Evaluation of Electron-Impact Ionization Cross Sections for Molecules

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Evaluation of Electron Impact Ionization Cross Sections for Molecules Satyendra Pal, Manoj Kumar, Rajbeer Singh, and Neeraj Kumar J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02021 • Publication Date (Web): 25 Apr 2019 Downloaded from http://pubs.acs.org on May 3, 2019

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The Journal of Physical Chemistry

Evaluation of Electron Impact Ionization Cross Sections for Molecules

Satyendra Pal,* Manoj Kumar, Rajbeer Singh and Neeraj Kumar Department of Physics, M.M.H. College, Ghaziabad- 201001 (UP) INDIA

Abstract: We describe the recent progress in the development of the semi-empirical approach developed by Jain and Khare for the calculations of ionization cross sections for molecules by electron impact. Along with the state-of-the-art description of this approach, the emphasis will be on the evaluation of cross sections for carbon dimer C2 and trimer C3. Single-differential ionization cross sections as a function of secondary or ejected electron energy and averaged secondary electron energy for C2 and C3 are calculated at fixed impinging electron energies of 100 and 200 eV. The integral ionization cross sections are also derived from ionization threshold to 2000 eV. Extensive comparisons of the presently evaluated direct ionization cross sections with the only available theoretical binaryencounter-dipole (BED) model calculations of Kim and Rudd, spherical-complex-opticalpotential (SCOP) model calculations of Nagama and Antony, (DM) model calculations of Deutsch and Märk, and the calculations of Michelin et al. based on the combination of the Schwinger variational iterative method (SVIM) and distorted wave approximation (DWA) revealed a satisfactory agreement. The present study also establishes the validity of the semiempirical approaches and so provides a solid foundation for further applications to the larger molecules.

. *

Communicating author.

E-mail address: [email protected]

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1. Introduction Ionization of molecules by electron impact is one of the most important fundamental processes in collision physics. Knowledge of the interaction between the edge plasma and plasma facing components is important for the development of the next generation tokomaks for controlled fusion energy.1-2 The rapidly growing technological importance of (i) lowtemperature plasmas in areas such as plasma-assisted etching of microstructures and the deposition of high quality films and (ii) high-temperature plasmas such as fusion devices; has created an urgent need for a variety of molecular electron- induced cross sections (excitation, ionization, dissociation, attachments etc.). A quantitative description of the fundamental collision processes leading to ionic species in terms of absolute production cross sections, appearance energies, angular distribution of ions etc. is required for a detailed understanding of the properties of these plasma reactors as well as for the modelling of these plasmas. Ionization and attachment cross sections, the ionization rate-coefficients and the kinetic energy release distribution play an important role in this context, since they determine the ionization balance in the plasma and thus influence the plasma parameters in a crucial way. Unfortunately, the database on collision cross sections for molecules of relevance to various plasma applications is still limited. Moreover, ionization cross sections have many applications in atomic and molecular physics, astrophysics, gas discharge, radiation physics etc.3-5 Ionization leading to secondary electron emission is also an important stage in the mechanism of radiation damage to DNA biopolymers induced by primary ionizing radiation. These secondary electrons ejected by the incident or primary electron impacts can produce further ionizations, initiating an avalanche effect, leading to genome damage through the energy transfer from the primary objects to sensitive biomolecular targets, such as nitrogenous bases, saccharides, and other DNA and peptide components. Not only the number of emitted electrons is relevant, but also their energy spectrum, because, it has been shown that low energy electrons (below ionization threshold) can also produce damage to biomolecules by dissociative electron attachment.6-8 Scattering in the area of plasma and atomic and molecular physics not only have many practical applications, but also form the testing ground for the underlying quantum collision theory, made possible by the affluence of available experimental data. Although ionisation cross section can, in principle, be evaluated quantum mechanically yet the complicated nature of the process due to the presence of more than one free particle in the


