The interaction energy of well-separated Skyrme solitons

TL;DR

This paper proves that Skyrme solitons have a well-defined multipole expansion, derives their interaction energy at large separation, and shows conditions under which they attract each other.

Contribution

It introduces a formalism for the multipole expansion of Skyrme solitons and derives an explicit expression for their interaction energy based on these multipoles.

Findings

Skyrme solitons have a non-trivial multipole expansion.

The interaction energy can be made negative, indicating attraction.

Attractive forces dominate when multipole orders differ by at most two.

Abstract

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of one of the Skyrme solitons in space and iso-space.We show that the linear interaction energy dominates for large separation if the orders of the Skyrme solitons' multipole moments differ by at most two. In that case there are therefore always attractive forces between the Skyrme solitons.