Chaoticity and Shell Effects in the Nearest-Neighbor Distributions

TL;DR

This paper analyzes how shell effects and surface deformations influence the statistical distribution of single-particle energy levels, revealing significant deviations from classical distributions depending on deformation and angular momentum.

Contribution

It provides a detailed comparison of Poisson and Wigner distributions in deformed potentials, highlighting the impact of shell effects and surface multipolarities on level statistics.

Findings

Distributions differ significantly at fixed angular momentum projection, resembling Wigner distribution.

Shell effects are prominent in nearest neighbor spacing, especially at smaller deformations.

Deformation influences the transition between Poisson-like and Wigner-like behaviors.

Abstract

Statistics of the single-particle levels in a deformed Woods-Saxon potential is analyzed in terms of the Poisson and Wigner nearest-neighbor distributions for several deformations and multipolarities of its surface distortions. We found the significant differences of all the distributions with a fixed value of the angular momentum projection of the particle, more closely to the Wigner distribution, in contrast to the full spectra with Poisson-like behavior. Important shell effects are observed in the nearest neighbor spacing distributions, the larger the smaller deformations of the surface multipolarities.