Near-BPS Skyrmions: Nonshell configurations and Coulomb effects

The relatively small binding energy in nuclei suggests that they may be well represented by near-BPS Skyrmions since their mass is roughly proportional to the baryon number A. For that purpose, we propose a generalization of the Skyrme model with terms up to order six in derivatives of the pion fields and treat the nonlinear sigma and Skyrme terms as small perturbations. For our special choice of mass term (or potential) V, we obtain well-behaved analytical BPS-type solutions with nonshell configurations for the baryon density, as opposed to the more complex shell-like configurations found in most extensions of the Skyrme model. Along with static and (iso)rotational energies, we add to the mass of the nuclei the often neglected Coulomb energy and isospin breaking term. Fitting the four model parameters, we find a remarkable agreement for the binding energy per nucleon B/A with respect to experimental data. These results support the idea that nuclei could be near-BPS Skyrmions.