  Numerical methods are used to compute sphaleron solutions of the Skyrme
model. These solutions have topological charge zero and are axially symmetric,
consisting of an axial charge n Skyrmion and an axial charge -n antiSkyrmion
(with n greater than one), balanced in unstable equilibrium. The energy is
slightly less than twice the energy of the axially symmetric charge n Skyrmion.
A similar configuration with n=1 does not produce a sphaleron solution, and
this difference is explained by considering the interaction of asymptotic pion
dipole fields. For sphaleron solutions with n greater than four the positions
of the Skyrmion and antiSkyrmion merge to form a circle, rather than isolated
points, and there are some features in common with Hopf solitons of the
Skyrme-Faddeev model.
