and dδ for the <italic>B</italic>′<sup>2</sup>Δ states; both direct and indirect mechanisms have been accounted for.
<figure id="psst205242fig01" pageposition="top"><graphic><graphic-file version="print" format="EPS" align="middle" filename="images/psst205242fig01.eps" width="XXX"></graphic-file><graphic-file version="ej" format="JPEG" align="middle" filename="images/psst205242fig01.jpg"></graphic-file></graphic><caption id="psst205242fc01" label="Figure 1"><p indent="no">Quasi-diabatic representation of NO super-excited states of all the relevant symmetries (from <cite linkend="psst205242bib33">Schneider <italic>et al</italic> 2000a</cite>). Some vibrational states of the NO<sup>+</sup> ground electronic state (fine continuous curve) are represented as black horizontal lines. The circles label values of the electronic couplings computed by the R-matrix method (Rabadán and Tennyson (<cite linkend="psst205242bib26">Rabadán and Tennyson 1996</cite>, <cite linkend="psst205242bib27">1997</cite>).</p></caption></figure></p><p>One can doubt about the sufficiency of the electronic states involved in the present series of computations—figure <figref linkend="psst205242fig01">1</figref>. Further excited dissociative states certainly exist within each symmetry. However, exploratory R-matrix calculations have shown that, for the <sup>2</sup>Π symmetry, the potential curve of the next higher dissociative state should cross that of the ion above the highest initial vibrational level of the target ion considered in this paper,
<inline-eqn></inline-eqn>. As for the other symmetries, the interactions of the next higher dissociative states with the electron–ion continuum seem to be weak. On the other hand, even if the very highly excited vibrational states (<italic>v</italic><sup>+</sup> > 14) may generate strong couplings between the ionization continuum and the high dissociative states, the relative weakness of the indirect process should prevent these latter states to play a major role. The situation would certainly change if the ion target were furthermore vibrationally excited (
<inline-eqn></inline-eqn>), in which case further <italic>ab initio</italic> computations of states and couplings would be required.</p></sec-level1><sec-level1 id="psst205242s4" label="4"><heading>Results and discussion</heading><p indent="no">We start this section by an illustration of the cross sections for all the processes (figure <figref linkend="psst205242fig02">2</figref>) for the case of the initial vibrational level
<inline-eqn></inline-eqn>, as an example, before presenting the rate coefficients. The cross sections exhibit structures due to the indirect process, i.e. the temporary capture on Rydberg states of the NO molecule. They present one or several broad peaks separated by pronounced dips which are, in general, due to the variation with the energy of the overlap of the vibrational and the dissociative wavefunctions (Franck–Condon effects). If we restrict ourselves to the direct process, there is one single vibrational wave function involved in the overlap integrals for DR and EC and two vibrational wave functions in the case of SEC and IC (<cite linkend="psst205242bib23">Nakashima <italic>et al</italic> 1987</cite>); this explains the larger number of dips observed for SEC and IC, related to the nodes of the vibrational wave functions involved.
<figure id="psst205242fig02" pageposition="top"><graphic><graphic-file version="print" format="EPS" align="middle" filename="images/psst205242fig02.eps" width="XXX"></graphic-file><graphic-file version="ej" format="JPEG" align="middle" filename="images/psst205242fig02.jpg"></graphic-file></graphic><caption id="psst205242fc02" label="Figure 2"><p indent="no">Total cross sections for DR, EC, SEC and IC of NO<sup>+</sup>(<italic>X</italic><sup>1</sup>Σ<sup>+</sup>), from the initial vibrational state
<inline-eqn></inline-eqn>. The total cross section is the sum of all the contributions from all the symmetries and, within each symmetry, from all the relevant dissociative states.</p></caption></figure></p><p>The peak around 6 eV in DR is similar to the one put in evidence by the ASTRID storage ring for the DR from the ground
<inline-eqn></inline-eqn> state and which was almost entirely found to be due to the 3<sup>2</sup>Π state. The EC cross sections present a global <italic>E</italic><sup>−1</sup> behaviour, and are about two to three orders of magnitude greater than those for DR, SEC and IC. The cross sections for SEC and ICs tend to a plateau for electron energies exceeding 8 eV, due to the fall-off of the DR cross sections which prevents from a flux loss to the dissociation channels. Those for ICs from a given initial vibrational state are non-zero only when the electron energy exceeds the excitation threshold and are of the same order of magnitude as those for the inverse SEC cross sections.</p><p>Maxwellian isotropic rate coefficients computed for the DR of NO<sup>+</sup> in its first 15 vibrational levels, i.e.
<inline-eqn></inline-eqn>, are represented in figure <figref linkend="psst205242fig03">3(<italic>a</italic>)</figref>. One may notice that, for any temperature, the rate coefficients for different initial vibrational levels hold within an order of magnitude and that the vibrationally relaxed ions recombine faster than the excited ones. Comparison has been made with three experiments for two situations:
<inline-eqn></inline-eqn> on one hand and a mixture of vibrationally excited states at <italic>T</italic> = 300 K on the other hand. The results are represented in figure <figref linkend="psst205242fig03">3(<italic>b</italic>)</figref>. The first experiment, based on an ion storage ring technique (<cite linkend="psst205242bib42">Vejby-Christensen <italic>et al</italic> 1998</cite>), ensured an entirely vibrationally relaxed ion population. Starting from the measured cross sections, the thermal (300 K) rate was calculated by numerical integration. In the second experiment, a flowing afterglow Langmuir probe-mass apparatus (<cite linkend="psst205242bib20">Mostefaoui <italic>et al</italic> 1999</cite>) was used, with NO as parent gas, justifying the assumption that NO<sup>+</sup> is almost entirely in its ground vibrational state. The rate coefficients derived at <italic>T</italic> = 300 K are identical, within the error bar, for the two experiments: (4 ± 1) × 10<sup>−7</sup> cm<sup>3</sup> s<sup>−1</sup> and 4 × 10<sup>−7</sup> cm<sup>3</sup> s<sup>−1</sup>, respectively. The third experiment used the same experimental setup with the second one, with N<sub>2</sub> and O<sub>2</sub> as parent gases! It was not possible, in this case, to obtain totally vibrationally relaxed NO<sup>+</sup> ions, but the population distribution of the different vibrational levels of NO<sup>+</sup> ions formed have been measured, as well as the DR rate coefficients of the so-obtained mixture of ions at <italic>T</italic> = 300 K.
