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REVIEW 3 major objections 5 minor 56 references

Vibrational excitation cross sections for non-equilibrium nitric oxide-containing plasma

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A full set of vibrationally resolved electron-impact excitation cross sections for nitric oxide, from v=0 to v=53, is computed ab initio and shown to bring simulated swarm parameters in NO into significantly better agreement with…

desk verdict Solid extension of the authors' own LCP work on NO vibrational excitation, with a genuine full v-set and an honest but imperfect swarm validation. read the letter →

arxiv 2411.09370 v1 pith:TBZBGP5L submitted 2024-11-14 physics.atom-ph physics.plasm-ph

V Laporta , L Vialetto , V Guerra This is my paper · ORCID
classification physics.atom-phphysics.plasm-ph
keywords nitricoxidevibrationalexcitationelectronimpactcrosssectionslocal-complex-potentialnon-equilibriumplasmastate-to-statekineticsswarmparametersLXCatdatabase
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to establish a complete set of vibrationally resolved cross sections for electron-impact excitation and de-excitation of nitric oxide, covering all 54 vibrational levels of the electronic ground state, from ab initio molecular data within the local-complex-potential resonance model. The authors show that this set, when fed into a state-to-state kinetic model, yields electron-vibration relaxation times for NO that are compatible with the available experimental measurement, and that when substituted for previous cross sections in a complete electron-impact set, it reduces the mismatch between simulated and measured electron swarm parameters in pure NO. If correct, the work provides the missing low-energy electron-impact data that NO plasma simulations—for atmospheric, re-entry, biomedical, and plasma-chemistry applications—have been lacking. The full dataset is released on the LXCat database.

What carries the argument

The load-bearing object is the local-complex-potential (LCP) cross-section formula for resonant vibrational excitation, Eq. (2), a resonance scattering model where the temporary NO$^-$ state is represented by a complex potential: for each of the five NO$^-$ resonances, the $v \to v'$ cross section is proportional to spin-multiplicity and degeneracy factors, the ratio of outgoing to incoming electron momenta, and the squared overlap $|\langle\chi_{v'}|V_r|\xi^r_v\rangle|^2$ between the final NO vibrational wavefunction and the resonance wavefunction built from the initial level. This machinery converts the ab initio potential-energy curves and autoionization widths of the five resonances into the full $54\times54$ matrix of VE and VdE cross sections. Two deliberate changes from the earlier LCP calculation carry the argument: suppressing the penetration factor $f_r$ restores the correct low-energy (below about 0.1 eV) behavior of the 0→0 channel, and adding the two higher $^3\Pi$ and $^1\Pi$ resonances produces the broad structure near 10 eV. The resulting cross sections are then used both in a state-to-state master-equation model of e-V relaxation and in the LoKI-B Boltzmann solver for swarm parameters.

What would settle it

A more precise measurement of the electron-vibration relaxation time in NO at low pressure (around 0.66 Torr) and electron temperatures near 200 K would test the state-to-state validation: the model gives $\tau_e \simeq 0.5\times10^{-6}$ s with $n_e\tau_e$ almost flat for $T_{vib}\lesssim2000$ K; a measured value outside a factor of two would indicate the VE cross-section set is missing significant channels.

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Extended reading notes

Core claim

The central claim is that resonant vibrational excitation of NO(X$^2\Pi$, v) by electrons, for all $v, v' = 0,\dots,53$, is quantitatively described by the local-complex-potential model using five NO$^-$ resonance states ($^3\Sigma^-$, $^1\Sigma^+$, $^1\Delta$, $^3\Pi$, $^1\Pi$) with potential curves and autoionization widths taken from earlier work, provided the previous ad hoc penetration factor is removed. The resulting excitation and de-excitation cross sections are mutually consistent through the detailed-balance relation, reproduce the measured low-energy cross sections and relaxation times, and—when embedded in the Hayashi-based cross-section set—bring the calculated electron drift velocity and characteristic energy in NO into substantially better agreement with swarm experiments than the sets of Campbell and Zhang. The authors conclude that the new cross sections are validated by swarm data and form a good starting point for a complete, consistent electron-impact set for NO.