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exit/ final channel makes the calculations quite difficult. The process which occurs in electron scattering by molecules more varied then those which occur in electron scattering by atoms and ions because of the possibility of existence of nuclear as well as electronic degree of freedom. In addition, the multi-centred and non-spherical nature of the electron molecule interaction considerably complicates the solution of the scattering problem by reducing its symmetry. There are other distinctive features of electron- molecule scattering. First, there is the crucial role that resonances play in vibrational excitation and dissociative attachment. For example, it is mainly near the resonances that the scattered electron spends sufficient time in the neighbourhood of the molecule to be able to excite the nuclear motion with sufficient probability. Secondly, the long-range interaction between an electron and molecule is more complicated than that between an electron and an atom. Quantum mechanically calculations for ionization cross sections (e,2e) are challenging since it is the most fundamental problem in Physics and Chemistry. Here it is customary to define the scattering amplitude in terms of scattering wave functions. Despite the fact that and notwithstanding the theoretical rigorous calculations, the analytical and semiempirical approaches play a useful role in producing the reliable and absolute data of cross sections.4-5 The purpose of this article is to present the recent progress in formal ionization theory and to show how it relates to the successful computational semiempirical technique developed by Jain and Khare,9-12 which aims to provide the authentic molecular data. In the present work, we have also applied this revisited formulation for the determination of ionization cross sections for C2 and C3 molecules observed in comets, as a testimony. Accurate ionization cross sections for these dicarbon and tricarbon are also important for the modelling of fusion edge plasma.13-15 To the best of our knowledge, no experimental determination is available for the differential cross sections of these homonuclear molecules. However, few theoretical determination of direct ionization cross sections comprising DM calculations of Deutsch and Märk,16-17 binary-encounter-dipole (BED) model calculations of Kim and Rudd,18-19 spherical-complex- optical-potential (SCOP) model calculations of Antony and co-workers,20-21 CADW calculations of Pindzola and co-workers,22 and the calculations of Michelin et al.23 based on the combination of the Schwinger variational iterative method (SVIM) and distorted wave approximation (DWA) are available for comparison of our results for integral direct ionization cross sections. The structure of the rest of the paper is as follows: in section 2 we provide the stateof-the-art description of the JK (herein after Jain and Khare) semiempirical formulation from Bethe theory, in section 3 we present the single differential ionization cross sections (function 3 ACS Paragon Plus Environment


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of secondary electron energy) and averaged secondary electron energies at 100 and 200 eV of impinging electrons, and the integral direct ionization cross sections in the incident electron energy range ionization threshold to 2000 eV. The section 4 deals with the conclusion.

2. Theory In this section, firstly, we briefly describe the Bethe theory24-25 for calculations of ionization cross sections and how JK semiempirical formulation was developed. In the theoretical treatments, the inelastic collision of charged particles (regarded as structureless) with atoms may be conveniently divided into two kinds, one dealing with fast collisions and the other one with slow collisions. The criterion used in making this classification involves the particle velocity relative to the mean orbital velocity of atomic electron in a shell or a subshell under consideration. The cross section for a process in which a fast projectile transfers amount of energy and momentum consists of two distinct factors, one dealing with the incident particle only and other dealing with target only. The first factor is almost trivial and the second involves the generalized oscillator strength of atom. Besides, a close relationship exists between fast collisions and the photoabsorption so that the theory of fast collisions provides means of cross checking data from these two independent sources, a procedure that proves valuable in many instances. In contrast, the problem of slow or soft collisions essentially involves a compound system of incident particle and target where the former has lost its individuality, at least for a short period of time.24 The inelastic scattering cross sections for atoms by electron impact were computed by Bethe using the first Born approximation, the differential cross section for the transition of an electron from ground state |0> to excited state |n> by the incident electron of energy E is given by

(

(

)

)

[ (

)]

(1)

where K, a0, R and Wn represent the momentum transfer, first Bohr radius, Rydberg’s constant and the energy utilized in the excitation, respectively. The term fn(Ka0) known as generalized oscillator strength (GOS) is defined by

(

)

(

)

|

|∑

(

|

|

(2)

Where rj is the position of the jth orbital electron. Integration of the differential cross section over the range of momentum transfer yields the ionization cross section per unit secondary electron energy ε i.e. 4 ACS Paragon Plus Environment

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(

(

)

)

[ (

)]

(3)

The GOS for an atomic system may be represented comprehensively by a threedimensional plot (known as Bethe surface) of df/dW as a function of E and (Ka0)2. The complete Bethe surface includes the GOS for discrete excitation as well as for transitions to continuum. In the event K→ 0, the generalized oscillator strength reduces to dipole oscillator strength that governs photoabsorption i.e. (

