# Two-neutron transfer reactions and quantum-chaos measure of nuclear spectra

## TL;DR

This paper introduces a statistical approach to analyze nuclear spectra using two-neutron transfer reactions, revealing intermediate chaos-order behavior and potential symmetry breaking in nuclear collective states.

## Contribution

It presents a novel application of NNSDs to nuclear spectra, combining experimental data with Wigner-Dyson theory to distinguish chaos and order contributions.

## Key findings

- NNSDs show intermediate behavior between chaos and order.
- Spectral shifts from chaos to order with increased spectrum length and angular momentum.
- Method enables analysis of symmetry breaking in nuclear states.

## Abstract

A new statistical interpretation of the nuclear collective states is suggested and applied recently in rare earths and actinide nuclei by the two-neutron transfer reactions in terms of the nearest neighbor-spacing distributions (NNSDs). Experimental NNSDs were obtained by using the complete and pure sequences of the collective states through an unfolding procedure. The two-neutron transfer reactions allow to obtain such a sequence of the collective states that meets the requirements for a statistical analysis. Their theoretical analysis is based on the linear approximation of a repulsion level density within the Wigner-Dyson theory. This approximation is successful to evaluate separately the Wigner chaos and Poisson order contributions. We found an intermediate behavior of NNSDs between the Wigner and Poisson limits. NNSDs turn out to be shifted from a chaos to order with increasing the length of spectra and the angular momentum of collective states. Perspectives for the statistical analysis of the symmetry breaking of states with the fixed projection of angular momenta $K$ are discussed.