Load-bearing premise

The whole set of cross sections rests on the assumption that five NO$^-$ resonance states, with potentials and widths taken from previous calculations, are enough to describe resonant vibrational excitation of NO up to its dissociation threshold.

Editorial extensions

If this is right

  • State-to-state plasma models of NO can now include all 54 vibrational levels with electron-impact excitation and de-excitation cross sections, rather than only the first few levels or approximate scaling laws.
  • Simulations of NO-containing plasmas—from the upper atmosphere to re-entry flows and plasma-based nitrogen fixation—will compute electron energy distributions and transport coefficients closer to measured swarm data than with the previous VE sets of Campbell or Zhang.
  • The electron-vibration relaxation time of NO is found to be of the same order as the heavy-particle V-V and V-T relaxation times, so electron-impact vibrational excitation cannot be neglected in NO kinetics and the two channels must be treated together.
  • The analytic fits to $n_e\tau_e$ in Table II provide a compact way to include e-V relaxation in fluid and global models without resolving all vibrational levels.
  • Removing the ad hoc penetration factor improves low-energy agreement, indicating that the earlier LCP data for NO should be revised even for the elastic channel.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An immediate extension is to apply the same five-resonance LCP machinery to other diatomics (e.g., CO or O$_2$) to see whether suppressing the penetration factor systematically improves low-energy VE cross sections, as it does for NO.
  • The paper validates the swarm agreement only within the Hayashi-based cross-section set, which it acknowledges is not self-consistent; a true test would embed the new VE cross sections in an independently swarm-optimized set and check whether the improvement persists.
  • The near-independence of $n_e\tau_e$ from the initial vibrational temperature below 2000 K suggests that a reduced description of NO e-V relaxation with a single relaxation time is valid for moderate vibrational temperatures, which could simplify large-scale atmospheric models.
  • Above about 10 eV the 'full set' is explicitly incomplete, so users of the LXCat data should restrict its use to electron energies below that threshold for accurate vibrational excitation, or supplement it with additional resonance states.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper calculates vibrationally resolved electron-impact excitation and de-excitation cross sections for NO(X2Π, v) with v=0..53 using the local-complex-potential (LCP) approach with five NO− resonance states. The molecular data are taken from the authors' earlier work. The authors verify detailed balance, compare selected cross sections and rate coefficients with literature data, apply the cross sections in a state-to-state model to obtain electron-vibration relaxation times, and insert the cross sections into a swarm calculation to compare drift velocity and characteristic energy with measurements. The central claim is that the new cross sections, combined with a fixed background set, significantly improve agreement with experimental swarm data and therefore validate the calculations.

Significance. If the results hold, the manuscript provides a useful full-manifold VE/VdE dataset for NO on LXCat, with value for kinetic modelling of NO-containing plasmas, hypersonic flows, and atmospheric chemistry. The paper has real strengths: the LCP approach is established, a detailed-balance check is made, the cross sections are compared with several independent experimental and theoretical sources (Allan, Zhang, Trevisan, Mojarrabi, Campbell), the relaxation-time model is compared with the Narasinga measurement, and the data are publicly available. However, the validation argument is weakened by three load-bearing issues: the ad hoc suppression of the penetration factor, the admitted need for additional NO− states above roughly 10 eV, and the explicit admission that the background set used in the swarm comparison is not a consistent set. These issues prevent the present version from fully supporting the strong validation claim, although they are addressable within the manuscript's scope.

