Aloof baby Skyrmions

Abstract

We show that a suitable choice for the potential term in the two-dimensional baby Skyrme model yields solitons that have a short-range repulsion and a long-range attraction. The solitons are therefore aloof, in the sense that static multi-soliton bound states have constituents that preserve their individual identities and are sufficiently far apart that tail interactions yield small binding energies. The static multi-soliton solutions are found to have a cluster structure that is reproduced by a simple binary species particle model. In the standard three-dimensional Skyrme model of nuclei, solitons are too tightly bound and are often too symmetric, due to symmetry enhancement as solitons coalesce to form bound states. The aloof baby Skyrmion results endorse a way to resolve these issues and provides motivation for a detailed study of the related three-dimensional version of the Skyrme model.

The dynamics of aloof baby Skyrmions

“…In section 2 we describe the model and briefly review some of the main results concerning static solitons and their point particle approximation using a binary species model. For a more detailed description of the aloof baby Skyrme model and its static solutions we refer the reader to [5]. In section 3 we study the dynamics of two solitons and introduce our dynamical version of the point particle model.…”

“…The spacetime coordinates are x µ , with µ = 0, 1, 2; and m is the mass of the fields φ 1 and φ 2 , associated with elementary excitations around the vacuum φ = (0, 0, 1). To agree with the choice in [5], we fix m 2 = 0.05 from now on. Finite energy imposes the boundary condition that φ tends to its vacuum value at spatial infinity.…”

“…The interation energy is the difference between this energy and twice the energy of a single soliton, that is, it is given by U χ (r) = E χ (r) − 2E 1 . In our earlier work [5] the interaction energy was computed numerically for χ = 0 (the repulsive channel) and χ = π (the attractive channel) and the data used to fit a Padé approximant of order [3/4] in each case. These Padé approximants are plotted in the left image in figure 1, and we refer the reader to [5] for the associated explicit constants in the two Padé approximants.…”

“…Minimal energy solitons for larger values of N have a similar cluster structure, composed of single solitons, and were studied in detail in [5] for N ≤ 12. Examples of particular relevance to the present work are the minimal energy N -solitons with N = 5, 6, 8, 9, which respectively take the form of a linear chain, a hexagon, an octagon and a 3 × 3 square.…”

“…The binary species point particle approximation, introduced in [5], makes use of the above property by considering N particles, with positions x (1) , . .…”