Electric field effects on the ground state hyperfine structure of hydrogenic atoms

The hyperfine structure of the ground state of the one-electron atom, with nuclear spin of 1/2, is discussed in terms of perturbation theory. The contact and dipolar hyperfine interactions plus the electric field effects from remote static charges are treated, performing exact summation over all discrete and continuum states, treating the second and third order mixed perturbation terms linear in the hyperfine Hamiltonian. Expressions for the energy terms, linear in the electric field gradient, quadratic in the electric field, and quadratic in the gradient are all derived, and their magnitudes evaluated for a simple field configuration.