Nonrelativistic dyon-dyon scattering

Abstract

The nonrelativistic problem of the scattering of two dyons (including the case of electron scattering by magnetic monopoles) is systematically studied, both classically and quantum mechanically, with a view toward the discrimination between various combinations of electric and magnetic charges. We analyze the classical cross section with particular attention to the interesting phenomena which occur for large angle scattering, the “rainbows” and “glory,” where the cross section becomes infinite. Quantum mechanically, we find that these infinities do not occur and that, when the partial wave scattering amplitude is summed, a very elaborate structure emerges for the cross section, which depends sensitively upon the electric and magnetic charges of the particles, as well as on their relative speed. We further discuss a large modification, leading to spin flip and nonflip amplitudes, due to the dipole moments of the particles. Numerical results are presented for a variety of values of these parameters. In principle, these results could be used to distinguish the δ-ray distributions produced by the various species of electrically and magnetically charged particles. Quite apart from the experimental implications of our numerical results, we have made a number of theoretical improvements and extensions. Numbered among these are the consideration of dyons and particles having dipole moments, and the explicit demonstration, based on the methods of angular momentum, that the differential cross section is independent of the choice of singularity line.