major comments (3)
  1. [Section V, penultimate paragraph; Section VI] The paper explicitly concedes that the electron impact cross sections used in the swarm calculations 'do not constitute a consistent set', and the background contains Hayashi data plus separately chosen rotational and elastic cross sections. Since the same background is used for all three VE sets, the observed improvement in drift velocity and characteristic energy could in principle come from compensation of errors in the background rather than from the accuracy of the new VE cross sections. This weakens the conclusion in Section VI that the swarm results 'reinforce the validity' of the VE cross sections. Please either validate the background set, perform sensitivity tests with alternative backgrounds, or explicitly reframe the claim as a demonstration within the adopted set.
  2. [Section II; Section III, paragraph after Fig. 3] The suppression of the penetration factor f_r is described as the only methodological change relative to Ref. [22], and the text states that the suppression was decided because it improves agreement with the experimental data of Allan and Zhang. This makes a parameter choice after seeing experimental data, and it directly affects the low-energy behaviour of the 0→0 cross section, which is central both to the low-energy comparison and to the swarm results. Please provide a physical justification for the suppression, show the cross sections with and without f_r, and quantify how the relaxation times and swarm parameters depend on this choice.
  3. [Section III, paragraph after Fig. 3] The text states that reproducing the measured 10-20 eV resonance structure would require additional NO− states beyond the five included. Therefore, the dataset is full in vibrational quantum number but knowingly incomplete in resonance content at higher energies. Since the swarm calculations extend to E/N = 100 Td, where the EEDF tail reaches this energy range, the possible influence of the missing resonance states on the swarm comparisons should be quantified or at least explicitly discussed as a limitation of the validation.
minor comments (5)
  1. [Abstract; Section II] The abstract and title describe the method as 'ab initio molecular dynamics', but the calculations are a local-complex-potential treatment using potential energy curves and widths taken from Refs. [20,21]; please replace this term with a description that matches the actual method.
  2. [Figure 3] The comparisons with experimental data are shown without experimental error bars; adding them would help the reader judge the quality of the agreement.
  3. [Table II] The fitting formula is written as 'a0 + a1 Te + a2 Te^2 + b/log(Te)' but the base of the logarithm and the units of Te are not specified; please define the formula and the fitting range explicitly.
  4. [Section VI] There are typographical errors in the Conclusions, including 'Set ofab initioelectron impact cross sections' and 'de-excitaiton'; please proofread the manuscript.
  5. [Figure 2] The caption refers to solid lines as 'elastic processes', but the reader may not know whether these are elastic momentum-transfer cross sections or v→0 contributions; please clarify the caption.

Circularity Check

1 steps flagged · score 4.0 of 10

Low-energy 0→0 validation is a selection loop: f_r suppressed to match Allan/Zhang, then Allan/Zhang used to validate; swarm comparison is external but background set is inconsistent.

  1. other [Section III, paragraph discussing Figure 3 (after Eq. (3))]
    "At the low energies, the discrepancy is due to the lack of the penetration factor fr in the present calculations, as explained in section II. We note that the factor fr affects only the low energies and otherwise the cross sections are identical. Moreover, the lack of the ad hoc factor fr in the 0 → 0 cross section improves the agreement with experimental results of Allan (orange line) and Zhang (red curve) at low energies and for this reason we decided to suppress that factor."

    The binary choice to include or suppress the penetration factor f_r is made on the basis of agreement with the measured 0→0 cross sections of Allan and Zhang at low energies. In the same paper, the same measurements are then presented as independent validation: the text remarks a global good agreement with Allan and Zhang below 2 eV, and Figure 5 claims a better agreement with Zhang. Consequently, the low-energy 0→0 agreement is a selection effect rather than an independent confirmation of the calculation. The rest of the cross-section set (higher v and higher energy) and the swarm/relaxation comparisons with Takeuchi, Mechlinska-Drewko and Narasinga are external benchmarks, though the swarm comparison is weakened by the paper's admission that the background set is not consistent.

