On the best average trajectory in the vicinity of energetic threshold

In a previous paper [Billing, Chem. Phys. Let. 30, 391, (1975)] it was shown that the transition probabilities obtained from the ’’classical trajectory’’ equations are improved significantly by introducing an average potential <ψ‖V‖ψ≳ (where ψ is the total wavefunction and V the interaction potential) and an average velocity. With this in mind we recalculated the low temperature values of the He–H2 relaxation time obtained in Billing [Chem. Phys. 9, 359, (1975)] using the arithmetic mean velocity in the energy range 10.786, 1.30 eV]. The relaxation time obtained at 100 K improved by the factor of two, but is still off by a factor of 15 from the experimental value. So far no rigorous derivation of the classical trajectory equations including the average potential velocity exists, but the resulkts shown indicate that suich a derivation should also deal with the prediction of the best average velocity to be used.