Quantum-Mechanical Calculations of the Inelastic Cross Sections for Rotational Excitation of Para and Ortho H2 upon Collision with He

Abstract

Using the method of amplitude densities, we derive the equations for computing the scattering $T$ matrix in the total‐angular‐momentum representation. We also show that in the appropriate limit this method reduces to a first‐order differential equation for the $T$ matrix. In an Appendix a similar discussion is presented for the reaction matrix. Using the T‐matrix approach, we have obtained numerical solutions to the helium‐atom–hydrogen‐molecule scattering problem in both the close‐coupling and distorted‐wave approximations. Cross sections were computed for the $\text{J\hspace{0.17em}=\hspace{0.17em}0}$ to $\text{J\hspace{0.17em}=\hspace{0.17em}2}$ transitions in parahydrogen and the $\text{J\hspace{0.17em}=\hspace{0.17em}1}$ to $\text{J\hspace{0.17em}=\hspace{0.17em}3}$ transition in orthohydrogen. These results were calculated using both an interaction potential computed by Roberts and a potential computed by Krauss and Mies. The close‐coupling and distorted‐wave results are compared, and it is found that, in general, the distorted‐wave cross sections are about 20% too high when Roberts potential is used and are about 10% too high when the less anisotropic Krauss and Mies potential is used.