Nuclei as near BPS Skyrmions

We study a generalization of the Skyrme model with the inclusion of a sixth-order term and a generalized mass term. We first analyze the model in a regime where the nonlinear sigma and Skyrme terms are switched to zero, which leads to well-behaved analytical Bogomol'nyi-Prasad-Sommerfeld-type solutions. Adding contributions from the rotational energy, we reproduce the mass of the most abundant isotopes to rather good accuracy. These BPS-type solutions are then used to compute the contributions from the nonlinear sigma and Skyrme terms when these are switched on. We then adjust the four parameters of the model using two different procedures and find that the additional terms only represent small perturbations to the system. We finally calculate the binding energy per nucleon and compare our results with the experimental values.