<figure id="psst205242fig03" pageposition="top"><graphic><graphic-file version="print" format="EPS" align="middle" filename="images/psst205242fig03.eps" width="XXX"></graphic-file><graphic-file version="ej" format="JPEG" align="middle" filename="images/psst205242fig03.jpg"></graphic-file></graphic><caption id="psst205242fc03" label="Figure 3"><p indent="no">(<italic>a</italic>) Computed Maxwellian isotropic rate coefficient of DR of NO<sup>+</sup>(<italic>X</italic><sup>1</sup>Σ<sup>+</sup>) initially in its first 15 vibrational levels, as a function of the temperature of the incident electrons. (<italic>b</italic>) Comparison with three experimental results: ground state using a storage ring (<cite linkend="psst205242bib42">Vejby-Christensen <italic>et al</italic> 1998</cite>) and flowing afterglow Langmuir probe (<cite linkend="psst205242bib20">Mostefaoui <italic>et al</italic> 1999</cite>) in black and mixture of vibrational states (<cite linkend="psst205242bib20">Mostefaoui <italic>et al</italic> 1999</cite>) in grey. In the case
<inline-eqn></inline-eqn>, the two experimental results are very close to each other: 4 × 10<sup>−7</sup> cm<sup>3</sup> s<sup>−1</sup> (<cite linkend="psst205242bib42">Vejby-Christensen <italic>et al</italic> 1998</cite>) and (4 ± 1) × 10<sup>−7</sup> cm<sup>3</sup> s<sup>−1</sup> (<cite linkend="psst205242bib20">Mostefaoui <italic>et al</italic> 1999</cite>).</p></caption></figure></p><p>Using the vibrational population distribution of the latter experiment (<cite linkend="psst205242bib20">Mostefaoui <italic>et al</italic> 1999</cite>), we obtain a weighted rate coefficient corresponding to the experimental mixture of vibrational states. The results represented in figure <figref linkend="psst205242fig03">3(<italic>b</italic>)</figref> show quite a good agreement with the experiment, at the temperature <italic>T</italic> = 300 K, thus confirming that for the excited vibrational levels the DR rate coefficient is lower than that for
<inline-eqn></inline-eqn>.</p><p>On the other hand, our electron impact vibrational excitation Maxwellian isotropic rates agree very well with those obtained from an R-matrix calculation (<cite linkend="psst205242bib29">Rabadán and Tennyson 1999</cite> for the transitions from
<inline-eqn></inline-eqn> to
<inline-eqn></inline-eqn> to 5, as shown in figure <figref linkend="psst205242fig04">4</figref>.
<figure id="psst205242fig04" pageposition="top"><graphic><graphic-file version="print" format="EPS" align="middle" filename="images/psst205242fig04.eps" width="XXX"></graphic-file><graphic-file version="ej" format="JPEG" align="middle" filename="images/psst205242fig04.jpg"></graphic-file></graphic><caption id="psst205242fc04" label="Figure 4"><p indent="no">Comparison of Maxwellian isotropic rate coefficients obtained in this work with those obtained from an R-matrix-based calculation of the electron impact vibrational excitation (<cite linkend="psst205242bib29">Rabadán and Tennyson 1999</cite>) for the transitions from
<inline-eqn></inline-eqn> to
<inline-eqn></inline-eqn>: black lines: this work; grey lines: <cite linkend="psst205242bib29">Rabadán and Tennyson (1999)</cite>.</p></caption></figure></p><p>In figures <figref linkend="psst205242fig05">5</figref> and <figref linkend="psst205242fig06">6</figref>, we represent the rate coefficients of all the processes for
<inline-eqn></inline-eqn>, and
<inline-eqn></inline-eqn>, respectively. It can be seen in these figures that the rate coefficient for ECs α<sub>EC</sub> is practically independent of
<inline-eqn></inline-eqn>, in contrast to the rate coefficients for DR (α<sub>DR</sub>) and SEC (α<sub>SEC</sub>). It can be also observed that the DR rate coefficients, which are greater than the SEC rates at low
<inline-eqn></inline-eqn>, are dominated by the first superelastic transitions at the high values of
<inline-eqn></inline-eqn>. The IC rate coefficients increase with
<inline-eqn></inline-eqn>. Moreover, whereas α<sub>EC</sub> scales globally as a power of the temperature, α<sub>DR</sub> and α<sub>SEC</sub> have a variable temperature dependence, due to the broad peaks observed on the corresponding cross sections.
