This is the published version, also available here: http://dx.doi.org/10.1063/1.451229.We extend the inhomogenous‐differential‐equation (IDE) approach of Dalgarno and Lewis for a detailed study of two‐photon dissociation (TPD) of HD+ from high vibrational levels of the 1sσ g electronic state. Contrary to the H+ 2 case, where the TPD cross sections σ(2) L are largest near TPD thresholds and decrease monotonically with increasing photon energy, the HD+ cross sections are characterized by rich resonant and interference structures. We present σ(2) L results for TPD from the initial v i =6, 8, 10, 12, 14, 16, and j i =0 levels as well as from v i =14, j i =0, 2, 4 levels for a wide range of wavelengths of linearly polarized radiation accessible by CO2 and CO lasers. It is found that while there are four TPD pathways, the channel 1sσ g (v i j i )→ω 1sσ g (v, j=j i ±1) →ω2pσ u (k, j f =j±1) dominates the two‐photon process in most of the cases we have studied. Further, the results show that σ(2) L increases rather rapidly as the initial vibrational quantum number v i increases, indicating that the hereronuclear diatomic molecules in high vibrational levels can be efficiently two‐photon dissociated by IR lasers. Consequently molecular structures near the dissociation limit may be conveniently probed by two‐photon spectroscopy—as has indeed been demonstrated recently by experiments. Our σ(2) L results thus provide complementary information to the HD+spectroscopic data obtained recently by Carrington e t a l
