Nondegenerate fermions in the background of the sphaleron barrier

We consider level crossing in the background of the sphaleron barrier for nondegenerate fermions. The mass splitting within the fermion doublets allows only for an axially symmetric ansatz for the fermion fields. In the background of the sphaleron we solve the partial differential equations for the fermion functions. We find little angular dependence for our choice of ansatz. We therefore propose a good approximate ansatz with radial functions only. We generalize this approximate ansatz with radial functions only to fermions in the background of the sphaleron barrier and argue that it is a good approximation there, too. copyright 1996 The American Physical Society