The time-dependent Schrödinger equation for the one-dimensional ${\mathrm{H}}_2^{+}$ molecule (with both nuclear and electronic degrees of freedom included) was solved numerically to study dissociative ionization. A wave-function splitting technique was used with projections onto Volkov states, which allows one to circumvent the problem of lost information on electron flux due to absorbing boundary methods. This technique allows us to calculate the above-threshold ionization (ATI) photo electron kinetic-energy spectra in the presence of moving nuclei, as well as complete spectra of dissociating protons, beyond the Born-Oppenheimer approximation. The ATI spectra are considerably enhanced with respect to the H-atom spectra due to electron molecule interaction. The peaks seen in calculated Coulomb explosion spectra of protons agree well with recent theoretical and experimental work related to the phenomenon of charge-resonance-enhanced ionization in molecules.

• Received 26 June 1997

DOI:https://doi.org/10.1103/PhysRevA.57.1176