Electro-nuclear dynamics of single and double ionization of H$_2$ in ultrafast intense laser pulses

Abstract: We present an efficient method for modeling the single and double ionization dynamics of the H$_2$ molecule in ultrashort intense laser fields. This method is based on a semi-analytical approach to calculate the time-dependent single and double molecular ionization rates and on a numerical approach to describe the vibrational motion that takes place in the intermediate molecular ion H$_2^+$. This model allows for the prediction of the single and double ionization probabilities of the H$_2$ molecule to be made over a wide range of frequencies and laser intensities with limited computational time, while providing a realistic estimate of the energy of the products of the dissociative ionization and of the Coulomb explosion of the H$_2$ molecule. The effect of vibrational dynamics on ionization yields and proton kinetic energy release spectra is demonstrated and, in the case of the latter, discussed in terms of basic strong-field molecular fragmentation mechanisms.