<figure id="psst205242fig05" pageposition="top"><graphic><graphic-file version="print" format="EPS" align="middle" filename="images/psst205242fig05.eps" width="XXX"></graphic-file><graphic-file version="ej" format="JPEG" align="middle" filename="images/psst205242fig05.jpg"></graphic-file></graphic><caption id="psst205242fc05" label="Figure 5"><p indent="no">Rate coefficients for DR (thick full curves), EC (thick dotted curves), SEC (full grey curves) and IC (thin black curves) of NO<sup>+</sup>(<italic>X</italic><sup>1</sup>Σ<sup>+</sup>), from the initial vibrational states
<inline-eqn></inline-eqn>. For SEC, the vibrational quantum number of the final states
<inline-eqn></inline-eqn> is indicated near the curve, wherever it is possible. The notation
<inline-eqn></inline-eqn>, with
<inline-eqn></inline-eqn>, is used when the curves are too close. For IC, the curves are plotted in the natural order for the first seven transitions.</p></caption></figure><figure id="psst205242fig06" pageposition="top"><graphic><graphic-file version="print" format="EPS" align="middle" filename="images/psst205242fig06.eps" width="XXX"></graphic-file><graphic-file version="ej" format="JPEG" align="middle" filename="images/psst205242fig06.jpg"></graphic-file></graphic><caption id="psst205242fc06" label="Figure 6"><p indent="no">Same as figure <figref linkend="psst205242fig05">5</figref> for
<inline-eqn></inline-eqn>.</p></caption></figure></p></sec-level1><sec-level1 id="psst205242s5" label="5"><heading>Fitting of the reaction rate coefficients</heading><p indent="no">In order to facilitate their use, the isotropic Maxwellian rate coefficients of the reactions investigated in this work for NO<sup>+</sup> ions have been fitted to a modified Arrhenius law, i.e:
<display-eqn id="psst205242eq019" eqnnum="5.1"></display-eqn>
where the subscript <italic>P</italic> indicates the process, <italic>T</italic><sub>e</sub> is the electron temperature,
<inline-eqn></inline-eqn> and
<inline-eqn></inline-eqn> are the initial and final vibrational quantum numbers of the target ion.</p><p>Naturally, the parameters <italic>A</italic>, γ and &thetas; depend only on
<inline-eqn></inline-eqn> for DR and EC, whereas they also depend on
<inline-eqn></inline-eqn> for the other reactions. These parameters have been calculated for the temperature range 2000 ⩽ <italic>T</italic><sub>e</sub> ⩽ 10 000 K for which NO<sup>+</sup> plays a major role in the thermal plasmas.</p><sec-level2 id="psst205242s5-1" label="5.1"><heading>Dissociative recombination</heading><p indent="no">The fitting of the DR rate coefficients for each
<inline-eqn></inline-eqn> gives
<inline-eqn></inline-eqn>. The <italic>global</italic> rate coefficient is obtained by averaging the
<inline-eqn></inline-eqn> on all possible vibrational levels assuming they are in Boltzmann equilibrium according to <italic>T</italic><sub>e</sub>, i.e.
<display-eqn id="psst205242eq020" eqnnum="5.2"></display-eqn>
where
<inline-eqn></inline-eqn> is the statistical weight of the vibrational level
<inline-eqn></inline-eqn>.</p><p>Proceeding as indicated above, we have found for DR the values of <italic>A</italic>, γ and &thetas; reported in table <tabref linkend="psst205242tab01">1</tabref> as well as the global rate coefficient:
<display-eqn id="psst205242eq021" eqnnum="5.3"></display-eqn><table id="psst205242tab01" type="formal" frame="topbot" colsep="no" rowsep="no"><caption id="psst205242tc01" label="Table 1"><p indent="no">Parameters <italic>A</italic>, γ and &thetas; for the DR,
<inline-eqn></inline-eqn>, expressed in cm<sup>3</sup> s<sup>−1</sup>.</p></caption><tgroup cols="8" colsep="no" rowsep="no" align="center" charoff="50" char=""><colspec colnum="1" colname="1" align="left" colwidth="1*"></colspec><colspec colnum="2" colname="2" align="left" colwidth="1*"></colspec><colspec colnum="3" colname="3" align="char" char="." colwidth="1*"></colspec><colspec colnum="4" colname="4" align="left" colwidth="1*"></colspec><colspec colnum="5" colname="5" align="left" colwidth="1*"></colspec><colspec colnum="6" colname="6" align="left" colwidth="1*"></colspec><colspec colnum="7" colname="7" align="char" char="." colwidth="1*"></colspec><colspec colnum="8" colname="8" align="char" char="." colwidth="1*"></colspec><thead><row rowsep="yes"><entry><italic>v</italic><sup>+</sup></entry><entry><italic>A</italic></entry><entry>γ</entry><entry>&thetas;</entry><entry><italic>v</italic><sup>+</sup></entry><entry><italic>A</italic></entry><entry>γ</entry><entry>&thetas;</entry></row></thead><tbody><row><entry>0</entry><entry>8.486 × 10<sup>−5</sup></entry><entry>0.793</entry><entry>859.99</entry><entry>8</entry><entry>1.071 × 10<sup>−4</sup></entry><entry>0.884</entry><entry>546.20</entry></row><row><entry>1</entry><entry>3.958 × 10<sup>−8</sup></entry><entry>0.0757</entry><entry>−661.83</entry><entry>9</entry><entry>1.445 × 10<sup>−5</sup></entry><entry>0.710</entry><entry>−67.49</entry></row><row><entry>2</entry><entry>1.664 × 10<sup>−5</sup></entry><entry>0.704</entry><entry>−39.13</entry><entry>10</entry><entry>2.145 × 10<sup>−5</sup></entry><entry>0.755</entry><entry>357.59</entry></row><row><entry>3</entry><entry>6.355 × 10<sup>−7</sup></entry><entry>0.383</entry><entry>−282.98</entry><entry>11</entry><entry>1.095 × 10<sup>−5</sup></entry><entry>0.695</entry><entry>703.00</entry></row><row><entry>4</entry><entry>2.970 × 10<sup>−7</sup></entry><entry>0.311</entry><entry>−632.21</entry><entry>12</entry><entry>8.897 × 10<sup>−6</sup></entry><entry>0.678</entry><entry>406.55</entry></row><row><entry>5</entry><entry>2.666 × 10<sup>−7</sup></entry><entry>0.297</entry><entry>−472.45</entry><entry>13</entry><entry>8.483 × 10<sup>−6</sup></entry><entry>0.677</entry><entry>276.17</entry></row><row><entry>6</entry><entry>3.623 × 10<sup>−7</sup></entry><entry>0.311</entry><entry>−1.109</entry><entry>14</entry><entry>8.149 × 10<sup>−6</sup></entry><entry>0.679</entry><entry>303.70</entry></row><row><entry>7</entry><entry>1.451 × 10<sup>−5</sup></entry><entry>0.672</entry><entry>852.89</entry><entry></entry><entry></entry><entry></entry><entry></entry></row></tbody></tgroup></table></p><p>We have to recall that the results displayed in section <secref linkend="psst205242s4">4</secref> have been calculated neglecting the rotational structure of the molecular ion, i.e. putting <italic>J</italic> equal to 0 and
<inline-eqn></inline-eqn> for all
<inline-eqn></inline-eqn>: any comparison between the previous rate coefficient and that derived from experience must be performed in the light of this limitation. Taking into account the rotational excitation and assuming a same rate coefficient whatever be the value of <italic>J</italic> for a given vibrational level (which is the consequence on rate coefficients of the fact that rotation do not play a role in the DR of NO<sup>+</sup>), the global rate coefficient is then
<display-eqn id="psst205242eq022" eqnnum="5.4"></display-eqn>
which is quite close to α<sub>DR</sub>(<italic>T</italic><sub>e</sub>) (equation (<eqnref linkend="psst205242eq021">5.3</eqnref>)). From a theoretical point of view, a comparison should be made between experimental results where they exist and the rate coefficient (<eqnref linkend="psst205242eq022">5.4</eqnref>) rather than with α<sub>DR</sub>(<italic>T</italic><sub>e</sub>), if the rotation is sufficiently excited.</p></sec-level2><sec-level2 id="psst205242s5-2" label="5.2"><heading>Superelastic and inelastic collisions</heading><p indent="no">Tables <tabref linkend="psst205242tab02" range="tab2,tab3,tab4">2–4</tabref> contain the parameters <italic>A</italic>, γ and &thetas; for SEC, EC and IC, as a function of
<inline-eqn></inline-eqn> and
<inline-eqn></inline-eqn>, where
<inline-eqn></inline-eqn> and
<inline-eqn></inline-eqn> have been chosen less than 6 in order to limit the size of the tables to be presented. At thermodynamic equilibrium, the two processes
<display-eqn id="psst205242eq023" eqnnum="5.5"></display-eqn>
and
<display-eqn id="psst205242eq024" eqnnum="5.6"></display-eqn>
with reaction rates α<sub>i→f</sub> and α<sub>f→i</sub> are perfectly balanced, due to the microreversibility. This has been verified by parametrizing the equilibrium constant,
<display-eqn id="psst205242eq025" eqnnum="5.7"></display-eqn>
in the form
<display-eqn id="psst205242eq026" eqnnum="5.8"></display-eqn>
where <italic>A</italic><sub>eq</sub> = <italic>A</italic><sub>f→i</sub>/<italic>A</italic><sub>i→f</sub>, γ<sub>eq</sub> = γ<sub>f→i</sub> − γ<sub>i→f</sub> and &thetas;<sub>eq</sub> = &thetas;<sub>f→i</sub> − &thetas;<sub>i→f</sub>. The parameters obtained for the equilibrium constant <italic>K</italic><sub>eq</sub> are represented in table <tabref linkend="psst205242tab05">5</tabref> where it can be seen that γ<sub>eq</sub> is close to 0, such that the temperature dependence of <italic>K</italic><sub>eq</sub> is contained mainly in the exponential factor. In addition, the fact that &thetas;<sub>eq</sub> is quite close to
<inline-eqn></inline-eqn> and that <italic>A</italic><sub>eq</sub> is close to 1 validate the fit of these rate coefficients.
