Interference effects on the H(2p) to H(2s) branching ratio in the photodissociation of hydrogen and deuterium

Photodissociation cross sections for both ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ above the H(n=1)+H(n=2) threshold are presented. The partial cross sections into H(1s)+H(2s) and H(1s)+H(2p), obtained by full numerical integration of coupled Schrödinger equations, show pronounced oscillations as a function of the excitation energy. These oscillations are the result of a quantum interference effect between two dissociation paths leading to the same final state. The condition for this interference to occur is the existence in the Franck-Condon region of two dissociative states (B and B’ in the case considered in this work) which can be excited at the same energy and which are coupled to each other by some nonadiabatic or other electronic interactions. The relationship between the full numerical calculation and the ‘‘half-collision’’ approximation is analyzed in detail. In addition, the predissociation of the D state, which occurs in the same spectral region, has also been studied. The line shapes obtained by solving the appropriate coupled Schrödinger equations are compared with those calculated by the use of perturbation theory. It is shown that, in order to have good agreement with the exact results, it is important to take into account contributions which are usually neglected, namely the contributions from the discrete spectrum of the final dissociative channel. Finally, the branching ratio Ω=σ(${\mathit{H}}_2$→H(1s)+H(2)σ(${\mathrm{H}}_2$p→H(1s)+H(2s) in the case of predissociation has been calculated and compared with other published calculations.