Near-BPS Skyrmions: Constant baryon density

Abstract

The Skyrme Model seems unable to reproduce the small binding energy in nuclei. It was realized recently that near-BPS Skyrme Models may be more appropriate in that regard since their solutions nearly saturate the Bogomol'nyi bound resulting therefore in a nuclear mass that is almost proportional to the baryon number A. We are interested in a class of such models which include terms up to order six in derivatives of the pion fields in the regime where the nonlinear σ and Skyrme terms are assumed to be relatively small. We demonstrate that with a proper choice of potential, one can obtain constant baryon density configurations, as opposed to the usual shell-like configurations emerging from the Skyrme Model. This four-parameter model also lead to a very good agreement of the binding energy per nucleon B/A with respect to experimental data.