Direct calculation of collisional properties that require energy derivatives of the S matrix: Results for the reaction He+H₂ ⁺⇌HeH⁺+H

The Darakjian-Hayes direct method for determining quantum lifetimes for three atoms scattering in three physical dimensions is used to determine accurate state-to-state time delays for the reaction of helium with H ₂⁺ for total angular momentum J=0. These results are compared with the time delays obtained by numerical differentiation of the S-matrix elements generated using the APH (adiabatically adjusting principal-axis hyperspherical) formulation of Pack and Parker. The direct method was found to be accurate and efficient for calculating the energy derivatives of the S matrix. The calculated eigenvalues of Smith's collision lifetime matrix (eigen lifetimes) for this reaction predict numerous long-lived metastable states, many with lifetimes over 0.5 ps. The extent of the coupling of metastable states to specific scattering states provides an indication of the nature and magnitude of the time delays associated with particular state-to-state scattering processes. The direct method for calculating the energy derivatives of the S matrix is also found to be accurate and efficient for determining the energy derivative of the cumulative reaction probability.