<table id="psst205242tab02" type="formal" frame="topbot" colsep="no" rowsep="no"><caption id="psst205242tc02" label="Table 2"><p indent="no">Parameters <italic>A</italic> for SEC and ICs,
<inline-eqn></inline-eqn> expressed in cm<sup>3</sup> s<sup>−1</sup>.</p></caption><tgroup cols="7" colsep="no" rowsep="no" align="center" charoff="50" char=""><colspec colnum="1" colname="1" align="left" colwidth="1*"></colspec><colspec colnum="2" colname="2" align="left" colwidth="1*"></colspec><colspec colnum="3" colname="3" align="left" colwidth="1*"></colspec><colspec colnum="4" colname="4" align="left" colwidth="1*"></colspec><colspec colnum="5" colname="5" align="left" colwidth="1*"></colspec><colspec colnum="6" colname="6" align="left" colwidth="1*"></colspec><colspec colnum="7" colname="7" align="left" colwidth="1*"></colspec><spanspec namest="1" nameend="7" spanname="s1to7" align="left"></spanspec><spanspec namest="2" nameend="7" spanname="s2to7" align="center"></spanspec><thead><row><entry></entry><entry spanname="s2to7" rowsep="yes"><inline-eqn></inline-eqn></entry></row><row rowsep="yes"><entry></entry><entry>0</entry><entry>1</entry><entry>2</entry><entry>3</entry><entry>4</entry><entry>5</entry></row></thead><tbody><row><entry spanname="s1to7"><inline-eqn></inline-eqn></entry></row><row><entry>0</entry><entry>4.011 × 10<sup>−5</sup></entry><entry>4.964 × 10<sup>−6</sup></entry><entry>1.844 × 10<sup>−5</sup></entry><entry>1.812 × 10<sup>−6</sup></entry><entry>7.777 × 10<sup>−8</sup></entry><entry>5.859 × 10<sup>−7</sup></entry></row><row><entry>1</entry><entry>9.229 × 10<sup>−6</sup></entry><entry>6.437 × 10<sup>−5</sup></entry><entry>1.744 × 10<sup>−7</sup></entry><entry>2.957 × 10<sup>−7</sup></entry><entry>5.292 × 10<sup>−7</sup></entry><entry>2.575 × 10<sup>−7</sup></entry></row><row><entry>2</entry><entry>1.862 × 10<sup>−5</sup></entry><entry>2.360 × 10<sup>−7</sup></entry><entry>4.837 × 10<sup>−5</sup></entry><entry>5.651 × 10<sup>−7</sup></entry><entry>8.495 × 10<sup>−9</sup></entry><entry>1.172 × 10<sup>−9</sup></entry></row><row><entry>3</entry><entry>2.284 × 10<sup>−6</sup></entry><entry>3.064 × 10<sup>−7</sup></entry><entry>1.362 × 10<sup>−6</sup></entry><entry>5.686 × 10<sup>−5</sup></entry><entry>1.932 × 10<sup>−7</sup></entry><entry>6.729 × 10<sup>−8</sup></entry></row><row><entry>4</entry><entry>7.187 × 10<sup>−8</sup></entry><entry>5.386 × 10<sup>−7</sup></entry><entry>8.653 × 10<sup>−9</sup></entry><entry>1.933 × 10<sup>−7</sup></entry><entry>6.255 × 10<sup>−5</sup></entry><entry>2.421 × 10<sup>−8</sup></entry></row><row><entry>5</entry><entry>6.873 × 10<sup>−7</sup></entry><entry>2.733 × 10<sup>−7</sup></entry><entry>1.050 × 10<sup>−9</sup></entry><entry>6.724 × 10<sup>−8</sup></entry><entry>2.091 × 10<sup>−8</sup></entry><entry>6.460 × 10<sup>−5</sup></entry></row></tbody></tgroup></table><table id="psst205242tab03" type="formal" frame="topbot" colsep="no" rowsep="no"><caption id="psst205242tc03" label="Table 3"><p indent="no">Parameters γ for SEC and ICs.</p></caption><tgroup cols="7" colsep="no" rowsep="no" align="center" charoff="50" char=""><colspec colnum="1" colname="1" align="left" colwidth="1*"></colspec><colspec colnum="2" colname="2" align="char" char="." colwidth="1*"></colspec><colspec colnum="3" colname="3" align="char" char="." colwidth="1*"></colspec><colspec colnum="4" colname="4" align="left" colwidth="1*"></colspec><colspec colnum="5" colname="5" align="char" char="." colwidth="1*"></colspec><colspec colnum="6" colname="6" align="char" char="." colwidth="1*"></colspec><colspec colnum="7" colname="7" align="left" colwidth="1*"></colspec><spanspec namest="1" nameend="7" spanname="s1to7" align="left"></spanspec><spanspec namest="2" nameend="7" spanname="s2to7" align="center"></spanspec><thead><row><entry></entry><entry spanname="s2to7" rowsep="yes"><inline-eqn></inline-eqn></entry></row><row rowsep="yes"><entry></entry><entry>0</entry><entry>1</entry><entry>2</entry><entry>3</entry><entry>4</entry><entry>5</entry></row></thead><tbody><row><entry spanname="s1to7"><inline-eqn></inline-eqn></entry></row><row><entry>0</entry><entry>0.484</entry><entry>0.773</entry><entry>0.982</entry><entry>0.802</entry><entry>0.514</entry><entry>0.747</entry></row><row><entry>1</entry><entry>0.844</entry><entry>0.530</entry><entry>0.373</entry><entry>0.594</entry><entry>0.629</entry><entry>0.612</entry></row><row><entry>2</entry><entry>0.983</entry><entry>0.405</entry><entry>0.502</entry><entry>0.517</entry><entry>0.231</entry><entry>−0.012</entry></row><row><entry>3</entry><entry>0.831</entry><entry>0.598</entry><entry>0.603</entry><entry>0.518</entry><entry>0.420</entry><entry>0.384</entry></row><row><entry>4</entry><entry>0.507</entry><entry>0.631</entry><entry>0.233</entry><entry>0.420</entry><entry>0.527</entry><entry>0.211</entry></row><row><entry>5</entry><entry>0.763</entry><entry>0.618</entry><entry>−0.024</entry><entry>0.384</entry><entry>0.196</entry><entry>0.531</entry></row></tbody></tgroup></table><table id="psst205242tab04" type="formal" frame="topbot" colsep="no" rowsep="no"><caption id="psst205242tc04" label="Table 4"><p indent="no">Characteristic temperature &thetas;(<italic>K</italic>) for SEC, EC and ICs.