Force on an atom in an electrostatic field: Feynman-Hellmann theorem and oscillator strengths

The force on a free atom or ion in a uniform electrostatic field is considered in the framework of the Feynman-Hellmann theorem. The contributions to the force from excited states are shown to be given directly by the "oscillator strengths" between these states and the occupied states in the atom or ion. Force calculations for atoms in molecules and solids are discussed in the light of these results. In the case of current carrying solids, the Feynman-Hellmann theorem is not applicable, yet the force expression for an ion in the solid retains the Feynman-Hellmann form. Because of this distinction, arguments based on local neutrality of an ion in a solid are relevant for an isolated solid but not for a current carrying solid. A previously derived sum rule for the force on the ions of a conducting solid is shown to be a statement of the oscillator-strength sum rule.