Dynamic response of an atom to an electric field

Abstract

We investigate the response of the electrons and the nucleus of an atom to a uniform electric field that oscillates in time. The standard calculation of the electric polarizability for a fixed-nucleus atom is generalized to the case that the nucleus is allowed to move. Our calculation provides a simple illustration of Ehrenfest's theorem and allows us to examine the validity of the Born-Oppenheimer approximation and the Feynman-Hellmann theory for nuclear dynamics. The dynamic form of the Feynman-Hellmann theorem is explicitly shown to describe correctly the dynamics of the nucleus to first order in the ratio of electron mass to nuclear mass. Explicit results are obtained to all orders in the electron- to nuclear-mass ratio in the case of the hydrogen atom. The concept of viscosity for a moving nucleus is also examined.