)

(4)

As W/E becomes smaller, the limit K→ 0 is approached more closely but is never precisely realized for any inelastic collision. The minimum momentum transfer for fixed W and E occurs at zero scattering angle and is given by

(

)

(5)

For W/E 1)

[

∑

]

∑

(24)

and finally,

[ {

∑ ∑

The values of

}]

(25)

and Si for the ions produced corresponding to increasing values of i

were found to be in decreasing order. The first term in the expression of the equation (25) was equal to CT, the total collision parameter. The explicit evaluation of Ci (i >1) with positive n value shows that they were greater than CT. Thus equation (25) yielded results for Ci relative to CT. The values of Ci provided better agreement between the calculated and experimental values of partial ionisation cross sections when compared with the case where Ci was considered to be independent of the nature of the ion species. The best fit value of n equal to 1.5 was used in the calculations.12 Keeping in view that the electrons in the exit channel are indistinguishable and hence there is equal probability of transfer of maximum primary electron energy (E-Ii) to the secondary electron hence limits of integration over ε in equations (16 & 17) become 0 to (EIi). Taking into account the same concept, Pal and co-workers27-42 employed this revisited approach to calculate the partial single differential cross sections (as a function of secondary/ ejected electron energy at fixed impinging electron energies), double differential cross sections ( as a function of secondary/ ejected electron energy and the scattering angle at fixed impinging electron energies) and the integral partial and total ionization cross sections as a function of incident electron energies for various types of molecules varying from diatomic to polyatomic molecules including the Bückminster fullerenes.27-42 Later on, Khare and co-workers43-45 deduced the input data of oscillator strength, in terms of molecular orbital properties that related the binary-encounter dipole model of Kim and Rudd.46 Moreover, the present version of Jain-Khare model (after reference 43) becomes more rigorous without any considerable success. In the preceding section, we have applied revisited JK formulation, after Pal et al.42 for the evaluation of single differential cross sections and the integral direct ionization cross sections for carbon dimer and trimer. 9 ACS Paragon Plus Environment


3. Result & Discussion The present revisited formulation is employed to evaluate the single differential cross sections Qi(E,W) and the integral ionization cross sections Qi(E) for C2 and C3. To calculate these cross sections, we require dipole oscillator strengths for the production of ith type of ions i.e. C2+ and C3+ during photoionization of molecules. In case of C2, the required dipole oscillator strengths are derived from the theoretically calculated photoionization cross sections by Padial et al.47 Using Frozen-Core Hartree-Fock approximation, Padial et al. calculated these photoionization cross sections in the photon energy range varying from ionization threshold to 50 eV. For higher photon energy range W > 50 eV, the same have been evaluated using TRK sum rule.48 To the best of our knowledge, the photoionization cross sections for C3 are not available in the literature. Without introducing much error, using the sum rule49, the same are derived from the C2 data.47 In their calculations for photoionization cross sections, Padial et al. considered low-lying ground states with all symmetries of the initial and final states. Since all orbitals, except, the σ are doubly degenerate in Ʌ. Low energy range (12-30 eV) included the contribution of ionization from πv. However, the contribution of degeneracy and spin-orbit interaction is accountable in excitation processes. In electron impact ionization of molecules the same contribution is negligible to account.6,47 The oscillator strength for the constituent atom may be calculated quantum mechanically, using Flexible Atomic Code (FAC).50 The mixing parameter ϵ0 (=40 eV), for both molecules has been calculated from the comparison of Bethe and Möller cross sections (for detail: see our publications). The collision parameter Ci (=0.0454/eV) for C2 and C3 are evaluated as discussed elsewhere.51 The ionization thresholds 11.4 eV and 13.0 eV corresponding to the direct ionization of C2 and C3, respectively are listed in the NBS data bank.52 Figure 1 depicts the secondary electron spectra in terms of single differential cross sections for considered molecules as a function of ejected/ secondary electron energy at fixed incident electron energies E=100 and 200 eV. To the best of our knowledge, neither experimental nor theoretical data is available to compare the present results. In the present formulation (equation 16), the first part (Born-Bethe part) for slow secondary electrons, corresponds to the growing contribution of the dipole-allowed interaction (known as glancing collision) and resembles the photo behaviour of the cross sections. The second part, accounts for the electron exchange effect, is non-dipole part that defines the knock-on-collision.


