Fermion scattering on topological solitons in the nonlinear O (3) sigma-model

Abstract

The scattering of Dirac fermions in the background fields of topological solitons of the (2+1)- dimensional nonlinear O3 [sigma]-model is studied using both analytical and numerical methods. General formulas describing fermion scattering are obtained and the symmetry properties of the partial scattering amplitudes and elements of the S-matrix are determined. Within the framework of the Born approximation, the scattering amplitudes, differential cross sections, and total cross sections of fermion-soliton scattering are obtained in analytical forms, and their symmetry properties and asymptotic behavior are investigated. The dependences of the first several partial elements of the S-matrix on the momentum of the fermion are obtained using numerical methods, and some properties of these dependences are ascertained and discussed.