One Plus Two-Body Random Matrix Ensembles with Parity: EGOE(1+2)-π

Abstract

Parity ratios of nuclear level densities, i.e. ratio of number of negative parity states to positive parity states in a atomic nucleus, is an important ingredient in nuclear astrophysical applications. In order to understand the general structure of parity ratios, one plus two-body embedded random matrix ensemble generated by parity (π) preserving random interactions is defined and a method for its construction is given. In this ensemble, called EGOE(1+2)-π, the single particle space is divided into positive and negative parity spaces with a spacing between them and the random two-body interaction has two parameters. Presented for this ensemble are binary correlation results for the lower order moments of fixed parity state densities and numerical results for the parity ratios for interaction parameters varying in a meaningful domain. Consistent with a Fermi gas model, it is found that the parity ratios will be zero up to an energy E 0 and then they start increasing and become larger than unity at an energy E′. From here on, parity ratios decrease and saturate quickly to unity.