Skyrmions up to Baryon Number 108

TL;DR

This paper constructs new Skyrmion solutions with baryon numbers up to 108, using a multi-layer rational map ansatz and numerical relaxation, revealing structures similar to the Skyrme crystal.

Contribution

It introduces a novel method combining geometric rational maps and numerical relaxation to find high-baryon-number Skyrmions.

Findings

Skyrmions up to baryon number 108 constructed

Solutions resemble chunks of the Skyrme crystal

New configurations obtained via multi-layer rational map ansatz

Abstract

The Skyrme crystal is built up of repeating units similar to the cubic Skyrmion of baryon number 4. Using this as guide, we construct new Skyrmion solutions in the massive pion case, with various baryon numbers up to 108. Most of our solutions resemble chunks of the Skyrme crystal. They are constructed using a multi-layer version of the rational map ansatz to create initial configurations, which are then relaxed numerically to find the energy minima. The coefficients of the rational maps are found by a geometrical construction related to the Skyrme crystal structure. We find some further solutions by numerical relaxation of clusters composed of baryon number 4 Skyrmions.