Statistical analysis of excitation energies in the actinide and rare-earth nuclei

TL;DR

This paper analyzes the statistical properties of excitation energies in actinide and rare-earth nuclei, revealing a transition from order to chaos in their spectral distributions across different energy ranges.

Contribution

It applies various approximations to NNSD analysis, demonstrating the intermediate spectral character and energy-dependent transition between order and chaos in nuclear spectra.

Findings

Spectra show intermediate order-chaos behavior.

Wigner distribution dominates at low energies.

Poisson distribution becomes prominent at higher energies.

Abstract

Statistical analysis of distributions of the collective states in the actinide and rare-earth nuclei is performed in terms of the nearest neighbor spacing distribution (NNSD). Several approximations, such as the linear approach to the level repulsion density and that suggested by Brody to the NNSDs were applied for the analysis. We found an intermediate character of the experimental spectra between the order and the chaos for a number of the rare-earth and actinide nuclei. They are more close to the Wigner distribution for energies limited by 3 MeV, and to the Poisson distribution for data including higher excitation energies and higher spins. The latter is in agreement with the theoretical calculations. These features are confirmed by the cumulative distributions, where the Wigner contribution dominates at smaller spacings while the Poisson one is more important at larger spacings.