  We study the loosely bound Skyrme model with the addition of two different
pion mass terms; this is the most general potential of polynomial form up to
second order in the trace of the Skyrme field. The two pion mass terms are
called the standard pion mass term and the modified pion mass term. We find
that the binding energies are not reduced by the introduction of the modified
pion mass, but it is analogous to the standard pion mass term with a decrease
in the value of the mass parameter of the loosely bound potential (for large
values of the latter parameter). We find by increasing the overall pion mass
that we can reduce the classical binding energy of the 4-Skyrmion to the 2.7%
level and the total binding energy including the contribution from spin/isospin
quantization is reduced to the 5.8% level.