</p></caption><tgroup cols="7" colsep="no" rowsep="no" align="center" charoff="50" char=""><colspec colnum="1" colname="1" align="left" colwidth="1*"></colspec><colspec colnum="2" colname="2" align="left" colwidth="1*"></colspec><colspec colnum="3" colname="3" align="left" colwidth="1*"></colspec><colspec colnum="4" colname="4" align="left" colwidth="1*"></colspec><colspec colnum="5" colname="5" align="left" colwidth="1*"></colspec><colspec colnum="6" colname="6" align="left" colwidth="1*"></colspec><colspec colnum="7" colname="7" align="left" colwidth="1*"></colspec><spanspec namest="1" nameend="7" spanname="s1to7" align="left"></spanspec><spanspec namest="2" nameend="7" spanname="s2to7" align="center"></spanspec><thead><row><entry></entry><entry spanname="s2to7" rowsep="yes"><inline-eqn></inline-eqn></entry></row><row rowsep="yes"><entry></entry><entry>0</entry><entry>1</entry><entry>2</entry><entry>3</entry><entry>4</entry><entry>5</entry></row></thead><tbody><row><entry spanname="s1to7"><inline-eqn></inline-eqn></entry></row><row><entry>0</entry><entry>−34.20</entry><entry>3890.5</entry><entry>7197.7</entry><entry>10398.5</entry><entry>12562.8</entry><entry>16479.4</entry></row><row><entry>1</entry><entry>706.8</entry><entry>57.59</entry><entry>4035.3</entry><entry>6961.8</entry><entry>10469.0</entry><entry>12452.1</entry></row><row><entry>2</entry><entry>563.9</entry><entry>152.4</entry><entry>33.31</entry><entry>3832.3</entry><entry>5216.8</entry><entry>8789.1</entry></row><row><entry>3</entry><entry>538.7</entry><entry>423.3</entry><entry>−84.99</entry><entry>40.11</entry><entry>2916.2</entry><entry>6516.6</entry></row><row><entry>4</entry><entry>−550.6</entry><entry>727.6</entry><entry>−1234</entry><entry>−287.1</entry><entry>69.01</entry><entry>1870.5</entry></row><row><entry>5</entry><entry>330.5</entry><entry>−420.0</entry><entry>−856.4</entry><entry>154.1</entry><entry>−1153</entry><entry>72.08</entry></row></tbody></tgroup></table><table id="psst205242tab05" type="formal" frame="topbot" colsep="no" rowsep="no"><caption id="psst205242tc05" label="Table 5"><p indent="no">Parameters <italic>A</italic><sub>eq</sub>, γ<sub>eq</sub> and &thetas;<sub>eq</sub> allowing the calculation of <italic>K</italic><sub>eq</sub> from
<inline-eqn></inline-eqn> and
<inline-eqn></inline-eqn>. The last column contains the remaining parameter of equation (<eqnref linkend="psst205242eq025">5.7</eqnref>),
<inline-eqn></inline-eqn> being equal to 1.</p></caption><tgroup cols="6" colsep="no" rowsep="no" align="center" charoff="50" char=""><colspec colnum="1" colname="1" align="left" colwidth="1*"></colspec><colspec colnum="2" colname="2" align="left" colwidth="1*"></colspec><colspec colnum="3" colname="3" align="char" char="." colwidth="1*"></colspec><colspec colnum="4" colname="4" align="left" colwidth="1*"></colspec><colspec colnum="5" colname="5" align="char" char="." colwidth="1*"></colspec><colspec colnum="6" colname="6" align="char" char="." colwidth="1*"></colspec><thead><row rowsep="yes"><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><italic>A</italic><sub>eq</sub></entry><entry>γ<sub>eq</sub></entry><entry>&thetas;<sub>eq</sub></entry><entry><inline-eqn></inline-eqn></entry></row></thead><tbody><row><entry>1</entry><entry>0</entry><entry>0.538</entry><entry>−0.071</entry><entry>3183.7</entry><entry>3339.1</entry></row><row><entry>2</entry><entry>0</entry><entry>0.990</entry><entry>−0.001</entry><entry>6633.8</entry><entry>6639.7</entry></row><row><entry>3</entry><entry>0</entry><entry>0.793</entry><entry>−0.029</entry><entry>9859.8</entry><entry>9892.3</entry></row><row><entry>4</entry><entry>0</entry><entry>1.082</entry><entry>0.007</entry><entry>13113.</entry><entry>13097.</entry></row><row><entry>5</entry><entry>0</entry><entry>0.852</entry><entry>−0.016</entry><entry>16149.</entry><entry>16253.</entry></row><row><entry>2</entry><entry>1</entry><entry>0.739</entry><entry>−0.032</entry><entry>3882.9</entry><entry>3300.7</entry></row><row><entry>3</entry><entry>1</entry><entry>0.965</entry><entry>−0.004</entry><entry>6538.5</entry><entry>6553.2</entry></row><row><entry>4</entry><entry>1</entry><entry>0.983</entry><entry>−0.002</entry><entry>9741.4</entry><entry>9757.4</entry></row><row><entry>5</entry><entry>1</entry><entry>0.942</entry><entry>−0.006</entry><entry>12872.</entry><entry>12914.</entry></row><row><entry>3</entry><entry>2</entry><entry>0.415</entry><entry>−0.086</entry><entry>3917.3</entry><entry>3252.5</entry></row><row><entry>4</entry><entry>2</entry><entry>0.982</entry><entry>−0.002</entry><entry>6450.8</entry><entry>6556.7</entry></row><row><entry>5</entry><entry>2</entry><entry>1.116</entry><entry>0.012</entry><entry>9645.5</entry><entry>9612.8</entry></row><row><entry>4</entry><entry>3</entry><entry>0.999</entry><entry>0.0</entry><entry>3203.3</entry><entry>3204.2</entry></row><row><entry>5</entry><entry>3</entry><entry>1.001</entry><entry>0.0</entry><entry>6362.5</entry><entry>6360.3</entry></row><row><entry>5</entry><entry>4</entry><entry>1.158</entry><entry>0.015</entry><entry>3023.5</entry><entry>3156.1</entry></row></tbody></tgroup></table></p></sec-level2><sec-level2 id="psst205242s5-3" label="5.3"><heading>Elastic collisions</heading><p indent="no">For ECs, the parameters <italic>A</italic>, γ and &thetas; derived from the fit of
<inline-eqn></inline-eqn> are represented in table <tabref linkend="psst205242tab06">6</tabref>. Assuming that the rotational effects are negligible in the ECs as in the case of DR, the rates are averaged like the
<inline-eqn></inline-eqn> in equation (<eqnref linkend="psst205242eq022">5.4</eqnref>) to obtain a global EC rate coefficient in the form
<display-eqn id="psst205242eq027" eqnnum="5.9"></display-eqn><table id="psst205242tab06" type="formal" frame="topbot" colsep="no" rowsep="no"><caption id="psst205242tc06" label="Table 6"><p indent="no">Parameters <italic>A</italic>, γ and &thetas; for the ECs,
