# Quantum phase transitions and collective enhancement of level density in odd-A and odd-odd nuclei

## TL;DR

This study investigates how specific interaction matrix elements influence nuclear collectivity and level density in odd-A and odd-odd nuclei, revealing a phase transition marked by increased level density and the dominance of single-particle transfer elements.

## Contribution

It demonstrates the role of particular matrix elements in inducing phase transitions and level density enhancement in odd-A and odd-odd nuclei within the shell model framework.

## Key findings

- Transition from normal to collective phase observed
- Level density enhancement occurs at the transition point
- Single-particle transfer matrix elements are key to the collective phase

## Abstract

The nuclear shell model assumes an effective mean-field plus interaction Hamiltonian in a specific configuration space. We want to understand how various interaction matrix elements affect the observables, the collectivity in nuclei and the nuclear level density for odd-A and odd-odd nuclei. Using the sd and pf shells, we vary specific groups of matrix elements and study the evolution of energy levels, transition rates and the level density. In all cases studied, a transition between a "normal" and a collective phase is induced, accompanied by an enhancement of the level density in the collective phase. In distinction to neighboring even-even nuclei, the enhancement of the level density is observed already at the transition point. The collective phase is reached when the single-particle transfer matrix elements are dominant in the shell model Hamiltonian, providing a sign of their fundamental role.