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Moreover, the cross sections are symmetrical about the W/2 wherein the energies of the incident and the secondary electrons are almost equal. The behaviours of cross sections are obvious and expected as for other molecules (see for instance our previous publications).

(a)

(b)

E=100 eV

E=200 eV

Qi(E,W) (cm2/eV)

Qi(E,W) (cm2/eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


C3 C2

W (eV)

C3 C2

W (eV)

Figure 1: (a) The single differential cross sections for the C2 and C3 molecules as a function of energy loss W (sum of ionization threshold Ii and the secondary electron energy ε) at fixed incident electron energy E=100 eV.

(b) Same as for (a) but at E = 200 eV. Single differential cross sections at fixed incident electron energies in terms of averaged energies of secondary electrons are useful in the study of irradiation of molecules and clusters with x-ray free-electron lasers and other plasma simulation.53-55 The averaged secondary electron energy is evaluated as, ∫

(

∫

) (

( )

(

)

(26)

)

Figure 2 shows the behaviour of averaged secondary electron energies as a function of incident electron energy. The calculated values for both molecules are generally equal at given energies. The trend of the curve is the same as for C atom derived by T.Kai.54



500

Figure 2: Variation of averaged

400

energy of secondary electron with impinging electron energy E.

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

200 100 0

10

100

1000

E(eV)

Since, no data seems to exist for differential cross sections, the corresponding derived integral or direct ionization cross sections (for i=1) from ionization threshold to 2000 eV, become important and are shown in the figure 3. In figure, we have presented the comparison of our ionization cross sections (ICS) for C2 with the established theoretical data sets.17,21-23 In their calculations, Deutsch et al.17 used DM formulation which relies on microscopic quantities in conjugation with a defect concept. Our calculations are in good agreement (within ± 10%) with those of DM calculations extracted from Deutsch et al.17 paper in the entire energy range. Using the same defect concept with straightforward value of exponent same as used in DM calculations, the derived ionization cross sections for C2, from BEB calculations for C atom19 are also in excellent agreement with our calculations. In the energy range threshold to 60 eV, our results overestimate the theoretical results derived from wellestablished spherical complex optical potential model by Nagma and Antony21 by 30%. Above 60 eV, good agreement with the same is noticed. On the other hand, calculations of Michelin et al.23 based on the Schwinger variational iterative method and distorted wave approximation show disagreement in the energy range E> 100 eV with our calculations as well as other calculations. The calculations for C2 made by Pindzola et al.22 using a configuration–average distorted wave method, a pure quantal method in energy range threshold to 50 eV, not shown in the figure, show disagreement with our results as well as other calculations. The same trend of the agreement with the available results17,21 for C3 is noticed. The present calculations also satisfy the various checks to access the consistency and reliability including those of Wannier threshold law5,56 (see for instance: reference 42 for detail description).


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6

5

(b)

(a)

5

C2 3 2

Qi(10-16 cm2)

4

Qi(10-16 cm2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

C3 4 3 2 1

0

0 10

100

1000

10

100

1000

E(eV)

E(eV)

Figure 3: (a) Ionization cross sections for the C2 molecules as a function of incident electron energy E. Solid line is the present calculations using JK formulation and solid-dot line is the present BEB calculations. Solid triangles are the DM calculations,17 solid rectangles are the SCOP calculations,21 and solid circles are the (SVIM+DWA) calculations.23

