Nuclear motion corrections to the binding energy in hydrogen

Abstract

Most of the calculations of nuclear recoil corrections to the atomic binding in hydrogen have been done using the covariant Bethe-Salpeter equation. In this paper an alternative to the Bethe-Salpeter approach in the form of a modified Dirac equation is presented. It contains the usual Hamiltonian for an electron in the field of a static proton, but it also includes the proton's kinetic energy and an interaction term due to transverse photons. The part of the interaction which produces the hyperfine splitting is extracted and treated perturbatively, whereas the remainder of the potential is retained, rearranged, and approximated in such a way as to make the resulting equation soluble. In a simple way, we are able to obtain reduced mass corrections to the fine structure and the hyperfine structure of hydrogen. An extension of the work, which enables us to calculate additional recoil terms not included in our lowest order effective potential, is briefly described.