Interactions of B = 4 Skyrmions

TL;DR

This paper extends Yukawa multipole theory to describe long-range interactions of Skyrmions with higher baryon numbers, focusing on the B=4 solution that models alpha particles, using numerical methods to quantify multipole interactions.

Contribution

It demonstrates the applicability of Yukawa multipole theory to higher baryon number Skyrmions and provides a numerical analysis of their multipole interactions.

Findings

Yukawa multipole theory applies to B=4 Skyrmion interactions.

Numerical values for quadrupole and octupole interaction strengths are obtained.

Results inform understanding of B=8, B=12 solutions and Skyrme crystal interactions.

Abstract

It is known that the interactions of single Skyrmions are asymptotically described by a Yukawa dipole potential. Less is known about the interactions of solutions of the Skyrme model with higher baryon number. In this paper, it is shown that Yukawa multipole theory can be more generally applied to Skyrmion interactions, and in particular to the long-range dominant interactions of the B = 4 solution of the Skyrme model, which models the alpha-particle. A method that gives the quadrupole nature of the interaction a more intuitive meaning in the pion field colour picture is demonstrated. Numerical methods are employed to find the precise strength of quadrupole and octupole interactions. The results are applied to the B = 8 and B = 12 solutions and to the Skyrme crystal.