The spherically symmetric hedgehog ansatz used in the description of the Skyrmion is believed to be inadequate for rotational states such as the nucleon $(I=J=\frac{1}{2})$ and the $\Delta$ $(I=J=\frac{3}{2})$ 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 or not the size of the soliton is allowed to change or not.

• Received 10 July 1997

DOI:https://doi.org/10.1103/PhysRevD.58.054002