Classical Skyrmions—static solutions and dynamics

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.

Classically isospinning Skyrmion solutions

“…15. For this D 4 -symmetric configuration, we verify numerically that the spin L ¼ −W 22 ω vanishes for all classically allowed isospin values K. Therefore, this configuration may become important for calculating excited states of the Deuteron with nonzero isospin [44].…”

“…It was argued in Ref. [44] that these two spatial orientations are the relevant ones for describing the rotational states of the deuteron.…”

A Skyrme model approach to the spin-orbit force

“…In this paper we develop an idea in [7] which provides an explanation for the spin-orbit force at shorter separations, inspired by the Skyrme model. We introduce the Skyrme model in section 2, describing the important features which shape the spin-orbit interaction.…”

Broken baby Skyrmions

“…The preprint (Manton 2011) contains several ideas related to those appearing in this paper. In particular, there is a similar proposal to identify quarks inside Skyrmions, and a suggestion that many new Skyrmions might be found as pieces of the Skyrme crystal; in the same way that the polyiamond solitons may be viewed as pieces of the soliton lattice.…”