Theory of tunneling ionization of molecules: Weak-field asymptotics including dipole effects

The formulation of the parabolic adiabatic expansion approach to the problem of ionization of atomic systems in a static electric field, originally developed for the axially symmetric case [Phys. Rev. A 82, 023416 (2010)], is generalized to arbitrary potentials. This approach is used to rederive the asymptotic theory of tunneling ionization in the weak-field limit. In the atomic case, the resulting formulas for the ionization rate coincide with previously known results. In addition, the present theory accounts for the possible existence of a permanent dipole moment of the unperturbed system and, hence, applies to polar molecules. Accounting for dipole effects constitutes an important difference of the present theory from the so-called molecular Ammosov-Delone-Krainov theory. The theory is illustrated by comparing exact and asymptotic results for a set of model polar molecules and a realistic molecular ion HeH2+ in the 2p sigma state.