Global analysis of the non-uniformity of nucleon density distributions

TL;DR

This study systematically analyzes nucleon density distributions across a wide range of nuclei, revealing mechanisms behind non-uniformities like bubble structures and their dependence on nuclear properties and forces.

Contribution

It introduces a generalized bubble parameter and uncovers the emergence of bubble structures related to shell effects, deformation, pairing, and Coulomb forces across nuclear mass regions.

Findings

Bubble structures appear near magic numbers and are influenced by shell effects.

Coulomb force enhances bubble features in superheavy nuclei.

Multi-layered bubble structures with internal density depressions are identified.

Abstract

Background: Saturation of nuclear density is a fundamental property of atomic nuclei but in reality, the nuclear internal density distribution is not uniform, e.g., some nuclei are known to have the so-called bubble structure, in which the central density is depressed. Purpose: We aim to unveil the emergent mechanism of the non-uniformity of the nucleon density distributions for whole nuclear mass regions, not only for a typical bubble structure. Method: We systematically investigate the nucleon density distributions using the Skyrme Hartree-Fock plus Bardeen-Cooper-Schrieffer calculation represented in the three-dimensional Cartesian coordinate space. The ground states of 1,389 even-even nuclei are generated. To quantify the nonuniformity of these density distributions, a ``generalized bubble parameter" is introduced. Results: We find that the bubble structure appears around the magic numbers, which correspond to the regions where the s orbit appears near the Fermi surface. The nuclear deformation and pairing correlations strongly affect the occupation probability, but the robust bubble structure of a medium mass nucleus, $^{100}$Sn, is found. We confirm that the Coulomb force enhances the bubble degree in the superheavy region. The nuclear non-uniformity is further generalized by the ``multi-layered" bubble structure, which exhibits some density depression in the internal regions of the density distributions. Conclusion: The non-uniformity of the internal density distribution occurs due to the deficiency of the specific single-particle orbits: the nodal $s$, $p$, and $d$ orbits. This is certainly reflected in the density distribution near the nuclear surface, which can be deduced from proton-elastic scattering.