High-order above-threshold ionization of the H2+ ion: The role of internuclear distance

Abstract

High-order above-threshold ionization (HATI) of the ${{\mathrm{H}}_{2}}^{+}$ ion by a linearly polarized laser field is investigated theoretically using numerical solutions of the full three-dimensional time-dependent Schr\odinger equation (TDSE). The photoelectron spectrum is calculated in two ways: by projecting the final wave function onto continuum states satisfying the incoming boundary condition and by using the window-operator method. Our numerical simulations show that the shape of the corresponding photoelectron energy spectra depends on the internuclear distance. For small internuclear distances the obtained HATI spectrum is very similar to the HATI spectrum for atomic targets. By increasing the internuclear distance, i.e., by stretching the molecule, some features emerge in the spectra. The cutoff position of the high-energy photoelectron spectrum extends from $10{U}_{p}$ (${U}_{p}$ is the electron ponderomotive energy) for small internuclear distances up to above $18{U}_{p}$ for very large internuclear distances. The second observed feature is that, with the increase of the internuclear distance, a low-energy plateau appears which is much higher than the above-mentioned extended plateau. For the internuclear distance of 18 a.u. this plateau extends up to $6{U}_{p}$. These features are further investigated by using solutions of the classical equation of motion for the electron in the strong laser field and by using quantum-orbit theory. The results of classical analysis are confirmed using two quantum-mechanical methods based on the analysis of the electron time-dependent probability density and of the electron energy-resolved probability density, obtained from the TDSE solutions.