Reaction probabilities and reaction cross sections for three-dimensional He+H₂⁺(v) collisions: a time-dependent quantum mechanical study

Abstract

Vibrational (v) state-selected reaction probabilities (P_vj^J) have been calculated for the reaction He+H₂⁺(v=0,1,2,3)→HeH⁺+H, for H₂⁺ in its ground rotational state (j=0) for a range of total angular momentum (J) values, for total energy (E) in the range 0.94-1.4 eV, using time-dependent quantum mechanical (TDQM) approach and centrifugal sudden approximation. The number of oscillations in P_v0^J(E) decreases with increase in J. In addition, there is a noticeable increase in the threshold energy (E_th) with increase in J. The magnitude of P_v0^J decreases with increase in J resulting in converged cross section values by the time J becomes 35-45, depending upon v and E under investigation. The resulting (converged) reaction cross section values are in excellent agreement with the experimental results at E=1.14 eV, both in terms of the magnitude and in terms of the observed vibrational enhancement. Interestingly, there is a noticeable discrepancy between our TDQM results and earlier time-independent quantum mechanical studies at higher energies, for v=1 and 2. For v=3, the difference between the two theoretical studies is the largest near the threshold. Our results for v=2 and 3 suggest that the oscillations in the vibrational state-selected reaction cross section values are amenable to experimental observation.