<inline-eqn></inline-eqn> expressed in cm<sup>3</sup> s<sup>−1</sup>.</p></caption><tgroup cols="8" colsep="no" rowsep="no" align="center" charoff="50" char=""><colspec colnum="1" colname="1" align="left" colwidth="1*"></colspec><colspec colnum="2" colname="2" align="left" colwidth="1*"></colspec><colspec colnum="3" colname="3" align="char" char="." colwidth="1*"></colspec><colspec colnum="4" colname="4" align="left" colwidth="1*"></colspec><colspec colnum="5" colname="5" align="left" colwidth="1*"></colspec><colspec colnum="6" colname="6" align="left" colwidth="1*"></colspec><colspec colnum="7" colname="7" align="char" char="." colwidth="1*"></colspec><colspec colnum="8" colname="8" align="left" colwidth="1*"></colspec><thead><row rowsep="yes"><entry><italic>v</italic><sup>+</sup></entry><entry><italic>A</italic></entry><entry>α</entry><entry>&thetas;</entry><entry><italic>v</italic></entry><entry><italic>A</italic></entry><entry>α</entry><entry>&thetas;</entry></row></thead><tbody><row><entry>0</entry><entry>4.011 × 10<sup>−5</sup></entry><entry>0.484</entry><entry>−34.20</entry><entry>8</entry><entry>4.013 × 10<sup>−5</sup></entry><entry>0.486</entry><entry>−37.15</entry></row><row><entry>1</entry><entry>6.437 × 10<sup>−5</sup></entry><entry>0.530</entry><entry>57.59</entry><entry>9</entry><entry>4.698 × 10<sup>−5</sup></entry><entry>0.502</entry><entry>7.05</entry></row><row><entry>2</entry><entry>4.837 × 10<sup>−5</sup></entry><entry>0.502</entry><entry>33.31</entry><entry>10</entry><entry>4.713 × 10<sup>−5</sup></entry><entry>0.506</entry><entry>−24.11</entry></row><row><entry>3</entry><entry>5.686 × 10<sup>−5</sup></entry><entry>0.518</entry><entry>40.11</entry><entry>11</entry><entry>5.157 × 10<sup>−5</sup></entry><entry>0.522</entry><entry>−35.50</entry></row><row><entry>4</entry><entry>6.255 × 10<sup>−5</sup></entry><entry>0.527</entry><entry>69.01</entry><entry>12</entry><entry>4.927 × 10<sup>−5</sup></entry><entry>0.525</entry><entry>−18.69</entry></row><row><entry>5</entry><entry>6.460 × 10<sup>−5</sup></entry><entry>0.531</entry><entry>72.08</entry><entry>13</entry><entry>4.578 × 10<sup>−5</sup></entry><entry>0.522</entry><entry>−17.97</entry></row><row><entry>6</entry><entry>6.682 × 10<sup>−5</sup></entry><entry>0.536</entry><entry>62.86</entry><entry>14</entry><entry>4.534 × 10<sup>−5</sup></entry><entry>0.522</entry><entry>−42.81</entry></row><row><entry>7</entry><entry>5.013 × 10<sup>−5</sup></entry><entry>0.508</entry><entry>−34.68</entry><entry></entry><entry></entry><entry></entry><entry></entry></row></tbody></tgroup></table></p></sec-level2></sec-level1><sec-level1 id="psst205242s6" label="6"><heading>Conclusions</heading><p indent="no">The cross sections and rate coefficients for reactive collisions (DR, EC, IC and SEC) between electrons and NO<sup>+</sup> ions, for the first 15 vibrational levels of the ground NO<sup>+</sup> (<italic>X</italic><sup>1</sup>Σ<sup>+</sup>) electronic state, have been computed. The energy range considered is 10<sup>−5</sup>–10 eV. The comparison with experiment, for a mixture of vibrational states at <italic>T</italic> = 300 K, gives a good agreement, thus confirming that NO<sup>+</sup> ions recombine less efficiently in vibrationally excited states than in the ground state.</p><p>The rate coefficients obtained have been fitted to a modified Arrhenius law, and the parameters generated in the temperature range, 2000 ⩽ <italic>T</italic> ⩽ 10 000 K, facilitate the use of these results in air plasma kinetic models. Moreover, the fact that now now the rate coefficients given for each vibrational level allows a complete calculation of the vibrational distribution of NO<sup>+</sup> under chemical non-equilibrium conditions. This is particularly important since the vibrational characteristic time scale is often long and since NO<sup>+</sup> is the major ionic species in N<sub>2</sub>/O<sub>2</sub> mixtures and air discharges.</p></sec-level1><acknowledgment><heading>Acknowledgments</heading><p indent="no">We are grateful to Professor Annick Suzor-Weiner for her constant support and encouragement.</p><p>We acknowledge financial support within the IHP programme of EC under contract no. HPRN-CT-2000-00141 ‘Electron Transfer Reactions’ and the French CNRS through the ‘Programme National: Physique et Chimie du Milieu Interstellaire’. IFS is grateful to the French Conseil Régional de la Région Haute Normandie for financial support through the project CPER ‘Combustion dans les moteurs’. FOWT acknowledges the financial support of the French Ministère des Affaires Etrangères (SCAC de Yaoundé, Cameroon) for a doctoral grant. IFS is grateful to the French CNRS GdR no 2495 ‘Cataplasme’. MF and IFS are grateful to the promoters of the ERASMUS/SOCRATES programme of cooperation between University of Bucharest and Université du Havre. OM is grateful to the Abdus Salam International Centre for Theoretical Physics where part of the computations were performed under his Associateship Scheme and to the Swedish International Development Agency for financial support.</p><p>This work has been supported by the International Atomic Energy Agency (IAEA) through the Coordinated Research Project no F4.30.12 ‘Data for Molecular Processes in Edge Plasmas’.</p></acknowledgment></body><back><references><heading>References</heading><reference-list type="alphabetic"><journal-ref id="psst205242bib01"><authors><au><second-name>Amitay</second-name><first-names>Z</first-names></au><others><italic>et al</italic></others></authors><year>1999</year><jnl-title>Phys. 