Landau-Zener crossing formalism

Fig. 8. Relative velocity dependence of integral cross sections calculated for Na + O collisions for the indicated exit channels. The solid curve is the charge transfer cross section calculated using a multichannel Landau-Zener formalism (see text). The dashed curve is the two-state Landau-Zener cross section. Charge transfer calculations by van den Bos are indicated by triangles. Full circles and squares are the respective excitation channels as determined using the multichannel Landau-Zener model.

On the basis of a Landau-Zener curve crossing formalism, Borgis and Hynes derived the nonadiabatic rate constant k, which is similar to that expressed by the DKL model but where the tunneling term Cnm found in Eq. (4) is significantly modified due to the influence of the low-frequency promoting mode Q, with a frequency 0)q, on the tunneling rate. The dependence of Cnm on Q is given by [13]... 

Published theoretical descriptions of the Ca(5 Pi) - Ca(5 Pj) alignment system have considered the formal Landau Zener curve crossing probability [29] and have used foil quantum mechanical descriptions [30]. Unfortunately, all the theoretical descriptions are limited by the lack of accurate potential surfaces for the van der Waals states of the electronic levels. However, in the future, accurate information may become available from recent experiments to investigate metal atom + rare gas van der Waals potentials using supersonic jet spectroscopy [31-34]. Thus there is an excellent chance that it will also be possible to obtain more accurate theoretical descriptions, which will elucidate important subtleties of alignment effects in energy transfer and reactions. 

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