Dissociation spectrum of H$_2^+$ from a short, intense infrared laser pulse: vibration structure and focal volume effects

The dissociation spectrum of the hydrogen molecular ion by short intense pulses of infrared light is calculated. The time-dependent Schrodinger equation is discretized and integrated in position and momentum space. For few-cycle pulses one can resolve vibrational structure that commonly arises in the experimental preparation of the molecular ion from the neutral molecule. We calculate the corresponding energy spectrum and analyze the dependence on the pulse time-delay, pulse length, and intensity of the laser for $lambda sim 790$nm. We conclude that the proton spectrum is a both a sensitive probe of the vibrational dynamics and the laser pulse. Finally we compare our results with recent measurements of the proton spectrum for 55 fs pulses using a Ti:Sapphire laser ($lambda sim 790 $nm). Integrating over the laser focal volume, for the intensity $I sim 3 times 10^{15}$W cm$^{-2}$, we find our results are in excellent agreement with these experiments.