Thesis (PhD (Physics))-University of Stellenbosch, 2009. / ENGLISH ABSTRACT: A binary cluster model is used to investigate the properties of the ground state band of 212Po, modelled as a 208Pb-alpha core-cluster system. The results obtained using a microscopic corecluster potential are compared to those obtained with a purely phenomenological potential. The two potentials were found to exhibit similar surface behaviour and thus give similar predictions for the ground state alpha decay half-life. They however generate very different energy spectra, with the results from the phenomenological potential clearly superior. We optimize the phenomenological potential parameters, and propose an additional short range interaction to improve the underbinding generally found for the J¼ = 0+ ground state. We then investigate two possible scenarios for generating the negative parity states in 212Po. We find that both are necessary in order to produce low-lying negative parity states which are able to decay via electric dipole transitions to the positive parity states of the ground state band. Finally we present a novel calculation of the properties of the low-lying positive and negative parity states of 218Rn described as a doubly closed 208Pb core plus a 10Be cluster. / AFRIKAANSE OPSOMMING: ’n Binêre bondel model word gebruik om die eienskappe van die grondtoestands energie band van 212Po, te modeleer as ’n 208Pb-alpha kern-bondel sisteem te ondersoek. Die resultate verkry vanaf ’n mikroskopiese kern-bondel potentiaal word vergelyk met die wat verkry is met ’n suiwer fenomenologiese potentiaal. Die twee potentiale is verkry om dieselfde oppervlakte toestande voor te stel en gee sodoende dieselfde voorspellings vir die grondtoestand alpha verval halfleeftyd. Alhoewel dit baie verskillende energie spektra genereer, toon die resultate van die fenomenologiese potentiaal dat dit duidelik beter is. Ons optimiseer hierdie fenomenologiese parameters en stel ’n addisionele kort ry-afstands interaksie voor om die algemene ondergebondenheid wat oor die algemeen by die J¼ = 0+ grondtoestand voorkom, te verbeter. Ons ondersoek ook hierdie twee moontlike scenarios om die negatiewe pariteitstoestande in 212Po te genereer. Ons vind dat beide scenarios noodsaaklik is om laagliggende pariteitstoestande te produseer, sodat verval deur elektriese dipool oorgange na die positiewe pariteitstoestande van die grondtoestandsband moontlik is. Laagliggende positiewe en negatiewe pariteitstoestande, van die 218Rn wat beskryf word as ’n dubbelgeslote 208Pb kern en ’n 10Be bondel.

This dissertation documents the results of two related efforts. Firstly, a model of nucleon-nucleon (NN) interactions is developed based on scalar field theory. Secondly, the relativistic 2-body Bethe-Salpeter equation (BSE) is generalized to handle inelastic processes in the ladder approximation. Scalar field theory describes the behavior of scalar particles, particles with spin 0. In the present work scalar field theory is used to describe NN interactions mediated by pion exchange. The scalar theory is applied to nucleons despite the fact that nucleons are fermions, spin 1/2 particles best described by fourcomponent Dirac spinor fields. Nevertheless, the scalar theory is shown to give a good fit to experiment for the total cross sections for several reactions [1]. The results are consistent with more elaborate spinor models involving one boson exchange (OBE). The results indicate that the spin and isospin of nucleons can to some extent be ignored under certain conditions. Being able to ignore spin and isospin greatly reduces the complexity of the model. A limitation of the scalar theory is that it does not distinguish between particle and anti-particle. Consequently one must decide how to interpret the s-channel diagrams generated by the theory, diagrams which involve particle creation and annihilation. The issue is resolved by extending the scalar theory to include electric charge, and formulating NN interactions in terms of complex scalar fields, which are able to describe both particles and anti-particles. A generalized Bethe-Salpeter equation (GBSE) is developed to handle inelastic processes in the ladder approximation. The GBSE, formulated using the scalar theory, is new, and introduces a systematic method for analyzing families of coupled reactions. A formalism is developed centered around the amplitude matrix M' defined for a given Lagrangian. M' gives the amplitudes of a family of reactions that arise from the Lagrangian. The formalism demonstrates how these amplitudes, to 2nd order, segregate into independent groups of coupled BSE's. The GBSE formalism is applied to the coupled BSE (CBSE) of Faassen and Tjon (FT) [2] for the reaction N+N->N+Delta, showing that the CBSE is missing a coupling channel, and in the expansion, under counts ladder diagrams. A proof is given of the equivalence of the series of ladder diagrams generated by M' and the S-matrix. A section on future work discusses several projects for further development and application of the GBSE.

Space radiation and its effects on human life and sensitive equipment are of concern to a safe exploration of space. Radiation fields are modified in quality and quantity by intervening shielding materials. The modification of space radiation by shielding materials is modeled by deterministic transport codes using the Boltzmann transport equation. Databases of cross sections for particle production are needed as input for transport codes. A simple model of nucleon-nucleon interactions is developed and used to derive differential and total cross sections. The validity of the model is verified for proton-proton elastic scattering and applied to delta-resonance production. Additionally, a comprehensive validation program of the nucleus-nucleus fragmentation cross section models NUCFRG2 and QMSFRG is performed. A database of over 300 experiments was assembled and used to compare to model fragmentation cross sections.