An L² representation of the continuum in heavy particle collisions
This thesis is concerned with the use of L² or square integrable functions as a representation of the electronic continua in ion-atom collisions. An exact representation of the continuum states is considered for comparison. The functions are optimised in an attempt to remove some of the arbitrary features present in such calculations. The original work of this thesis is mainly concerned with the calculation of single electron processes in collisions between He²⁺ ions and neutral lithium atoms. The cross sections for single electron capture were calculated in a close-coupled approximation, using the semi-classical impact parameter method. A maximum of thirty-two atomic orbitals with plane-wave translational factors attached were centred upon the target and projectile. Satisfactory agreement with experimental data is obtained over the He(^2+)laboratory energy range from 8 to 2000 keV. The results show the importance of the continuum over a restricted range of impact energies. The rest of the research is concerned with direct excitation and ionisation in the same collision system and results are given for He²⁺ laboratory energies between 20 and 6000 keV. The calculations used a similar close-coupled approximation with up to sixty-five basis states. The best ionisation cross sections reproduce the experimental data apart from a normalization factor. The excitation results were more sensitive to basis set choice. The ionisation cross sections were also investigated using an exact representation of the continuum states, using the First Born Approximation and a t-matrix approximation in an attempt to improve upon the L² results. The relationship between the present calculations and some previous methods are discussed and suggestions for future work are made. These are the first close-coupled estimates of ionisation for this sytem and show that contributions from target d- and f- states dominate the ionisation cross section around its maximum.