How atomic nuclei cluster

TL;DR

This paper investigates the origin of clustering in nuclei, revealing that the depth of the nuclear potential influences nucleonic density clustering, with relativistic functionals predicting more pronounced cluster structures.

Contribution

It demonstrates that the depth of the confining nuclear potential determines clustering, using energy density functionals to connect potential depth with nucleonic localization and cluster formation.

Findings

Relativistic functionals predict more pronounced clustering.

Deep nuclear potentials lead to increased nucleonic localization.

Clustering is a transitional phase between crystalline and quantum liquid states.

Abstract

Nucleonic matter displays a quantum liquid structure, but in some cases finite nuclei behave like molecules composed of clusters of protons and neutrons. Clustering is a recurrent feature in light nuclei, from beryllium to nickel. For instance, in $^{12}$C the Hoyle state, crucial for stellar nucleosynthesis, can be described as a nuclear molecule consisting of three alpha-particles. The mechanism of cluster formation, however, has not yet been fully understood. We show that the origin of clustering can be traced back to the depth of the confining nuclear potential. By employing the theoretical framework of energy density functionals that encompasses both cluster and quantum liquid-drop aspects of nuclei, it is shown that the depth of the potential determines the energy spacings between single-nucleon orbitals, the localization of the corresponding wave functions and, therefore, the degree of nucleonic density clustering. Relativistic functionals, in particular, are characterized by deep single-nucleon potentials. When compared to non-relativistic functionals that yield similar ground-state properties (binding energy, deformation, radii), they predict the occurrence of much more pronounced cluster structures. More generally, clustering is considered as a transitional phenomenon between crystalline and quantum liquid phases of fermionic systems.