The two-state field-aligned (1-D) model has been employed to investigate the dissociation dynamics of a hydrogen molecular ion and its isotopes under the Born-Oppenheimer approximation without rotation. The emphasis of this work was on the role of mass during the dynamical dissociation processes and on the laser-induced branching ratios between different photon pathways.

Firstly, we have found that scaling the pulse duration of the laser pulse, applied to H[subscript]2+ and D[subscript]2+ , by the square root of the mass ratio of these isotopes will produce similar structure in the nuclear kinetic energy release (KER) spectra. In fact, the similarity of the spectra is enhanced by including some averaging that is necessary for comparison with experiment. For this to occur, the same broad initial vibrational distribution and a short pulse are preferred. Using this scaling idea, it is possible to produce effectively shorter laser pulses by studying heavier isotopes, like D[subscript]2+.

Secondly, we have demonstrated analytically and numerically that there is a carrier-envelope phase effect in the total dissociation probability (TDP) of H[subscript]2+, and this effect grows with nuclear mass. We further show that under the same laser conditions, the CEP effect in the asymmetry between breakup channels decreases with mass. Our analytic expressions enhance the idea that CEP effects can be understood as an interference between different n-photon processes.

Thirdly, the trends in the dissociation dynamics of H[subscript]2+ and D[subscript]2+ in a 800nm ultra short intense laser field were demonstrated by studying the dissociation branching ratios of multiphoton processes as a function of the laser peak intensity (from 8[times]10[superscript]9 to 10[superscript]14 W/cm[superscript]2) or pulse length (5fs-7.5fs). Based on the two-state approximation, an energy-analysis method (EAM) was employed to separate multiphoton processes. The results show that the one-photon dissociation process dominates over all other photon processes under all the laser conditions applied in the calculations and that the zero-photon process contributes to a surprisingly large fraction of the total dissociation. Two- and three- photon dissociation are weaker processes, but become more and more important as the laser peak intensity and pulse length increases. A two-state Floquet method was used to check the accuracy of the EAM, and good agreement between the two methods was found, demonstrating the reliability of the EAM. In comparison with H[subscript]2+, D[subscript]2+ displays stronger two and three photon branching ratios (above-threshold dissociation - ATD), which can be attributed to the late arrival of D[subscript]2+ to the critical distance for ATD to occur due to its heavier mass. Therefore, this "mass" effect can be used to steer the molecular dissociation pathways.