  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 non-shell 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.
