Statistical Nuclear Spectroscopy: New Methods and Applications; Level Densities and Related Functions for Interacting-Particle Nuclei

摘要

This thesis develops a new theory of state densities for interacting particle (IP) systems of nucleons. This is a general theory, based on central limit theorems and unitary group decomposition of the microscopic Hamiltonian. The density appears in terms of convolutions of noninteracting particle (NIP) densities with easily calculable interaction functions given explicitly in terms of Hamiltonian matrix elements. This allows for easy incorporation of interaction information and yields simple expressions that are much more compact than any previous spectral averaging theory of state densities. The convolution form for the state density is shown to extend to the expectation of one-body and two-body operators, this having immediate application to the calculation of occupancies and spin cut-off factors. A compact method of calculating the state density is developed and, for NIP, is compared to the exact procedure with excellent results this allowing extension of statistical spectroscopy to indefinitely large spaces. By using the new NIP plus convolution results ab initio calculations of fixed-J level densities in the resonance region have been done with very high accuracy for 37 nuclei. The associated interaction strengths for sample nuclei are given. Tables of state density parameters (for a two parameter form) calculated by fitting to statistical spectroscopic results as well as the parameters for reproducing the energy dependence of the spin-cut-off factor are given. The spin cut-off factors are shown to exhibit excellent agreement with results obtained from empirical fitting to experimental data by other authors. 44 refs., 13 figs., 16 tabs. (ERA citation 12:044560)