Scattering of positrons by Helium atoms and the use of a graphical display device

The scattering of slow positrons by Helium atoms is of particular interest now that positron beam experiments are being performed. The purpose of this thesis is to carry out an examination of past theoretical investigations of the problem as well as to explore various approximation schemes for describing the problem within the framework of the close-coupling method, where the total wave function is expanded in terms of the eigenstates of the target Hamiltonian and of the positronium system. The numerical techniques associated with solving the ensuing coupled intego-differential equations are described in detail. A novel use of a graphical display device as an aid to debugging the computer code is illustrated. The theoretical approximations include (l) allowing for all partial waves (2) taking into account the 2P states of both Positronium and Helium (3) the addition of correlation terms (a means of allowing for short-range effects.).