Date of Award

1981

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Abstract

Statistical nuclear spectroscopy or spectral distribution methods have been developed by French and coworkers as an alternative, applicable in huge model spaces, to the conventional shell model approach for studying nuclear structure. The theory is based on the operation of a central limit theorem in large model spaces which yields a shape close to Gaussian for the smoothed eigenstate density distribution. The theory emphasizes the importance of traces of bilinear products of operators acting in a model space. Utilizing this and partitioning the model space according to group symmetries leads to an algorithm for expanding any interaction in terms of simpler operators. Detailed shell model comparison of excitation spectra, eigenstate overlaps and B(E2) transition strengths in ('20)Ne and ('22)Ne with a realistic interaction and its SU(3) trace-equivalent approximations are presented. SU(3) symmetry breaking by single-particle shell effects is also studied. Spectral distribution methods are used to develop a statistical procedure for calculating alpha particle transfer strengths that is valid in large model spaces. The theory gives the strength function as a bilinear expansion in orthogonal polynomials defined by moments of the interaction in the initial and final state model spaces. Rapid convergence is assured by the operation of the central limit theorem. The method involves partitioning the fixed J,T initial (target nucleus) and final (residual nucleus) state model spaces according to the supermultiplet symmetry. Moments of a statistical approximation to the Brown-Kuo interaction are used to estimate the eigenenergies and configuration intensities for the initial and final state subspaces. Specific predictions for the reactions ('18)O + (alpha) (DBLARR) ('22)Ne and ('20)Ne + (alpha) (DBLARR) ('24)Mg are made. The results are compared with experimental values and with predictions of other nuclear models. A unique feature of the study, unlike what has been found for E2, M1, E4 strengths, is that the density weighted strength is not dominated by the density of states factor.

Pages

181

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