(b) Same as for (a) but for C3. 4. Conclusion Growth of experimental determination of electron impact ionization cross sections for different types of molecules served as a provocation to revisit the state of the theoretical calculations for ionization cross sections by electron collision. This work provides the stateof-the-art development of Jain-Khare semi-empirical formulation based on the Bethe theory of electron impact ionization of atoms. This formulation was applied for evaluation of single differential cross sections as a function of secondary electron energy, double differential cross sections as a function of secondary electron energy and angle of scattering, at fixed incident electron energies and integral/ total ionization cross sections for various types of ionization processes including those direct, dissociative and double ionization of molecules by electron impact. In most cases there was a very good to at least satisfactory agreement between the calculated and the experimental and/or theoretical results. Most noteworthy exceptions comprise the partial ionization cross sections where the experimental information is also quite poor. Here we have also applied this approach rely on the straightforward input data, easily available and/ or obtainable theoretically, for the evaluation of energy dependent 13 ACS Paragon Plus Environment


cross sections at 100 and 200 eV. The averaged energies of secondary electrons useful in plasma simulations are also calculated at fixed energies. The integral ionization cross sections in the energy range ionization varying from ionization threshold to 2000 eV for the formation of C2+ and C3+ ions through direct ionization processes of homonuclear dicarbon C2 and homonuclear tricarbon C3, respectively, by electron impact are also evaluated. The present results may facilitate the assimilation of evaluated cross sections into cross section data sets of molecules for modelling codes and other applications.

Acknowledgement: R. Singh is thankful to SERB/DST for Senior Research Fellowship Award with its grant no. EMR/2015/000647.


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References: (1) Hawryluk, R. J.; Campdell, D.J.; Janeschitz, G.; Thomas, P.R.; Albanese, R.; Ambrosino, R.; Bachmann, C.; Daylor, L.; Becoulet, M.; Benfatto, I., et al. Principal physics developments evaluated in the ITER design review. Nucl. Fusion 2009, 49, 065012. (2) Märk, T.D.; G.H. Dunn, in Electron Impact Ionization, Springer Ver., Wien, 1985. (3) Janav, R. K. Atomic and Molecular Processes in Fusion Edge Plasmas, Plenum Press, New York, 1995. (4) Burke, P.G.; Berrington, K.A.; Bell, K.L. Eds. Atomic, Molecular Data and Their Applications. AIOP Publication, 2000, Vol. 155. (5) Secondary Electron Spectra by Charged Particles Interactions. In Proceeding; International Commission on Radiation Units and Measurements ICRU report. 1996, Vol.55. (6) Baccarelli, I.; Bald, I.; Gianturco, F.A.; Illenberger, E.; Kopyra, J. Electron induced damage of DNA and its components: Experiments and Theoretical models. Phys. Rep. 2011, 508, 1-44. (7) Mineav, B.F.; Shafranyosh, M.I.; Svida, Yu; Sukhoviya, M. I.; Shafranyosh, I.I. Fragmentation of the adenine and guanine molecules induced by electron collisions. J. Chem. Phys. 2014, 140, 175101. (8) Sanche, L.; Parenteau, L. Surface reactions between O2 and hydrocarbons induced by dissociative electron attachment. J. Chem. Phys. 1990, 93, 7476-7486. (9) Jain, D. K.; Khare, S. P. Ionizing collisions of electrons with CO2, CO, H2O, CH4 and NH3. J. Phys. B 1976, 9, 1429-1438. (10) Jain, D. K.; Khare, S. P. Ionizing collisions of electrons with C 2H4 and C2H6. Ind. J. Pure & Appl. Phys. 1976, 14, 201-207. (11) Khare, S. P.; Meath, W. J. Cross sections for the direct and dissociative ionisation of NH3, H2O and H2S by electron impact. J. Phys. B 1987, 20, 2101-2116. (12) Khare, S. P.; Prakash, S; Meath, W. J. Dissociative Ionization of NH3 and H2O Molecules by electron impact. Int. J. Mass Spectrom. Ion Proc. 1989, 88, 299-308. (13) Isler, R. C.; Colchin, R. J.; Brook, N. H.; Evans, T. E.; Whyte, D. G. Spectroscopic determinations of carbon fluxes, sources and shielding in the DIII- D divertors. Phys. Plasmas 2001, 8, 4470-4482. (14) Helbert, J.; Rauer, H.; Boice, D. C.; Huebner, W. F. The chemistry of C2 and C3 in the coma of Comet C/1995 O1 (Hale-Bopp) at heliocentric distances rh ≥ 2.9 AU. Astron. Astrophys. 2005, 442, 1107-1120. 15 ACS Paragon Plus Environment


