Skyrmions in the Skyrme model revisited

TL;DR

This paper reexamines boundary conditions and numerical methods in the Skyrme model to better understand skyrmions, revealing the existence of half-integer topological skyrmions and analyzing their static properties.

Contribution

It introduces a finite radius boundary condition and combines global analysis with numerical computation, providing improved results and new insights into skyrmion solutions.

Findings

Half-integer topological skyrmions exist in the model.

Baryon masses are overestimated compared to experimental data.

Isoscalar radii and axial coupling constants can be fitted within 20% error.

Abstract

The possible boundary value problems of the skyrmions are reexamined in the original Skyrme model with two new viewpoints. The first one suggests to replace the infinity boundary point by the finite radius R, which is related to the density of the surrounding nuclear matter. The second viewpoint suggests to combine the global analysis with the numerical computation to give better results by avoiding the errors. It is interesting that the half integer topological skyrmions do exist in the model. Finally, the static properties of all possible skyrmions are calculated with the model parameters Subscript[F, \[Pi]] = 186 MeV, Subscript[m, \[Pi]]= 138 MeV and 1.57 < e < 4.17. The baryon masses are found to be too high compared to the experimental values, while the mass splitting between them is too small. On the other hand, the isoscalar radii and the axial coupling constant can be fitted with the experimental data with an error of 20% within the Balachandra's bound.