Larmor diamagnetism and Van Vleck paramagnetism in relativistic quantum theory: The Gordon decomposition approach

We consider a charged Dirac particle bound in a scalar potential perturbed by a classical magnetic field derivable from a vector potential A(r). Using a procedure based on the Gordon decomposition of a field-induced current, we identify diamagnetic and paramagnetic contributions to the second-order perturbationtheory correction to the particle's energy. In contradiction to earlier findings, based on the sum-over-states approach, it is found that the resulting diamagnetic term is epsilon(d)((2)) = (q(2)/2m) [Psi((0))\betaA(2)Psi((0))], where Psi((0))(r) is an unperturbed eigenstate and beta is the matrix associated with the rest-energy term in the Dirac Hamiltonian.