Random close packing of binary hard spheres favors the stability of neutron-rich atomic nuclei

TL;DR

This paper introduces a geometric model based on random close packing of binary spheres to explain the stability of neutron-rich nuclei, suggesting a new factor influencing nuclear structure beyond electrostatics.

Contribution

It provides a novel geometric perspective using sphere packing theory to account for the stability of neutron-rich nuclei, complementing existing nuclear models.

Findings

Most stable nuclei have a Z/N ratio of approximately 0.75.

The model predicts a geometric contribution to nuclear stability.

Neutron size is assumed to be 20% larger than proton size.

Abstract

In spite of the success of the Bethe-Weizs\"acker mass formula in its modern numerical and predictive implementations, the common-knowledge principle that it is electrostatics which, ultimately, favors neutron-rich nuclei still presents unclear aspects. For example, while it is true that the Coulomb interaction promotes the tendency towards neutron-rich nuclei, the opposite effects of Majorana exchange forces and Pauli exclusion are known to counteract this tendency. We show that a recent analytical progress in the mathematical description of random close packing of spheres with different sizes provides a missing contribution to the theoretical description of the $Z$ versus $N$ slope in the nuclides chart. In particular, the theory suggests, on geometric grounds and with a physically-reasoned assumption that the excluded-volume size of neutrons is 20\% larger than that of protons, that the most stable nuclei are those with ratio $Z/N\approx 0.75$. This new ``geometric'' random-packing contribution to the semi-empirical mass formula may be the missing aspect of nuclear structure that tilts the balance towards neutron-rich nuclei in the Segr\`e stability chart.