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Rev.</jnl-title><volume>172</volume><pages>198</pages></journal-ref></reference-list></references></back></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="eng"><title>Reactive collisions between electrons and NO ions: rate coefficient computations and relevance for the air plasma kinetics</title></titleInfo><titleInfo type="abbreviated"><title>Reactive collisions of NO ions</title></titleInfo><titleInfo type="alternative" lang="eng"><title>Reactive collisions between electrons and NO ions: rate coefficient computations and relevance for the air plasma kinetics</title></titleInfo><name type="personal"><namePart type="given">O</namePart><namePart type="family">Motapon</namePart><affiliation>Centre for Atomic, Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala, PO Box 8580, Douala, Cameroon</affiliation><affiliation>Junior associate of the Abdus Salam ICTP, Strada Costiera 11, 34014 Trieste, Italy.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M</namePart><namePart type="family">Fifirig</namePart><affiliation>Department of Chemistry, University of Bucharest, R-70900 Bucharest, Romania</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A</namePart><namePart type="family">Florescu</namePart><affiliation>Laboratoire de Photophysique Molculaire, Universit Paris-Sud, F-91405 Orsay, France</affiliation><affiliation>Laboratoire de Physique des Atomes, Lasers, Molcules et Surfaces, Universit de Rennes I, France.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">F O</namePart><namePart type="family">Waffeu Tamo</namePart><affiliation>Centre for Atomic, Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala, PO Box 8580, Douala, Cameroon</affiliation><affiliation>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">O</namePart><namePart type="family">Crumeyrolle</namePart><affiliation>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">G</namePart><namePart type="family">Varin-Brant</namePart><affiliation>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A</namePart><namePart type="family">Bultel</namePart><affiliation>CORIA, Universit de Rouen, Avenue de l'Universit, 76800 Saint-Etienne du Rouvray, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">P</namePart><namePart type="family">Vervisch</namePart><affiliation>CORIA, Universit de Rouen, Avenue de l'Universit, 76800 Saint-Etienne du Rouvray, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J</namePart><namePart type="family">Tennyson</namePart><affiliation>Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">I F</namePart><namePart type="family">Schneider</namePart><affiliation>Laboratoire de Mcanique, Physique et Gosciences, UFR Sciences et Techniques, Universit du Havre, 25, rue Philippe Lebon, BP 540, 76058 Le Havre, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="paper">paper</genre><originInfo><publisher>Institute of Physics Publishing</publisher><dateIssued encoding="w3cdtf">2006</dateIssued><copyrightDate encoding="w3cdtf">2006</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><note type="production">Printed in the UK</note></physicalDescription><abstract>Extensive calculations of the rate coefficients for dissociative recombination (DR), elastic collisions, inelastic collisions (ICs) and superelastic collisions of NO ions on initial vibrational levels, , with electrons of energy between 105 and 10eV have been performed, with a method based on multichannel quantum defect theory. Comparisons of the DR rate coefficients with the plasma experimental results give a good agreement, confirming that the vibrationally excited NO ions recombine more slowly than those in the ground state. Also, our ground state IC rate coefficients are very similar to previously computed R-matrix data. The rate coefficients have been fitted to a modified Arrhenius law, and the corresponding parameters are given, in order to facilitate the use of the reaction data in kinetical plasma modelling.</abstract><classification authority="pacs">34.80</classification><classification authority="pacs">52.20</classification><classification authority="pacs">25</classification><classification authority="pacs">72</classification><relatedItem type="host"><titleInfo><title>Plasma Sources Science and Technology</title></titleInfo><titleInfo type="abbreviated"><title>Plasma Sources Sci. Technol.</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0963-0252</identifier><identifier type="eISSN">1361-6595</identifier><identifier type="PublisherID">psst</identifier><identifier type="CODEN">PSTEEU</identifier><identifier type="URL">stacks.iop.org/PSST</identifier><part><date>2006</date><detail type="volume"><caption>vol.</caption><number>15</number></detail><detail type="issue"><caption>no.</caption><number>1</number></detail><extent unit="pages"><start>23</start><end>32</end><total>10</total></extent></part></relatedItem><identifier type="istex">C898871B5008A5E711FD46362558AD8E0900283A</identifier><identifier type="DOI">10.1088/0963-0252/15/1/004</identifier><identifier type="PII">S0963-0252(06)05242-X</identifier><identifier type="articleID">205242</identifier><identifier type="articleNumber">004</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><enrichments><json:item><type>multicat</type><uri>https://api.istex.fr/document/C898871B5008A5E711FD46362558AD8E0900283A/enrichments/multicat</uri></json:item></enrichments><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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