Nucleon thermalization hindered by isospin symmetry: Violation of eigenstate thermalization hypothesis in atomic nuclei

TL;DR

This paper investigates the validity of the assumption that nucleons in atomic nuclei reach thermal equilibrium, revealing that isospin symmetry can hinder thermalization and cause violations of the eigenstate thermalization hypothesis.

Contribution

It demonstrates that isospin symmetry can prevent nucleon thermalization and shows how breaking this symmetry restores thermalization within the shell model framework.

Findings

Long-time averages deviate from microcanonical ensemble in certain cases.

Isospin symmetry causes violation of the eigenstate thermalization hypothesis.

Breaking isospin symmetry restores nucleon thermalization.

Abstract

Bohr's compound nucleus theory is one of the most important models in nuclear physics, with far-reaching applications in nuclear science and technology. This model generally assumes that the participating nucleons attain a thermal equilibrium characterized by the microcanonical ensemble before subsequent decays. However, from a theoretical viewpoint, it remains uncertain whether this assumption is universally valid. In this Letter, we critically examine this longstanding assumption through the lens of the eigenstate thermalization hypothesis (ETH), a cornerstone of the modern quantum thermalization theory. Utilizing the time-dependent configuration interaction shell model, it is found that, in certain cases, the long-time averages of nucleon occupation numbers can exhibit significant deviations from the microcanonical ensemble averages, in contrast to the conventional expectation. We attribute this discrepancy primarily to the violation of the ETH in the presence of isospin symmetry and discover that incorporating a substantial isospin-breaking term into the shell-model Hamiltonian can effectively restore the nucleon thermalization.