Investigation of the impact parameter method for electron-atom collisions

Abstract

In this thesis we develop and investigate the use of a semi-classical impact parameter method for treating the excitation of atoms by electron impact. Our particular interest is forbidden, non-exchange transitions. Chapter 1 contains a brief description of the method along with reasons for considering such a method. Previous work employing the same general ideas is reviewed, as are other theoretical calculations and experimental results of direct relevance to this thesis. The paper of Seaton (1962) which applies the impact parameter method to optically allowed transitions is reviewed in some detail as our treatment of the subject is based largely on this work. In Chapter 2 we derive expressions for the transition probabilities and introduce the idea of the averaged probabilities. Cross section formulae are given which are applicable to dipole and quadrupole transitions and which include a strong coupling form. The formulae are generalized to apply to an incident point particle of arbitrary mass and charge. Chapter 3 contains formulae for the averaged probabilities for arbitrary interaction potentials and these are applied to the case where the potential is a sum of spherical tensor operators. Expressions for cross sections, applicable to arbitrary transitions induced by electron or proton impact, are given and the explicit form evaluated for the case of hydrogen. In Chapter 4 are presented results of calculations of cross sections for certain forbidden transitions in hydrogen and helium, both for electron and proton impact. We examine the validity of the approximations made and discuss the choice of the cut-off. Chapter 5 contains an evaluation of the method as well as suggestions for improving it and for further applications. The derivation of certain results used in the thesis is presented in the appendices.