full rationale

The derivation chain is otherwise self-contained: Eq. (2) applies the standard local-complex-potential formula, and the molecular data are taken from the same group's earlier papers [20,21], but those are parameter-free quantum-chemistry calculations whose consequences are tested here against external experimental benchmarks. No fitted parameter is renamed as a prediction, no uniqueness claim is imported from the authors, and no known result is relabeled. One genuine validation loop exists: the suppression of the penetration factor f_r was decided because it improved agreement with Allan/Zhang at low energies, and the same Allan/Zhang data are then used to validate the low-energy 0→0 cross sections. This raises the score to 4 rather than higher because the central cross-section set is not reduced to that single choice and the swarm/relaxation comparisons remain external. The admitted inconsistency of the background set in Section V is a correctness risk in the validation logic, not a circularity.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. The main inputs are the LCP model, molecular data from the authors' earlier papers, the ad hoc decision to drop the penetration factor, and an assembled supporting cross section set for the swarm calculation. Table II fit coefficients are outputs, not inputs to the cross sections.

free parameters (2)
  • Penetration factor f_r = suppressed (set to 1)
    Introduced ad hoc in Laporta 2012 to fix low-energy behavior; removed here because comparisons with Allan and Zhang improve. This is a data-guided model choice rather than a derived parameter.
  • Relaxation time fit coefficients a0, a1, a2, b = Table II, vary with T_vib0
    Empirical fits to the simulated ne*tau_e curves in Figure 7; presented as an analytic representation and not used to compute cross sections.
assumptions (6)
  • domain assumption The local complex potential model is valid for resonant vibrational excitation of NO by electron impact.
    Section II and Eq. (2) assume the VE process is dominated by five NO- resonances and that LCP gives accurate cross sections.
  • domain assumption The potential energy curves and autoionization widths for the five NO- resonances from Refs [20,21] are accurate.
    These molecular data are taken from earlier papers without recomputation or error estimates; they are the foundation of the cross section calculation.
  • domain assumption Molecular rotation can be neglected for the energies considered.
    Section II uses j=0 potentials and states that rotation is at thermodynamic equilibrium, so rotational effects are not included.
  • domain assumption The state-to-state model assumptions in Section IV: no dissociation, Maxwellian electrons, isothermal bath, and no V-V or V-T transfers.
    These assumptions define the relaxation time calculation and limit its direct applicability to other conditions.
  • domain assumption The supporting electron collision set from the Hayashi database and Born rotational cross sections is accurate enough for the swarm validation.
    Section V uses this assembled set and the authors note it is not a consistent swarm-derived set, so the improvement attributed to the VE cross sections depends on this premise.
  • ad hoc to paper The penetration factor suppression is justified.
    Section II removes the factor because experimental agreement improves, not from a first-principles derivation; this is a post hoc modeling choice.

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Pith. "Pith review of Vibrational excitation cross sections for non-equilibrium nitric oxide-containing plasma." pith.science (2026). https://pith.science/paper/TBZBGP5L

@misc{pith2026241109370,
  author       = {Pith},
  title        = {Pith review of: Vibrational excitation cross sections for non-equilibrium nitric oxide-containing plasma},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TBZBGP5L}},
  note         = {Machine review of arXiv:2411.09370}
}
read the original abstract

A full set of vibrationally-resolved cross sections for electron impact excitation of NO(X2{\Pi}, v) molecules is calculated from ab initio molecular dynamics, in the framework of the local-complex-potential approach. Electron-vibration energy exchanges in non-equilibrium thermodynamic conditions are studied from a state-to-state model accounting for all electron impact excitation and de-excitation processes of the nitric oxide vibration manifold, and it is shown that the calculated vibration relaxation times are in good agreement with the experimental data. The new vibrational excitation cross sections are used in a complete electron impact cross section set in order to obtain non-equilibrium electron energy distributions functions and to calculate electron transport parameters in NO. It is verified that the new cross sections bring a significant improvement between simulations and experimental swarm data, providing an additional validation of the calculations, when used within the complete set of cross sections investigated in this work.

