Alpha-particle condensation: a nuclear quantum phase transition

TL;DR

This paper investigates the quantum phase transition from homogeneous to alpha-clustered states in nuclei, using microscopic energy density functional calculations to predict a Mott-like transition at about one-third of saturation density.

Contribution

It provides a detailed microscopic analysis of alpha-particle condensation as a nuclear quantum phase transition, including the evolution of single-particle spectra and symmetry breaking.

Findings

Mott-like transition predicted at ~1/3 saturation density

Spatial localization properties confirm the Mott density

Symmetry breaking from rotational to tetrahedral group observed

Abstract

When the density of a nuclear system is decreased, homogeneous states undergo the so-called Mott transition towards clusterised states, e.g. alpha clustering, both in nuclei and in nuclear matter. Here we investigate such a quantum phase transition (QPT) by using microscopic energy density functional (EDF) calculations both with the relativistic and the Gogny approaches on the diluted $^{16}$O nucleus. The evolution of the corresponding single-particle spectrum under dilution is studied, and a Mott-like transition is predicted at about 1/3 of the saturation density. Complementary approaches are used in order to understand this QPT. A study of spatial localisation properties as a function of the density allows to derive a value of the Mott density in agreement with the one obtained by fully microscopic calculations in $^{16}$O and in nuclear matter. Moreover a study of the spontaneous symmetry breaking of the rotational group in $^{16}$O, down to the discrete tetrahedral one, provides further insight on the features displayed by the single-particle spectrum obtained within the EDF approach.The content of the tetrahedrally deformed A-nucleon product state in terms of spherical particle-hole configurations is investigated. Finally a study of quartet condensation and the corresponding macroscopic QPT is undertaken in infinite matter.