Isotopic branching in (He,HD<SUP>+</SUP>) 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)&#8594;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 &#915;=PR(HeH+)/PR(HeD+) generally remains less than unity for different v states at different Etrans in agreement with experiment. But at Etrans=1.0eV, for v=4, &#915; 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, &#915; is strongly dependent on j, in contrast to the marginal dependence shown by the earlier quasiclassical trajectory calculations