Figures

Figures reproduced from arXiv: 2411.09370 by the authors.

Figure 1
Figure 1. FIG. 1: Molecular data involved in the calculations as determined in the article in Ref. [20]. Left: Potential energy curves for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Summary on vibrational-excitation (VE dashed lines) and -de-excitation (VdE dotted lines) cross sections for NO [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Comparison of the cross sections obtained in the present paper (thick lines) with the data of Laporta-2012 [22], [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Summary on vibrational-excitation rate coefficients for electron-NO collisions. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Comparison of the rate coefficients obtained in the present paper (thick lines) with the data of Laporta-2012 [22], [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Electron-vibration energy exchange for a NO plasma out of equilibrium. (plot on the top-left) Time evolution of [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Electron-vibration relaxation time for NO molecule as obtained in the StS approach as a function of the electron [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Calculated EEDFs with LoKI-B solver [50] at (a) [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: (a) Electron drift velocity and (b) characteristic energy for a NO gas at 300 K, as a function of the reduced electric [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

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Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages

  1. [22]

    Laporta, R

    V. Laporta, R. Celiberto, and J. M. Wadehra, Plasma Sources Science and Technology 21, 055018 (2012)

    work page 2012

  2. [1]

    Bouziane, M

    A. Bouziane, M. A. Ferdi, and M. Djebli, Advances in Space Research 69, 905 (2022)

    work page 2022

  3. [2]

    Sahai, C

    A. Sahai, C. O. Johnston, B. Lopez, and M. Panesi, Journal of Quantitative Spectroscopy and Radiative Transfer 242, 106752 (2020)

    work page 2020

  4. [3]

    Munaf` o, S

    A. Munaf` o, S. A. Alfuhaid, J.-L. Cambier, and M. Panesi, Journal of Applied Physics 118, 133303 (2015)

    work page 2015

  5. [4]

    Panesi and A

    M. Panesi and A. Lani, Physics of Fluids 25, 057101 (2013)

    work page 2013

  6. [5]

    K. M. Naseem, Molecular Aspects of Medicine 26, 33 (2005). 10

    work page 2005

  7. [6]

    Feng, Coordination chemistry reviews 256, 393 (2012)

    C. Feng, Coordination chemistry reviews 256, 393 (2012)

    work page 2012

  8. [7]

    Moncada and E

    S. Moncada and E. A. Higgs, British Journal of Pharmacology 147, S193 (2006)

    work page 2006

Show all 56 references
  1. [8]

    K.-J. Jeon, R. Sharma, J.-W. Seo, and S. Kwon, Journal of Nanomaterials 2014, 523646 (2014)

    2014

  2. [9]

    H. Chen, D. Yuan, A. Wu, X. Lin, and X. Li, Waste Disposal & Sustainable Energy 3, 201 (2021)

    2021

  3. [10]

    Vervloessem, M

    E. Vervloessem, M. Aghaei, F. Jardali, N. Hafezkhiabani, and A. Bogaerts, ACS Sustainable Chemistry & Engineering 8, 9711 (2020)

    2020

  4. [11]

    K. H. R. Rouwenhorst, F. Jardali, A. Bogaerts, and L. Lefferts, Energy Environ. Sci. 14, 2520 (2021)

    2021

  5. [12]

    Jardali, S

    F. Jardali, S. Van Alphen, J. Creel, H. Ahmadi Eshtehardi, M. Axelsson, R. Ingels, R. Snyders, and A. Bogaerts, Green Chem. 23, 1748 (2021)

    2021

  6. [13]

    O. S. Bahnamiri, C. Verheyen, R. Snyders, A. Bogaerts, and N. Britun, Plasma Sources Science and Technology 30, 065007 (2021)

    2021

  7. [14]

    M. S. Bak and M. A. Cappelli, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, 20140331 (2015)

    2015

  8. [15]

