Solutions of the Dirac equation for fermions in Skyrme fields

Solutions of the Dirac equation are obtained for bound states of fermions in step-function Skyrme fields in three-dimensional space. When the local structure of the Skyrme field is changed, but its topological number is not, bound states appear and disappear, and the energy of a bound state can change from positive to negative, which indicates a change in the spectral asymmetry. These results are compared with similar ones for one-dimensional space and discussed in relation to the fermion number of the many-particle ground state.