Coulomb energy of a proton in the relativistic nuclear shell model

We examine the Dirac equation for a proton in a nucleus, with a shell-model potential consisting of nuclear and Coulomb parts. When the Dirac equation is reduced to a Schrödinger-like equation, the effective potential W in it exhibits two Coulomb-related effects that are absent in the usual nonrelativistic treatment: (I) W contains a Coulomb-nuclear interference term; (II) W depends strongly on the proton energy, which in turn depends on the Coulomb energy. If the shell-model potential consists of a strongly attractive Lorentz scalar and a strongly repulsive Lorentz vector, effect I by itself is very large. However, effect II counteracts effect I, leaving a small yet significant decrease in the Coulomb energy as compared with its nonrelativistic counterpart.