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

Abstract

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 (P_v,j^R) is shown to increase with v over the collision energy (E_trans) range (0.95-2.25 eV) investigated for both the exchange channels, in accord with the experimental results. The isotopic branching ratio Γ=P^R(HeH⁺)/P^R(HeD⁺) generally remains less than unity for different v states at different E_trans in agreement with experiment. But at E_trans=1.0eV, 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 P_v,j^R is found to be j dependent for both the channels. While P_v,j^R (HeH⁺) decreases initially with increase in j from 0 to 2 and then increases when j is increased further to 3, P_v,j^R (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.