Electron-helium atom scattering (second Born approximation)

Abstract

In chapter I of this thesis the Born series solution of the Schrodinger equation for the scattering of a structure less particle by a static potential is derived and known results about its radius and rate of convergence given. The derivation is generalised to electron-atom scattering in chapter II. It is proved that the second Born scattering amplitude satisfies relationships analagous to the optical theorem and the dispersion relation conjectured by Gerjuoy and Krall. Various approximate methods of evaluating the second born correction to the scattering amplitude are discussed. In chapter III the method used to reduce the second born correction to the scattering amplitude to a sum of known integrals is given and chapter IV contains the method of evaluating these known integrals. The results obtained from applying various forms of the simplified second born approximation to elastic and inelastic collisions of electrons with Helium and Hydrogen atoms are presented in Chapter V. At incident electron energies of up to twenty times threshold a correction of between 5% and 10% to the first Born total cross sections is obtained for the following collisions:- [diagram] For transitions between the ground state and excited d states of both Hydrogen and Helium atoms induced by electrons with impact energy of twenty times threshold the correction to the first Born total cross section is less than 3%, apart from the excitation of the 31D state of Helium when it is 15%. Differential and total cross sections are given for the excitation of model doubly excited states of Helium.