Retardation effects and the Born-Oppenheimer approximation: theory of tunneling ionization of molecules revisited.

We show that retardation in adjusting an electronic state to an instantaneous internuclear configuration caused by the finiteness of the electron's velocity breaks the validity of the Born-Oppenheimer (BO) approximation at large electron-nuclei distances. This applies even to the ground state. As a result, the BO approximation in the theory of tunneling ionization of molecules breaks down at sufficiently weak fields. We also show that to account for nuclear motion the weak-field asymptotic expansion for the tunneling ionization rate must be restructured. The predictions for the rate using the BO approximation and the asymptotic expansion are compared with numerical results for a one-dimensional three-body system modeling a diatomic molecule, with both electronic and nuclear motions treated exactly.