(15) Hinkle, K. H.; Keady J. J.; Bernath, P. F. Detection of C3 in the circumstellar shell of IRC+10216. Science 1998, 241 1319-1322. (16) Deutsch, H.; Becker, K.; Matt S.; Märk, T.D. Theoretical determination of absolute electron-impact ionization cross sections of molecules. Int. J. Mass Spectrom. 2000, 197, 3769. (17) Deutsch, H.; Becker, K.; Märk, T. D. Calculation of absolute electron-impact ionization cross-sections of dimers and trimmers. Eur. Phys. J. D 2000, 12, 283-287. (18) Kim, Y. -K.; Rudd, M.E. Binary-encounter-dipole model for electron-impact ionization. Phys. Rev. A 1994, 50, 3954-3967. (19) Kim, Y. -K.; Desclaux, J.P. Ionization of carbon, nitrogen and oxygen by electron impact. Phys. Rev. A 2002, 66, 012708. (20) Naghma, R.; Mahato, B.N.; Vinodkumar, M.; Antony, B.K. Electron impact ionization cross sections for atoms with Z = 49-54. J. Phys. B 2011, 44, 105204. (21) Naghma, R.; Antony, B. Electron impact ionization cross-section of C2, C3, Si2, SiC, SiC2 and Si2C. Mol. Phys. 2013, 111, 269-275. (22) Pindzola, M. S.; Ballance, C. P.; Ludlow, J. A.; Loch, S. D. ; Colan, J. Electron-impact ionization of C2. J. Phys. B 2010, 43, 065201. (23) Michelin, S. E.; Oliveira, H. L.; Soares, L.S.S.; Veiteinheimer, E.; Luz,C. A. R.; Mazon, K. T.; Fujimoto, M. M.; Lee, M. T. Cross sections for electron-C2 collisions. Chem. Phys. 2005, 309, 177-182. (24) Inokuti, M. Inelastic Collisions of fast charged particles wit Atoms and Molecules: The Bethe Theory Revisited. Rev. Mod. Phys. 1971, 43, 297-347. (25) Inokuti, M.; Dillon, M.A.; Miller, J.H.; Omidvar, K. Analytic representation of secondary-electron spectra. J. Chem. Phys. 1987, 87, 6967-6972. (26) Lassettre, E. N.; Skerbele, A.; Dillon, M. A. Generalized oscillator strength for Transition of Helium: Theory of limiting oscillator strengths. J. Chem. Phys. 1969, 50, 1829-1839. (27) Pal, S.; Prakash, S.; Kumar, S. Dissociative Ionization of Methane by Electron Impact. Int. J. Mass Spectrom. 1996, 153, 79-86. (28) Pal, S.; Prakash, S.; Kumar, S. Ionization of CO molecule by Electron Impact. Int. J. Mass Spectrom. 1997, 164, 13-17. (29) Pal, S.; Prakash, S.; Kumar, S. Partial Doubly Differential Cross Sections for the Ionization of H2 by Electron Impact. Int. J. Mass Spectrom. 1998, 175, 247-252.


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(30) Pal, S.; Prakash, S.; Kumar, S. Differential cross sections for the ionization of the CO molecule by Electron Impact. Int. J. Mass Spectrom. 1999, 184, 201-205. (31) Pal, S.;

