ROTATIONAL AND VIBRATIONAL EFFECTS IN THE E 1-SIGMA-G+-X 1-SIGMA-G+ 2-PHOTON TRANSITIONS OF H2, HD, AND D2

A theoretical study is reported for the dependence of the E, F 1-SIGMA-g+-X 1-SIGMA-g+ (upsilon-E = 0, upsilon-X) Q-branch two-photon transitions on the initial vibrational and rotational quantum numbers upsilon-X and J for H-2, HD, and D2. The magnitude of the two-photon transition moment \M(fo)\ increases with upsilon-X between 0 and 2, then decreases rapidly at higher upsilon-X. This behavior is ascribed to (constructive and destructive) interference effects in the two-photon transition, which vary with the nodal behavior of the initial-state vibrational wave function. The J dependence of \M(fo)\ is most strongly affected by the changes in vibrational wave functions caused by centrifugal distortion of the vibrational potentials. At low to intermediate J, the Franck-Codon overlap improves, resulting in a slow, monotonic increase of \M(fo)\ with J. At higher J, resonant tunneling between the inner and outer wells of the E,F state introduces sharp variations in the \M(fo)\ structure. Near the top of the barrier, nonresonant tunneling in the E-state vibrational wave function causes a general decrease in \M(fo)\ with J.