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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=1/2) and the Delta (I=J=3/2) 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.