Complete momentum spectrum of H$_2^+$ ionization by short laser pulses from model Born-Oppenheimer calculations

We have performed one dimensional Born-Oppenheimer (BO) calculations for H$_2^+$ ionization in intense laser pulses. Here, one dimensional implies one degree of freedom each for the electron and the internuclear distance. Our scheme allows us to clearly separate dissociation and ionization without making any further approximation within the model. The results have been analyzed to qualitatively answer several important questions about different approximations and models proposed for interpreting and predicting the Kinetic energy spectrum of the protons following ionization, in particular above threshold Coulomb explosion (ATCE).