Applications of group theory to few-body physics

Abstract

Over the past fifteen years, there have been persistent claims of anomalous nuclear reactions in condensed matter environments. A Unified Model [38] has been proposed to systematically account for most of these anomalies. However, all the work done so far has used simple scalar nuclear Hamiltonians. In this thesis, we develop the tools necessary to use a realistic nuclear Hamiltonian in the Unified Model. A natural way to include a realistic nuclear potential in the Unified Model is via the method of coupled-channel equations. The phenomenological nuclear interaction chosen is the Hamada-Johnston potential [40]. The major portion of the thesis is devoted to deriving the coupled-channel equations with explicit symmetry constraints for the Hamada-Johnston potential. A critical input in this derivation is the calculation of the matrix elements of the various channels. We develop a systematic method, based on group theory, for calculating matrix elements of few-body correlated spatial wavefunctions. This method can, in some sense, be considered a generalization of Racah's viewpoint [17] of calculating shell-model matrix elements. Towards the end, two related, but somewhat different topics are explored. Firstly, a simple phonon-coupled nuclear reaction, the photodisintegration of the deuteron, is investigated. While no observable results are computed, this work should be considered a first step in calculating the effects of the lattice on nuclear reactions. Secondly, Lie algebra theory is used to understand the coherent decay, from the highest symmetry state in N-level systems, in terms of the usual Dicke [21] algebra.