Convergent series representation for the generalized oscillator strength of electron-impact ionization and an improved binary-encounter-dipole model

Abstract

The use of the Bethe cross section in the binary-encounter-dipole ͑BED͒ model for electron-impact ionization is studied. While the dipole contribution in the Born approximation accounts for the longest-range interaction in electron-neutral atom/molecule inelastic collisions at any incident energy, the Bethe formula is applicable only at high energies. To derive a suitable representation of the Born cross section for dipoleallowed transitions, a convergent series representation for the generalized oscillator strength ͑GOS͒ of electronimpact ionization is studied. It is shown that by transforming to a new variable determined by the location of the singularities of the GOS on the complex plane of momentum transfer K, a series representation for the GOS is obtained that is convergent at all physically attainable values of K. An approximate representation of the GOS that truncates the series representation to the first three terms is also given. The approximate GOS describes the interaction of the electron with a shielded dipole potential and satisfies both Lassettre's limit theorem at Kϭ0 and the asymptotic behavior at large K derived by Rau and Fano ͓A. R. P. Rau and U. Fano, Phys. Rev. 162, 68 ͑1967͔͒. The dipole-Born cross section so obtained is applicable at all incident energies and goes to the Bethe cross section at the high-energy limit. It provides a more suitable representation of the dipole contribution in the BED model than the Bethe cross section and is valid over the entire energy range. A similar analysis of the optical-oscillator strength ͑OOS͒ as a function of the complex momentum for the ejected electron k p , plus the requirement that the OOS satisfies both the low-and high-k p limits produces an analogous series representation for the OOS. An approximate one-term representation of the OOS is also developed that can be used in modeling calculations. Numerical examples of total ionization cross sections of N 2 , H 2 O, CO 2 , CH 4 , and CF 4 using the new analytical representation are presented to illustrate the applicability of the improved BED model.

Evaluation of electron impact excitation of N2 X 1Σg+(0) into the N2+ X 2Σg+(v), A 2Πu(v), and B 2Σu+(v) states

“…Many theoretical investigations have been concerned with semi‐empirical and semi‐classical formulae. Among these are the binary‐encounter‐dipole (BED) and binary‐encounter‐Bethe (BEB) models by Kim and Rudd [1994] and Hwang et al [1996], improved BED models proposed by Saksena et al [1997], Khare et al [1999], and Huo [2001], and the Deutsch‐Märk model by Deutsch et al [2000] and Probst et al [2001]. While these models are typically capable of reproducing experimental peak cross sections within 5%–15%, they are difficult to apply to partial ionization because binary‐encounter models are based on collisions between a free and a bound electron.…”

Partial-ionization cross sections of aCO2molecule due to impact of 10–26-keV electrons

“…This difference may be arising due to the usage of a nonrelativistic BEB theory in the present calculations, which is not expected to be valid at energies used in our experiments. As a matter of fact, the BEB theory gives higher values of cross sections for even lower impact energies than the present energy range [25]. To the best of our knowledge, there are no other experimental or theoretical data available in the literature for the considered energy range to compare with.…”

Electron impact ionization cross-sections of SF3 and SF5

“…In the iBED model [20], the electron impact cross-section σ iBED po of ionizing an electron initially in orbital o of the target and resulting in an ion state p is given by…”

“…In the iBED model, the OOS are either deduced from experiment or determined from ab initio calculations. In the simplified version of the iBED model (siBED), the following approximate expression is used based on the f-sum rule and the proper representation of the OOS in the complex k p plane [20],…”

“…The lack of an adequate description of this bonding characteristics in the theoretical models mentioned in the preceding paragraph is the source of the large discrepancy between theory and experiment. The improved binary-encounter dipole model (iBED) developed by one of us [20], and the simplified version of this model (siBED), accounts for the shielding of the long-range dipole potential by the repulsive field in the bonding region. The shielding parameter is deduced using ab initio calculations of the electric field that the molecular charge distribution exerts on the incoming electron.…”