Theoretical partial ionization cross sections by electron impact for production of cations from CH₃OH, CO₂ and NH₃

Highlights

• We have employed Plane Wave Born Approximation along with Generalized Oscillator Strength of Weizsacker-Williams to Calculate the partial ionization cross sections for cross sections due to electron impact for production of cations from CH₃OH(CH₃OH⁺,CH₂OH⁺,CH₂O⁺,CH₃⁺,CH₂⁺CHO⁺,CH⁺,C⁺,CO⁺,OH⁺,H₂⁺ H⁺) from CO₂ (CO₂⁺,CO⁺,O⁺ C⁺) and from NH₃ (NH₃⁺,NH₂⁺,NH⁺, N⁺ H⁺) respectively from the ionization threshold to 1 keV.

• We have also calculated the total ionization cross sections by summing all the partial ionization cross sections.

• The present cross sections are compared with other available data in literature. The ionization cross sections are found in good agreement with experimental data.

Abstract

In the present article, the Plane Wave Born Approximation (PWBA) along with Generalised Oscillator Strength (GOS) proposed by Weizsacker-Williams has been employed to calculate the partial ionization cross sections due to electron impact for production of cations (CH₃OH⁺, CH₂OH⁺, CH₂O⁺, CH₃⁺, CH₂⁺ CHO⁺, CH⁺, C⁺, CO⁺, OH⁺, H₂⁺ and H⁺) from methanol, for production of cations (CO₂⁺, CO⁺, O⁺ and C⁺) from carbon dioxide and for production of cations (NH₃⁺, NH₂⁺, NH⁺, N⁺ and H⁺) from ammonia from the ionization threshold to 1 keV. The use of GOS given by Weizsacker-Williams breaks the expression of cross section into two terms, Bethe cross section and Mott cross section. Both terms depend on Optical Oscillator Strength (OOS). Furthermore, binary encounter theory has also been used. By summing all the partial ionization cross sections, total ionization cross sections are also obtained. The calculated cross sections are compared with the previously available experimental data and theoretical cross sections. The present calculations are found in remarkable agreement with available experimental data and other previous theoretical results.

Introduction

The ionization cross sections of molecules have an importance in many applications such as astrophysics, atmospheric science biological science and plasma modelling [1], [2], [3]. Methanol is the smallest alcohol and has an importance as it can be supposed to be a prototype for larger alcohols. Interaction of methanol with electrons is a subject of interest because it can be used as fuel which is the alternative to traditional fossil fuels. This fuel releases less toxic and greenhouse gases on burning in the internal combustion engines in comparison of fossil fuels. The plasma modelling is required to make the theoretical model of car engines because the plasma is created during combustion of bio-fuel in the engines. The ionization cross sections may be used as input parameter [4], [5], [6], [7]. In industries, ammonia is used as the source of nitrogen to fabricate nitride films. Ammonia is also used to produce the N₂-H₂ plasma. Carbon dioxide is widely used in low temperature plasma devices in laboratories. Furthermore, these molecules are detected in the interstellar space medium and also in the atmosphere of planets in the solar system which play important role in the chemistry of these environments [8], [9], [10].

Total and partial electron impact ionization cross sections for CH₃OH, CO₂ and NH₃ have been measured by a number of groups using the different experimental methods. Recently, Nixon et al. [7] have measured the electron impact absolute partial ionization cross sections of methanol by using quadrupole mass spectrometer. Srivastava et al. [11] have also investigated the experimental partial ionization cross sections for 10 cations of methanol by electron impact. Rejoub et al. [12] have measured the absolute partial ionization cross section for groups of cations CH_nO⁺ (CH₃OH⁺ + CH₂OH⁺ + CH₂O⁺ + CHO⁺ + CO⁺) and CH_n⁺ + H_nO⁺ (CH₃⁺ + CH₂⁺ + CH⁺ + C⁺ + H₂O⁺ + OH⁺ + O⁺) with similar mass of cations from methanol. However, Hudson et al. [13] and Djuric et al. [14] have measured the total ionization cross sections for methanol by collecting all fragmentation product simultaneously. For the production of ions CO₂⁺, CO⁺, O⁺ and C⁺ from CO₂, Lindsay & Mangan [15], Orient & Srivastava [16] and Crowe & McConkey [17] have reported the partial ionization cross sections. Krishankumar [18] measured the cross sections only for CO₂⁺. Hudson et al. [19] and Rapp & Englander-Golden [20] have measured the total ionization cross sections directly (all fragmentation products are collected simultaneously). Rao & Srivastava [21], Bederski et al. [22], Crowe & McConkey [23] and Mark et al. [24] have investigated experimentally the partial ionization cross sections for production of ions NH₃⁺, NH₂⁺, NH⁺, H⁺ and N⁺ from NH₃ while Rejoub et al. [25] have measured the partial ionization cross sections in group of ions NH_n⁺ (NH₃⁺ + NH₂⁺ + NH⁺ + N⁺). Recently, Itikawa [10] reported the experimental data of Rejoub et al. [25] for cations from ammonia separately. Theoretical partial ionization cross sections were only calculated by Pal [26] by using Khare-Jain approach for cations from methanol.

Theoretical calculation of ionization cross sections of the molecules by using quantum mechanics is an involved problem even in first born approximation. Hence a number of semi empirical and semi empirical classical formulae have been proposed. Some of these methods are Khare-Jain method [26], Kim-Binary Encounter Bethe (BEB) [27], Khare-Binary Encounter Bethe (BEB) [28], [29], [30], [31], Deutsch-Mark (DM) method [32], complex scattering potential ionization contribution method [33] and Saksena model [34]. As we have seen in literature survey, most of researchers measured the partial ionization cross sections and summed them to obtain the total ionization cross sections. On the other hand, most of theoretical methods provide the total ionization cross sections. Only limited theoretical methods are available to calculate the partial ionization cross sections of cations from molecules due to electron impact. One of successful semi empirical approaches is Khare-Jain method [26]. Khare-Jain method requires Optical Oscillator Strength (OOS), ionization threshold, collisional parameters and mixing parameters to calculate the partial and total cross sections for molecules. Another method was proposed by Saksena et al. [34] but their cross sections are found low at near ionization threshold energies and are greater at intermediate impact energies.

In the present investigation, we have used the Plane Wave Born Approximation (PWBA) and employed the expression of Generalised Oscillator Strength (GOS) given by statistical model of Weizsacker-Williams [35] to calculate the partial ionization cross sections for production of twelve cations (CH₃OH⁺, CH₂OH⁺, CH₂O⁺, CH₃⁺, CH₂⁺, CHO⁺, CH⁺, C⁺, CO⁺, OH⁺, H₂⁺ and H⁺) from methanol, for production of four cations (CO₂⁺, CO⁺, O⁺ and C⁺) from carbon dioxide and for production of five cations (NH₃⁺, NH₂⁺, NH⁺, N⁺ and H⁺) from ammonia molecule. In PWBA, it is well known that the cross sections overestimate the experimental data at low impact energies. This overestimation is supposed to be due to distortion of the incident electron wave function which is the result of electrostatic attractive field of the nucleus of target. This field increases the kinetic energy of incident electron. It is very difficult task to include this effect in theory. To reduce this overestimation in cross sections, we have employed binary encounter theory [28], [35] and multiply cross sections by E/[E + 2I], where E and I are the incident energy and ionization threshold energy (or appearance potential), respectively. The term 2I represents the increase in the kinetic energy of incident electron due to acceleration by the field of target nucleus. Furthermore, we have also modified the Mott term to improve agreement between the theoretical results and experimental data.