Single-particle spatial dispersion and clusters in nuclei

TL;DR

This paper investigates how single-nucleon wave functions localize or delocalize in nuclei, showing that light nuclei with certain states can form clusters, while heavier nuclei tend to exhibit a quantum liquid phase.

Contribution

It provides an analytic expression for the localization parameter considering the radial quantum number and analyzes nucleon localization across different nuclei.

Findings

Localization depends mainly on the radial quantum number n.

Light nuclei with n=1 states can form cluster structures.

Heavier nuclei tend to be delocalized, exhibiting a quantum liquid phase.

Abstract

The spatial dispersion of the single-nucleon wave functions is analyzed using the self-consistent mean-field framework based on nuclear energy density functionals, and with the harmonic oscillator approximation for the nuclear potential. It is shown that the dispersion depends on the radial quantum number n, but displays only a very weak dependence on the orbital angular momentum. An analytic expression is derived for the localization parameter that explicitly takes into account the radial quantum number of occupied single-nucleon states. The conditions for single-nucleon localization and formation of cluster structures are fulfilled in relatively light nuclei with $A \leq 30$ and $n=1$ states occupied. Heavier nuclei exhibit the quantum liquid phase of nucleonic matter because occupied levels that originate from $n > 1$ spherical states are largely delocalized. Nevertheless, individual $\alpha$-like clusters can be formed from valence nucleons filling single-particle levels originating from $n=1$ spherical mean-field states.