  We study a generalization of the loosely bound Skyrme model which consists of
the Skyrme model with a sixth-order derivative term - motivated by its
fluid-like properties - and the second-order loosely bound potential -
motivated by lowering the classical binding energies of higher-charged
Skyrmions. We use the rational map approximation for the Skyrmion of
topological charge B=4, calculate the binding energy of the latter and estimate
the systematic error in using this approximation. In the parameter space that
we can explore within the rational map approximation, we find classical binding
energies as low as 1.8% and once taking into account the contribution from
spin-isospin quantization we obtain binding energies as low as 5.3%. We also
calculate the contribution from the sixth-order derivative term to the electric
charge density and axial coupling.
