Electron-heliumS-wave model benchmark calculations. I. Single ionization and single excitation

Abstract

A full four-body implementation of the propagating exterior complex scaling (PECS) method [J. Phys. B 37, L69 (2004)] is developed and applied to the electron-impact of helium in an S-wave model. Time-independent solutions to the Schrödinger equation are found numerically in coordinate space over a wide range of energies and used to evaluate total and differential cross sections for a complete set of three-and four-body processes with benchmark precision. With this model we demonstrate the suitability of the PECS method for the complete solution of the full electron-helium system. Here we detail the theoretical and computational development of the four-body PECS method and present results for three-body channels: single excitation and single ionization. Four-body cross sections are presented in the sequel to this article [Phys. Rev. A 81, 022716 (2010)]. The calculations reveal structure in the total and energy-differential single-ionization cross sections for excited-state targets that is due to interference from autoionization channels and is evident over a wide range of incident electron energies.

Electron-heliumS-wave model benchmark calculations. II. Double ionization, single ionization with excitation, and double excitation

“…These same equations are used to evaluate the double-excitation and ionization-with-excitation cross sections presented here, simply by using the appropriate final-state atom/ion wave function in Eqs. (26) and (36) of the preceding article [12]. A method for evaluating cross sections for the remaining four-body channel, double ionization is developed here.…”

“…The preceding article [12] detailed the PECS four-body method for calculating the scattering wave functions for electron-helium collisions in the S-wave model, along with surface integral methods for evaluating non-breakup and single-ionizing collisions. In summary, this method numerically solves the full time-independent Schrödinger equation for electron-helium on a numerical mesh in coordinate space.…”

“…In the preceding article [12], this surface integral technique was used to calculate excitation and single-ionization cross sections for the four-body electronhelium S-wave model. These same equations are used to evaluate the double-excitation and ionization-with-excitation cross sections presented here, simply by using the appropriate final-state atom/ion wave function in Eqs.…”

“…In the preceding article [12] we described the propagating exterior complex scaling (PECS) four-body method for calculating electron-helium scattering wave functions and presented benchmark excitation and single-ionization (without excitation) cross sections (total and energy-differential) for the S-wave model. Here we complete our study of the S-wave model.…”

Convergent close coupling versus the generalized Sturmian function approach: Wave-function analysis

“…Today there are many methods which can solve the quantum three-body problem in addition to the ECS: convergent close coupling (CCC), the J matrix, the R matrix, time-dependent close coupling [2][3][4], and more recently the generalized Sturmian function approach (GSF) [5]. However, processes such as double ionization of helium by high-energy electron impact show that this problem is not closed or completely understood [6,7], though some benchmark results for the S-wave model exist [8,9]. At high incident energies the four-body (e,3e) problem can be reduced to a three-body one [5].…”