Prakash, S. Partial Differential Cross Sections for the Ionization of the SO2

Molecule by Electron Impact. Rapid Commun. Mass Spectrom. 1998, 12, 297-301. (32) Pal, S. Partial double and single-differential cross-sections for CO2 by electron collision. Chem. Phys. Letters 1999, 308, 428-436. (33) Pal, S.; Prakash, S.; Kumar, S. Determination of partial single differential electron ionization cross sections of H2. J. Elect. Spectro. Rel. Phen. 2000, 109, 227-232. (34) Pal, S.; Bhatt, P.; Kumar, J. Electron Impact Ionization of the Cl2 molecule. Int. J. Mass Spectrom. 2003, 229, 151-156. (35) Pal, S.; Kumar, J.; Bhatt, P. Electron impact ionization cross sections for the N2 and O2 molecules. J. Elect. Spectro. Rel. Phen. 2003, 129, 35-41. (36) Pal, S.; Kumar, J.; Märk, T.D. Differential, partial and total electron impact ionization cross sections for SF6. J. Chem. Phys. 2004, 120, 4658-4663. (37) Pal, S. Determination of single differential and partial cross-sections for the production of cations in electron-methanol collision. Chem. Phys. 2004, 302, 119-124. (38) Bhatt, P.; Pal, S. Determination of cross sections and rate coefficients for electron impact dissociation of NO2. Chem. Phys. 2006, 327, 452-456. (39) Kumar, N.; Pal, S. Evaluation of direct ionization cross sections for C60 by electron interaction. J. Phys. (conf. ser.) 2009, 163, 012029. (40) Pal, S.; Anshu; Kumar, N. Electron ionization cross sections for neutral fullerene C70. Ind. J. Phys. 2011, 85, 1729-1737; (41) Pal, S.; Kumar, R.; Singh, R. Electron impact ionization cross sections of the CO2 clusters. J. Elect. Spectro. Rel. Phenom. 2012, 185, 625-629. (42) Singh, R.; Kumar, M.; Pal, S. Electron impact ionization cross sections for methylamines. J. Elect. Spectro. Rel. Phenom. 2018, 226, 22-25. (43) Saksena, V.; Kushwah, M.S.; Khare, S.P. Ionization cross-sections of molecules due to electron impact. Physica B 1997, 233, 201-212. (44) Khare, S.P.; Sharma, M.K.; Tomar, S. Electron impact ionization of methane. J. Phys. B 1999, 32, 3147-3156. (45) Kumar, Y.; Tiwari, N.; Kumar, M.; Tomar, S. Total ionization cross-sections of atmospheric molecules due to electron impact. Ind. J. Pure & Appl. Phys. 2010, 48, 621-625. (46) Kim, Y. K.; Rudd, M.E. Electron impact ionization of methane. J. Phys. B 2000, 33, 1981-1984. 17 ACS Paragon Plus Environment


(47) Padial, N. T.; Collins, L. A.; Schneider, B. I. Photoionization of ground-state molecular carbon C2. Astrophys. J. 1985, 298, 369-374. (48) Burton, G.R.; Chan, W.F.; Cooper, G.; Brion, C.E.; Kumar, A.; Meath, W. J. Valance shell absolute photoabsorption oscillator strengths, constrained dipole oscillator strength distributions and dipole properties for CH3NH2, (CH3)2NH and (CH3)3N. Can. J. Chem. 1994, 72, 529-546. (49) Zeiss, G. D.; Meath, W. J.; MacDonald, J. C. F.; Dawson, D. J. Dipole oscillator strength distributions, sums and some related properties for Li, N, O, H2, N2, O2, NH3, H2O, NO and N2O. Can. J. Phys. 1977, 55, 2080-2100. (50) Gu, M. F. Indirect X-Ray line-formation processes in iron L-shell ions. Astrophys. J. 2003, 582, 1241-1250. (51) Reike, F. F.; Prepejchal, W. Ionization cross sections of gaseous atoms and molecules for high-energy electrons and positrons. Phys. Rev. A 1972, 6, 1507-1521. (52) Ionization Potentials, Appearance Potentials and Heats of Formation of Gaseous Positive Ions; Franklin, J.L.; Dillard, J.G.; Rosenstock, H.M.; Herron, J.T.; Draxl, K.; Field, F.H.; National Standard Reference Data Series 26, National Bureau of Standard, USA (http://cccbdb.nist.gov/) (53) Kai, T.; Moribayashi, K. Effects of electron-impact ionization on the damage to biomolecules irradiated by XFEL. J. Phys. (Conference series) 2009, 163, 012035. (54) Kai, T. Single-differential and integral cross sections for electron-impact ionization for the damage of carbon clusters irradiated with x-ray free-electron lasers. Phys. Rev. A 2010, 81, 023201. (55) Ziaja, B.; Wabnitz, H.; Weckert, E.; Möller, T. Femtosecond non-equilibrium dynamics of clusters irradiated with short intense VUV pulsesNew J. Phys. 2008, 10, 043003. (56) CRC Handbook of Chemistry and Physics, 86th edition, Lide, D.R. Ed.; Taylor and Frances, Boca Raton, CD ROM Ver. 2006.


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