Stability of the rotating Skyrmion

We find, numerically, that internally rotating classical Skyrmions corresponding to the N and the Δ cannot be stabilized, even in the presence of a pion-mass term, unless the fourth-order Skyrme term is also retained. We give arguments explaining this finding. Upon including the Skyrme term, and using reasonable parameters, we find that a stable localized solution exists for the N, but not for the Δ. This is in agreement with earlier results in the literature