Relativistic Corrections in the Nuclear-Plus-Electromagnetic Hamiltonian

Abstract

We investigate the problem of relativistic corrections to the Hamiltonian of two nucleons interacting with each other and with an external electromagnetic field. We find, in addition to well-known corrections to the kinetic energy and to the Foldy-Wouthuysen reduction, a correction to the potential energy. This effect depends on the way in which the nonrelativistic limit of the dynamical variables is taken. The correction vanishes in the c.m. system, but leads to a nonzero correction to the electromagnetic Hamiltonian. We define the current and charge densities, verify the conservation of current, and verify the low-energy theorem for bremsstrahlung.