Weak-field asymptotic theory of tunneling ionization including the first-order correction terms: Application to molecules

The weak-field asymptotic theory (WFAT) of tunneling ionization including the first-order correction terms is validated for molecules by comparison with accurate calculations of molecular Siegert states in a static electric field. Both fundamental observables related to tunneling ionization, namely, the ionization rate and transverse momentum distribution of the ionized electrons, are considered. This complements our previous study of atoms [V. H. Trinh et al., Phys. Rev. A 87, 043426 (2013)]. Similarly to the atomic case, the first-order terms essentially improve the agreement between the WFAT and accurate results in a wide interval of fields up to the onset of over-the-barrier ionization. This establishes the WFAT including the first-order correction terms as an appealing alternative to accurate calculations in the tunneling regime. In addition to demonstrating the quantitative performance of the WFAT, the theory is shown to be helpful for understanding the field and orientation dependencies of the observables. In particular, we show that the first-order terms account for a deviation of the shape of the orientation dependence of the ionization rate of a molecule from that of the ionizing orbital as the field grows, which has important implications for strong-field molecular imaging techniques. This prediction of the WFAT is confirmed by comparison with time-dependent calculations.