    Campbell, M

    L. Campbell, M. J. Brunger, Z. L. Petrovic, M. Jelisavcic, R. Panajotovic, and S. J. Buckman, Geophysical Research Letters 31 (2004)

    2004

  9. [16]

    Song, J.-S

    M.-Y. Song, J.-S. Yoon, H. Cho, G. P. Karwasz, V. Kokoouline, Y. Nakamura, and J. Tennyson, Journal of Physical and Chemical Reference Data 48, 043104 (2019)

    2019

  10. [17]

    Itikawa, Journal of Physical and Chemical Reference Data 45, 033106 (2016)

    Y. Itikawa, Journal of Physical and Chemical Reference Data 45, 033106 (2016)

    2016

  11. [18]

    Armenise and F

    I. Armenise and F. Esposito, Chemical Physics 551, 111325 (2021)

    2021

  12. [19]

    Esposito and I

    F. Esposito and I. Armenise, The Journal of Physical Chemistry A 125, 3953 (2021)

    2021

  13. [20]

    Laporta, J

    V. Laporta, J. Tennyson, and I. F. Schneider, Plasma Sources Science and Technology 29, 05LT02 (2020)

    2020

  14. [21]

    Laporta, I

    V. Laporta, I. F. Schneider, and J. Tennyson, Plasma Sources Science and Technology 29, 10LT01 (2020)

    2020

  15. [23]

    J. N. Bardsley and F. Mandl, Reports on Progress in Physics 31, 471 (1968)

    1968

  16. [24]

    Domcke, Physics Reports 208, 97 (1991)

    W. Domcke, Physics Reports 208, 97 (1991)

    1991

  17. [25]

    Dub´ e and A

    L. Dub´ e and A. Herzenberg, Phys. Rev. A20, 194 (1979)

    1979

  18. [26]

    Laporta, R

    V. Laporta, R. Agnello, G. Fubiani, I. Furno, C. Hill, D. Reiter, and F. Taccogna, Plasma Physics and Controlled Fusion 63, 085006 (2021)

    2021

  19. [27]

    Celiberto, K

    R. Celiberto, K. L. Baluja, R. K. Janev, and V. Laporta, Plasma Physics and Controlled Fusion 58, 014024 (2016)

    2016

  20. [28]

    Laporta, J

    V. Laporta, J. Tennyson, and R. Celiberto, Plasma Sources Science and Technology 25, 06LT02 (2016)

    2016

  21. [29]

    Laporta, R

    V. Laporta, R. Celiberto, and J. Tennyson, Plasma Sources Science and Technology 22, 025001 (2013)

    2013

  22. [30]

    Allan, J

    M. Allan, J. Phys. B: At. Mol. Opt. Phys. 38, 603 (2005)

    2005

  23. [31]

    Zhang, W

    Z. Zhang, W. Vanroose, C. W. McCurdy, A. E. Orel, and T. N. Rescigno, Phys. Rev. A 69, 062711 (2004)

    2004

  24. [32]

    C. S. Trevisan, K. Houfek, Z. Zhang, A. E. Orel, C. W. McCurdy, and T. N. Rescigno, Phys. Rev. A 71, 052714 (2005)

    2005

  25. [33]

    Mojarrabi, R

    B. Mojarrabi, R. J. Gulley, A. G. Middleton, D. C. Cartwright, P. J. O. Teubner, S. J. Buckman, and M. J. Brunger, Journal of Physics B: Atomic, Molecular and Optical Physics 28, 487 (1995)

    1995

  26. [34]

    Sanche and M

    L. Sanche and M. Michaud, The Journal of Chemical Physics 81, 257 (1984)

    1984

  27. [35]

    Szmytkowski and K

    C. Szmytkowski and K. Maciag, Journal of Physics B: Atomic, Molecular and Optical Physics 24, 4273 (1991)

    1991

  28. [36]

    R. N. Schwartz, Z. I. Slawsky, and K. F. Herzfeld, The Journal of Chemical Physics 20, 1591 (1952)

    1952

  29. [37]

