Retardation (or Casimir) potential for the Rydberg hydrogen molecule

The retardation (or Casimir) potential for Rydberg H[sub 2]---a hydrogen molecule with one electron in a highly excited, hydrogen-atom-like electronic state and an H[sub 2][sup +] core---is determined using time-dependent quantum electrodynamics in the Coulomb gauge. The potential obtained is valid over a range of [ital r], the Rydberg electron-core separation, from several [ital a][sub 0] to infinity, and accurate numerical results for the magnitude of the corresponding energy shift are calculated using a discrete representation of the electric dipole oscillator-strength spectrum. The prospects for measurement are analyzed.