Adiabatic theory of strong-field ionization of molecules including nuclear motion: Rescattering

We extend the adiabatic theory of strong-field ionization of molecules including nuclear motion developed in our previous paper [J. Svensmark et al., Phys. Rev. A 101, 053422 (2020)] to describe rescattering processes. The adiabatic regime in which the electronic timescale is much smaller than that of the nuclei and laser field is considered. The asymptotics of rescattering parts of the solution to the time-dependent Schrodinger equation (TDSE) and ionization amplitude are obtained, and thus vibrationally resolved photoelectron momentum dis-tributions (PEMDs) in the whole range of the photoelectron momentum are found. The ionization dynamics is described in terms of a nuclear wave packet in the molecular ion created as a result of ionization of the molecule, its evolution until rescattering, and a nuclear wave packet after rescattering. This complements the three-step model by accounting for what happens with the nuclear subsystem between ionization and rescattering events. A uniform asymptotics defining the PEMDs near a backward rescattering caustic is obtained, which enables one to extract the nuclear wave packet after rescattering from the PEMDs. The theory is illustrated by comparing its predictions with accurate numerical results obtained by solving the TDSE for a one-dimensional molecule with one electronic and one internuclear degree of freedom modeling H-2.