Classical Skyrmions -- Static Solutions and Dynamics

TL;DR

This paper explores classical Skyrmions as models for nuclei, proposing new methods to find solutions, analyzing their dynamics, and connecting them to nuclear phenomena like spin, collisions, and resonances.

Contribution

It introduces a novel approach to discovering Skyrmions of arbitrary baryon number as crystal fragments and models nuclear states with classically spinning Skyrmions, extending beyond rigid motions.

Findings

Skyrmions can be constructed as crystal fragments with various baryon numbers.

Classically spinning Skyrmions approximate quantized nuclear states like protons and neutrons.

Spatially modulated motions may describe nuclear vibrations and giant resonances.

Abstract

Skyrmions with a realistic value of the pion mass parameter are expected to be quite compact structures, but beyond baryon number B=8 only a few examples are known. The largest of these is the cubically symmetric B=32 Skyrmion which is a truncated piece of the Skyrme crystal. Here it is proposed that many more such Skyrmions could be found, without any restriction on the baryon number, as pieces of the Skyrme crystal. Particular attention is given to the possibility of reducing B by 1 by chopping a corner off a cubic crystal chunk. Nuclei are modelled by Skyrmions with quantised spin and isospin. Here it is argued that these quantised states can be approximated by classically spinning Skyrmions. The orientations of the spinning Skyrmions corresponding to polarised protons, neutrons and deuterons are identified. Nuclear collisions and the nuclear spin-orbit force are discussed in terms of classically spinning Skyrmions. Going beyond the rigid collective motions of Skyrmions, there are spatially modulated collective motions, which are oscillatory in time. They are argued to describe not just vibrational excitations of nuclei, but also giant resonance states. A speculative proposal for identifying quarks inside Skyrmions is briefly discussed.