A semiclassical theoretical model for (e-2e) processes

Abstract

A semiclassical method used previously for high-energy proton-atom collisions is adapted to the case of electron-impact ionisation of atomic targets at intermediate and high energies. Incident electron trajectories are calculated classically using the spherically averaged field of the target. Scattered and ejected electron trajectories are calculated using the averaged field of the residual ion, their starting conditions being determined by taking approximate account of classical momentum conservation at the instant of transition. Scattering angles and related ejected electron angular distributions are thus obtained for particular impact parameters and collision times. The corresponding ionisation probability is determined quantum mechanically using the time-dependent perturbation of the target system calculated from the incident trajectory.

Correlations in the autoionising region of He measured by the (e, 2e) technique

“…Surprisingly, results for the angular dependence of the direct ionisation cross section f,, although determined, were not presented. Their absence is perhaps explained in the paper of Tweed and Langlois (1986), who pointed out that the direct ionisation cross sections calculated by Pochat et a1 (1982) were significantly different from their experimental results in the recoil collision region. We pointed out earlier how inaccuracies in the treatment of direct ionisation necessarily limit the accuracy of resonance parameter calculations, as the expressions used to calculate a, and b, involve amplitudes describing the direct ionisation process (equations ( 5) and ( 6)).…”

“…It should, however, be noted that there appears to be an inconsistency between the calculated and experimental results reported by Pochat et al The calculated and experimentally derived values of a, and b, are presented for each resonance in polar diagrams, although their signs are not given. The signs of their calculated a, and b, parameters can in fact be deduced from the paper of Tweed and Langlois (1986), where the earlier 100 eV results of Pochat et a1 (1982) are compared with those from further calculations performed at 70 and 80 eV. In particular, for the (2s2)'S resonance profile, it is seen that the theory of Pochat et a1 (1982) predicts the b, parameter to be positive and the a, parameter negative at an ejection angle of -6OO.…”

“…The incident beam energy in this calculation was 100 eV and the fixed scattered electron detection angle was 15O. In the paper of Tweed and Langlois (1986), the kinematical range of these calculations waa extended with additional calculations performed at incident energies of 70 and 80 eV, again for a scattering angle of 15O. These later calculations, however, did not include results for the (2p2)'D state.…”

“…The model employed by Pochat el a1 (1982) and Tweed and Langlois (1986) closely resembles that used by Balashov el a1 (1980) in which the distorted wave Born approximation is used to calculate triple differential cross sections for excitation of the 4d-'5p 'P autoionising state in cadmium. In these calculations the process of direct ionisation was neglected, the justification based on the assumption that the ionisation continuum is weak in the vicinity of this resonance.…”

Quantum-mechanical analogies for classical post-collision interaction effects in (e, 2e) collisions

“…It is possible to introduce the repulsion between the two outgoing electrons in the equations of the classical trajectories as proposed by Tweed and Langlois [17] and, by an iterative procedure, to deduce both the potential at any point of the space and the trajectories. However, in a first approximation, we will neglect the angular components of the forces and assume, …”