Exact electromagnetic matrix elements and selection rules for relativistic hydrogenic atoms

We give the exact matrix elements (i.e., with retardation taken into account exactly) for the electromagnetic interaction for relativistic hydrogenic atoms in terms of integrals of the atomic radial functions. The present paper represents an extension of earlier results for the nonrelativistic case. The matrix elements can be used to obtain the exact selection rules and transition probabilities per unit time for the emission of a photon.