Isotopic branching in (He, HD+) collisions: A time-dependent quantum mechanical study in three dimensions

A time-dependent quantum mechanical approach has been used to investigate the reaction He+HD+(v=0–4,j=0–3)→HeH++D; HeD++H in three dimensions for total angular momentum J=0. The vib-rotation (v,j) state-selected reaction probability (Pv,jR) is shown to increase with v over the collision energy (Etrans) range (0.95–2.25 eV) investigated for both the exchange channels, in accord with the experimental results. The isotopic branching ratio Γ=PR(HeH+)/PR(HeD+) generally remains less than unity for different v states at different Etrans in agreement with experiment. But at Etrans=1.0 eV, for v=4, Γ obtained from our calculations for j=0 of HD+ is ∼0.8, in excellent agreement with the earlier quasiclassical trajectory calculations, but a factor of 2 less than that obtained from experiment. This difference could arise from the inclusion of nonzero j states in the experimental study, as Pv,jR is found to be j dependent for both the channels. While Pv,jR (HeH+) decreases initially with increase in j from 0 to 2 and then increases when j is increased further to 3, Pv,jR (HeD+) reveals an unusual j dependence; it is larger for even j states of HD+ than for odd j. As a result, Γ is strongly dependent on j, in contrast to the marginal dependence shown by the earlier quasiclassical trajectory calculations.