Quantum suppression and enhancement of the quasiclassical Landau-Lifshitz matrix elements: Application to the inelastic H2-He scattering at ultralow energies
The Landau-Lifshitz method of calculating quasiclassical matrix elements is generalized for the case when one of the states is not quasiclassical in the JWKB sense but possesses JWKB asymptotics. The generalized Landau-Lifshitz matrix elements are expressed via the standard Landau-Lifshitz matrix elements and the suppression-enhancement amplitudes. An analytical expression for the latter quantity is presented for the Morse potential. The results obtained are used for a simple interpretation of the recent numerical data [N. Balakrishnan, R. C. Forrey, and A. Dalgarno, Phys. Rev. Lett. 80, 3224 (1998)] for the s-wave vibrational relaxation of H2 on He.