Anapole dark matter quantum mechanics

Abstract

The dynamics of an anapole seen as dark matter at low energies is studied by solving the Schrödinger-Pauli equation in a potential involving the Dirac delta and its derivatives in three dimensions. This is an interesting mathematical problem that, as far as we know, has not been previously discussed. We show how bound states emerge in this approach, and the scattering problem is formulated (and solved) directly. The total cross section is in full agreement with independent calculations in the standard model.