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The intranuclear cascade is an approximate microscopic model of heavy-ion collisions in which the space-time evolution of the nucleons is followed as they collide with one another. This model is used: (a) to test the validity of simpler models as the two-fireball model; (b) to estimate the validity of the assumption of chemical equilibrium and to calculate the total pion production cross-sections; (c) to investigate the average primordial charge multiplicity and the number of participants as a function of the beam energy.

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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.

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The Convergent Close Coupling (CCC) method is applied, for the first time, to the scattering of positrons on helium. The helium target wave functions are obtained within various configuration interaction (CI) expansions. In the full CI expansion the two electrons are treated equally and thus all electron-electron correlations are taken into account. In the frozen-core (FC) approximation the CI expansion fixes one of the electrons to be described by a pure 1s orbital of He+, while maintaining the required singlet and triplet symmetries. Lastly, the multi-configuration (MC) approximation relaxes the FC approximation to allow the description of the inner electron to include several low-lying orbitals and is therefore more accurate than the FC approximation. The accuracy of the target wave functions is tested by comparing the calculated energy levels with the experimental data. Based on positron-hydrogen scattering, comprehensive close-coupling formulas for positron-helium scattering are developed. The reduced two-centre V-matrix elements are derived in momentum space for various channels. These include direct, excitation and rearrangement channels, i.e. positronium formation. We first consider low energy positron-helium elastic scattering for energies below the positronium formation threshold of 17.8 eV. Utilizing a single-centre expansion the elastic cross section and phase shifts have been calculated as a function of the positron incident energy. The calculations agree very well with the experimental data and the variational calculations, but not previous single- or double-centre close-coupling calculations. We then consider energies above the first ionization threshold (24.6 eV) and calculate helium elastic, excitation, fragmentation and total cross sections within the single-centre expansion approach. Good agreement with the available experimental and other theoretical results has been obtained. The studies have proved that a single-centre expansion, with accurate target state description, can deliver accurate data of practical value over a broad range of energies. However in the low-energy region, between the positronium formation threshold of 17.8 eV and the ionization threshold of 24.6 eV, implementation of the two-centre expansion is required. We expect this work to be undertaken in the near future, based on the derivations presented in this thesis.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 2004. / Vita. Abstract. Includes bibliographical references (p. 234-243).

Thesis (M.S.)--University of Michigan, 1966.