Electron-impact ionization cross sections and bound-free generalized oscillator strengths for atomic systems

Abstract

%ithin the Born approximation, a general formulation is given for differential cross sections corresponding to electron-impact ionization of an-arbitrary L-S-coupled atomic system. Expressions for the generalized oscillator strength and total cross section are also given. Correlation eA'ects are explicitly included in the formulation through the use of a configuration-interaction wave function to describe the initial bound target state, and a close-coupling wave function to describe the final free target state. Two independent computer codes have been constructed which allow these functions to be of arbitrary complexity for any atom. The codes use recently developed, but different, techniques for solving the closecoupling equations. Test results are obtained for the hehum atom, and they agree well with previous correlated calculations.

Initial-state, final-state and higher-order effects in electron impact ionization of helium atoms

“…The general trend is typical in that the binary peak is predicted too large and the recoil peak is predicted too low by such theories, which also predict the two peaks to be along the direction of the positive (binary) and negative (recoil) momentum transfer. However, it is interesting to note that the results of the standard 3-state R-matrix model (see also Robb et al 1975) are substantially different from those obtained in the other three calculations, particularly for the recoil peak. The calculation with the Hartree-Fock 1s orbital yields good, though not perfect, agreement with the results obtained by Byron et al (1986).…”

Absolute triple differential cross sections for electron impact ionization of helium: Comparison between experimental and theoretical results at 256 eV collision energy

“…Similar to the calculations of Jung et al the recoil peak is too small by about a factor of two in all cases. The value of the binary/recoil-ratio is much too low in the approximation used by Robb et al [15].…”

Double processes ine − — He collisions

“…In fact, the term Tz above corresponds to the use of Green's function operators G+ (ro; rl, r21r;; r'l, rl) = 2 lim fdk2(co~Z--k2+iO--1 ~0 + ¥ ' 1%fdr0; rl, r2)) (%;k(r0, r'l rl)l (13) acting from the left on I ~ ' ' ' ~d;ko(ro, rl, r~)) or from the right on (~(ko(ro; rl, r2)l. In the special case which we are considering, where the projectile is represented by plane waves, at least in the intermediate state, this operator can alternatively be expressed in terms of Gg, the free particle Green's function: G + (ro; rs, rz Ir•; rl, r~) = 2 2 1 ~( r s , r2)) (05~(rs, r2) l ag (o9~; ro, r;) v 1 expico I r -r ' I G0~(co; r, r')= 4n l r -r ' l (14) For details, see (1-I25) to (1--127) of [-32]. The usual way to calculate the second order contribution is to make use of the well-known theorem…”

“…[9]. Tweed and Langlois [11] use correlated wavefunctions for the target initial state and distorted waves for the ejected electron and Jacobs [12] and Robb et al [13] use correlated target initial states with coupled channel wavefunctions for the target final state (ejected electron plus residual ion), but all these models are first order both for the projectile wavefunctions and in the interaction potential. Tweed and Langlois [11] use correlated wavefunctions for the target initial state and distorted waves for the ejected electron and Jacobs [12] and Robb et al [13] use correlated target initial states with coupled channel wavefunctions for the target final state (ejected electron plus residual ion), but all these models are first order both for the projectile wavefunctions and in the interaction potential.…”