On angular momentum and parity dependence of nuclear level densities in a simple random sampling approach

Abstract

Abstract Based on simple random sampling (SRS), we propose a Monte Carlo method for faster computation of the smoothed part of the density of nuclear states. To test the applicability of the SRS approach we study in this framework the excitation energy ( E ), angular momentum ( J ) and parity dependence of nuclear level densities for an independent particle system. As an illustrative example, we consider a pf -shell nucleus, 48 Cr. It is found that the values of a few lower order moments for the state density I ( E ) calculated using SRS and combinatorial (or direct counting) methods are almost the same and a locally smoothed part of the state density can be constructed using these moments in a univariate Edgeworth expansion. We calculate the energy dependent spin-cutoff factor and parity asymmetry and find that for both cases the SRS approach works quite well. We use the SRS moments to construct different forms of the bivariate distribution for I ( E , M ) ( M is the z -component of J ) namely (a) a bivariate Edgeworth expansion, (b) a product of the univariate Edgeworth expansion ( I ( E )) and a Gaussian form for conditional M distribution I( M E ) and (c) a product of the univariate Edgeworth expansions for both I ( E ) and I( M E ) and compare the resulting fixed- J level density I l ( E , J ) with the corresponding combinatorial results.