Statistical theory of deformation distributions in nuclear spectra

TL;DR

This paper develops a method to compute the distribution of intrinsic quadrupole deformations in nuclei using AFMC, enabling better understanding of nuclear shape effects on level densities, especially in samarium isotopes.

Contribution

It introduces a novel approach to calculate deformation distributions within AFMC, extending the theory beyond mean-field approximations and including higher-order polynomial expansions.

Findings

The method accurately describes deformation distributions across different samarium isotopes.

A fourth-order Landau-like expansion suffices for precise modeling of deformation distributions.

Results reveal the variation of nuclear shapes from spherical to deformed in the studied isotopes.

Abstract

The dependence of the nuclear level density on intrinsic deformation is an important input to dynamical nuclear processes such as fission. Auxiliary-field Monte Carlo (AFMC) method is a powerful method for computing nuclear level densities. However, the statistical distribution of intrinsic shapes is not readily accessible due to the formulation of AFMC in a spherical configuration-interaction shell-model approach. Instead, theory of deformation up to now has largely relied on a mean-field approximation which breaks rotational symmetry. We show here how the distributions of the intrinsic quadrupole deformation parameters can be calculated within the AFMC method, and present results for a chain of even-mass samarium nuclei ($^{148}$Sm, $^{150}$Sm, $^{152}$Sm, $^{154}$Sm) which includes spherical, transitional, and strongly deformed isotopes. The method relies on a Landau-like expansion of the Helmholtz free energy in invariant polynomials of the quadrupole tensor. We find that an expansion to fourth order provides an excellent description of the AFMC results.