Electron scattering by the rare gases

Abstract

In the first part of this thesis an optical potential approach is applied to the problem of elastic electron-helium scattering at low energies. First the deficiencies in the second order calculation of Pu and Chang arc removed and then third order corrections to the phase shifts are considered. In Chapter I a short review of Brueckner-GoIdstone perturbation theory is presented and explicit expressions for the second order phase shifts are derived. The methods of computing these expressions are considered in Chapter II. Various other theoretical models are discussed in Chapter III where also our second order results for the s, p and d-wave phase shifts are given. Chapter IV comprises our calculation of the polarisability of helium, using a Brueckner-Goldstone approach. In Chapter V a method of determining all the distinct Feynmann diagrams of any order is given, and third order corrections to the d-wave phase shift are discussed.

The aim of the work described in Part II of this thesis has been to test for electron-neon scattering the dispersion relation conjectured by Gerjuoy and Krall. An introduction to the dispersion relation and the technique of phase shift analysis is given in Chapter VI and previous work on electron-helium scattering is reviewed. In Chapter VII the various quantities which have to be calculated in order to test the validity of the dispersion relation for electron-neon scattering are discussed. In particular, the analysis involved is the calculation of the Born exchange scattering amplitude,S_B(O, k2) is given. A more accurate evaluation of this amplitude for zero energy, using a configuration interaction ground state wave function, is described in Chapters VIII and IX. Preliminary results for g_B(O, 0) are given in Chapter X.