Use of semiclassical collision theory to compare analytic fits to the interaction potential for vibrational excitation of H2 by He

Vibrational transition probabilities for strongly classically forbidden single-quantum and two-quantum transitions calculated by two semiclassical methods involving real-valued trajectories are compared to quantum mechanical close coupling for various analytic fits to the ab initio interaction potential for the He--H2 system. The final-value-representation integral expression from classical S matrix theory and the classical-trajectory forced-quantum-oscillator method are found to be in semiquantitative agreement with the quantum mechanical calculation even for transition probabilities as small as about 10-6. Further, the semiclassical methods reproduce the important trends in the results as functions of the interaction potential. The reliability of these semiclassical calculations allows one to determine the region of the potential energy surface which is sufficient for calculation of vibrational excitation probabilities. The important region for the present calculations is in the classically allowed region of the potential energy surface and at the fairly high total energy of 0.14 Hartree includes the range of H2 distances 1.195--1.467 Bohr for the forced quantum oscillator methods and the wider range 0.927--2.000 Bohr for the more accurate final value representation. The region which must be known for an accurate calculation is more restricted than previous discussions had suggested. At lower energies, an even more restricted range of the potential energy surface contributed to the semiclassical calculations