Oblate Skyrmions

The spherically symmetric hedgehog ansatz used in the description of the skyrmion is believed to be inadequate for the rotational states such as the nucleon ( I = J = 12 ) and the ∆ ( I = J = 32 ) due to centrifugal forces. We study here a simple alternative: an oblate spheroidal solution which leads to lower masses for these baryons. As one might expect, the shape of the solution is flatter as one increases I = J whether the size of the soliton is allowed to change or not.