ar X iv : n uc l - th / 9 91 10 36 v 1 9 N ov 1 99 9 Parity Dependence of Nuclear Level Densities

A simple formula for the ratio of the number of oddand even-parity states as a function of temperature is derived. This formula is used to calculate the ratio of level densities of opposite parities as a function of excitation energy. We test the formula with quantum Monte Carlo shell model calculations in the (pf+g9/2)-shell. The formula describes well the transition from low excitation energies where a single parity dominates to high excitations where the two densities are equal. Typeset using REVTEX 1 Parity is a fundamental property of nuclear levels, and its statistical distribution is important for describing parity-violating processes and neutron-capture reactions. Most theoretical models for level densities are based on the Fermi gas model [1]. Shell corrections and correlations due to residual interactions are included empirically. An empirical modification of the Fermi gas formula – the backshifted Bethe formula (BBF) – was successful in fitting many experimental level densities by adjusting both the single-particle level density parameter and the backshift parameter [2]. Only limited data are available for the parity dependence of level densities since the neutron p-wave resonances are much weaker than the s-wave resonances at low energies and more difficult to measure. Ericson [3] argued that the excitation of a relatively small number of single-particle levels with opposite parity can lead to an equal number of evenand odd-parity many-particle densities. The assumption of equal densities of opposite parities in the neutron resonance region is commonly accepted [4] and used in the calculations of neutron-capture rates for s and r processes in nucleosynthesis [6]. Yet various theoretical studies [7] as well as analysis of experimental data [8] indicate that level densities can have a significant parity dependence. Parity properties can in principle be calculated within the interacting shell model, the basic theory of nuclear structure. However the calculation of level densities in the shell model requires large model spaces that are often beyond the reach of conventional diagonalization methods. Such methods are presently limited to A < ∼ 50 [9,10] (in the pf -shell). Recently, quantum Monte Carlo methods [11,12] were used to calculate total and parity-projected level densities [13] in the framework of the interacting shell model. The methods were applied to nuclei in the iron-to-germanium region using the complete (pf + g9/2)-shell model space. The total level densities were found to be in good agreement with the experimental level densities, and significant parity dependence was found for A < ∼ 65. The Monte Carlo calculations of the parity-projected level densities accurately take into account shell effects and correlations due to the residual two-body interactions, but they are computationally intensive. In this paper we derive a simple formula for calculating the ratio of the number of oddand even-parity states as a function of temperature. The formula 2 is applied to nuclei in the iron region and compared with the Monte Carlo calculations. It reproduces well the crossover from low temperatures, where one parity dominates, to higher temperatures, where both densities become equal. Using the BBF for the total level density, the results of the model can be converted to a ratio of parity-projected level densities at fixed excitation energies. The Monte Carlo approach is based on the Hubbard-Stratonovich representation of the many-body imaginary-time propagator, e = ∫ D[σ]G(σ)Uσ, where G(σ) is a Gaussian weight and Uσ is a one-body propagator that describes non-interacting nucleons moving in fluctuating time-dependent fields σ(τ). The canonical thermal expectation value of an observable O can be written as 〈O〉A = ∫