    E. E. Nikitin and J. Troe, Phys. Chem. Chem. Phys. 10, 1483 (2008)

    2008

  30. [38]

    Laporta and D

    V. Laporta and D. Bruno, The Journal of Chemical Physics 138, 104319 (pages 9) (2013)

    2013

  31. [39]

    K. L. Heritier, R. L. Jaffe, V. Laporta, and M. Panesi, The Journal of Chemical Physics 141, 184302 (2014)

    2014

  32. [40]

    L. L. Alves, P. Coche, A. M. Ridenti, and V. Guerra, The European Physical Journal D 70, 1 (2016)

    2016

  33. [41]

    Laporta, K

    V. Laporta, K. Heritier, and M. Panesi, Chemical Physics 472, 44 (2016)

    2016

  34. [42]

    S. F. Gimelshein, I. J. Wysong, A. J. Fangman, D. A. Andrienko, O. V. Kunova, E. V. Kustova, F. Morgado, C. Garbacz, M. Fossati, and K. M. Hanquist, Journal of Thermophysics and Heat Transfer 0, 1 (0), https://doi.org/10.2514/1.T6462, URL https://doi.org/10.2514/1.T6462

    doi

  35. [43]

    Robben, The Journal of Chemical Physics 31, 420 (1959)

    F. Robben, The Journal of Chemical Physics 31, 420 (1959)

    1959

  36. [44]

    L. D. Landau and E. Teller, Phys. Z. Sowjetunion 10 (1963)

    1963

  37. [45]

    Narasinga Rao and R

    K. Narasinga Rao and R. Taylor, Physics Letters A 27, 296 (1968)

    1968

  38. [46]

    Hagelaar and L

    G. Hagelaar and L. Pitchford, Plasma Sources Science and Technology 14, 722 (2005)

    2005

  39. [47]

    Hayashi database, www.lxcat.net, retrieved on October 13, 2021

    2021

  40. [48]

    R. H. Fowler, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 47, 257 (1924)

    1924

  41. [49]

    Vialetto, A

    L. Vialetto, A. B. Moussa, J. van Dijk, S. Longo, P. Diomede, V. Guerra, and L. L. Alves, Plasma Sources Sci. Technol. 30 (2021)

    2021

  42. [50]

    Tejero-del-Caz, V

    A. Tejero-del-Caz, V. Guerra, D. Gon¸ calves, M. L. da Silva, L. Marques, N. Pinh˜ao, C. D. Pintassilgo, and L. L. Alves, Plasma Sources Sci. Technol. 28 (2019)

    2019

  43. [51]

    Takeuchi and Y

    T. Takeuchi and Y. Nakamura, IEEJ Trans. 121, 481 (2001)

    2001

  44. [52]

    Mechlinska-Drewko, W

    J. Mechlinska-Drewko, W. Roznerski, Z. L. Petrovic, and G. P. Karwasz, J. Phys. D: Appl. Phys. 32, 2746 (1999)

    1999

  45. [53]

    Z. L. Petrovi´ c, S. Dujko, D. Mari´ c, G. Malovi´ c,ˇZ.. Nikitovi´ c, O.ˇSaˇ si´ c, J. Jovanovi´ c, V. Stojanovi´ c, and M. Radmilovi´ c- Radjenovi´ c, J. Phys. D: Appl. Phys.42 (2009)

    2009

  46. [54]

    P. W. Stokes, R. D. White, L. Campbell, and M. J. Brunger, J. Chem. Phys. 155 (2021)

    2021

  47. [55]

    Josic, T

    L. Josic, T. Wr´ oblewski, Z. L. Petrovic, J. Mechlinska-Drewko, and G. P. Karwasz, Chemical Physics Letters 350, 318 (2001)

    2001

  48. [56]

    Laporta database, www.lxcat.net/Laporta, retrieved on October 13, 2021

    2021

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