Lightly Bound Skyrmions, Tetrahedra and Magic Numbers

TL;DR

This paper explores how certain Skyrmions in the lightly bound Skyrme model form tetrahedral clusters with baryon numbers matching nuclear magic numbers, linking geometric arrangements to nuclear shell model predictions.

Contribution

It identifies a sequence of strongly bound Skyrmion clusters with baryon numbers corresponding to tetrahedral numbers times four, connecting geometric Skyrmion configurations to nuclear magic numbers.

Findings

Skyrmion clusters form tetrahedral arrangements with specific baryon numbers.

The baryon number sequence matches magic numbers in nuclear physics.

Connections to FCC lattice geometry and nuclear shell model are established.

Abstract

In the lightly bound Skyrme model, several Skyrmions having particularly strong binding are clusters of unit baryon number Skyrmions arranged as truncated tetrahedra. Their baryon numbers form the sequence B = 4, 16, 40, 80, 140, 224. This is the standard sequence of tetrahedral numbers multiplied by four, and therefore agrees with the sequence of magic proton and neutron numbers 2, 8, 20, 40, 70, 112 that occurs in the nuclear shell model in the absence of strong spin-orbit coupling. This sequence includes several of the magic numbers that are predicted for tetrahedrally deformed nuclei, and also appears in the context of the FCC lattice geometry investigated long ago by Wigner and revived more recently.