Magnetic Dichroism in the one-electron atom

The difference in absorption rate of right or left circularly polarized x-rays by magnetic materials is known as magnetic dichroism and is a well established method of investigating the magnetic properties of materials on a microscopic level. In this paper we illustrate this effect with a study of magnetic dichroism in the one-electron atom. The standard relativistic one-electron atom is solved. First-order perturbation theory is used to calculate eigenfunctions in an applied constant magnetic field. These eigenfunctions are used in a golden rule calculation of the absorption rate for right and left circularly polarized light as a function of applied field. All calculations have been done analytically. The difference in absorption rates for right and left circularly polarized light for 1s to 2p1/2 is of opposite sign to the difference for 1s to 2p3/2. We comment on the significance of these results in the interpretation of dichroism experiments on magnetic materials.