Generation of vortex electrons in tunneling ionization of polyatomic molecules: Exact results in the zero-range potential model

The theory of molecular Siegert states in a static electric field in the zero-range potential model is developed. The model admits extended analytical and accurate numerical treatments, which enables one to study tunneling ionization of large polyatomic molecules with complex geometry in strong fields beyond the weak-field approximation. The theory is illustrated by calculations for three model molecules reproducing the geometry of the real water, benzene, and leucine molecules. The field and orientation dependence of two major ionization observables, the ionization rate and the transverse momentum distribution of liberated electrons, is analyzed. The calculations reveal a number of strong-field effects not accounted for by the weak-field asymptotic theory. In particular, it is shown that vortex electrons are efficiently generated in tunneling ionization of large molecules at sufficiently strong fields, which opens a perspective for enantiosensitive rescattering photoelectron spectroscopy. The mechanism of tunneling-induced electron diffraction and its manifestation in the transverse momentum distribution are discussed.