  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 BPS-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.
