In this paper the uniform WKB theory is applied to predissociations of N curve crossing systems as an extension of the study we made in a previous paper. We have obtained transition amplitudes (S-matrix elements) explicitly for three-state and N-state problems in terms of the transition factors and phase integrals used previously in our study of two-state problems. The expressions obtained in the local pairwise coupling approximation are extremely simple, physically transparent, and easy to compute. Within the framework of this model we have obtained the resonance characteristics for predissociative N-curve crossing problems. The level width formula is given in terms of the transition factors χi and is new. The transition amplitudes for the corresponding inelastic scattering problems were also derived.

The optical-potential method (OPM) developed in the previous paper is applied to the calculation of a large manifold of transitions of the type v--1, j, mj -->v' = O, j', mj in Li + N~ collisions. Trends related to the dependence of the cross section av,Lmj~v'J',raj on the states j, j' and m t are observed and analysed in terms of the physical effects involved. An information-theoretic model of the cross sections is tested as a means for a simple parametric representation of the results. I. INTRODUCTIONSeveral sophisticated theoretical methods were introduced in recent years for the calculation of rib-rotational transition rates in atom-molecule collisions [1]. Applications of these methods, the most notable of which is the coupled-state approximation [2], were, however, confined to systems in which the molecular collision partner is a very light diatomic (e.g. cases such as He + H~, He + D 2, Li+H 2 [I]). This limitation is a consequence of the great computational difficulty for systems involving heavier molecules where the dense rotational energy spacings give rise to a large number of rotational states that play a role in the process, hence to scattering equations of enormous dimensionality [3]. The difficulty can be overcome by two approaches suggested recently in the literature. One of these schemes is an analytical model for rib-rotational transitions, applicable to systems with a potential surface of a certain type [4]. The second approach is an optical-potential method (OPM) described in reference [5] (referred to below as paper I). Tests on the He+H~ system have shown the above methods to be of good accuracy [4,5], and the loss of precision that these schemes entail is compensated by a much increased range of applicability. In the OPM approach the effect of the large manifold of open rotational channels on a rib-rotational transition of interest is incorporated through optical (absorptive) potentials. In this way the effort required to calculate a single rib-rotational cross section is virtually independent of the number of open rotational channels, and a drastic simplification of the computational effort ensues.

Predissociation and preassociation phenomena are theoretically investigated by means of uniform semiclassical wavefunctions for all cases of energy in two-state models. Three different sets of transition probability amplitudes are obtained for three different cases of energies, i.e., E≳Vmin; Vmax<E<Vmin; and E<Vmax, where Vmin and Vmax are the minimum and maximum of the upper and lower adiabatic potentials. The theory is different from the semiclassical theory previously used by other authors in semiclassical theory of predissociation, but leads to formally similar transition probability amplitudes for the case of E≳Vmin. For other cases of energy comparison is not possible owing to the lack of other theories.

No abstract

An optical-potential method is developed for the calculation of cross sections for vib-rotational transitions in atom-molecule collisions. In this framework the multi-channel scattering equations are replaced by a pair of coupled equations for each vib-rotational transition. The effect of the large manifold of open rotational channels is introduced through an optical potential in each of the coupled equations. Both a phenomenological (trial function) procedure and a theoretical approximate method for obtaining the optical potentials are given. The method remains computationally feasible even in systems with very many open channels.To test the method, the cross section for the 10~00 transition in He + H~, He + D2, He + T2 was calculated over a wide range of energies and compared with results in the literature. An interesting scaling property is observed to hold with respect to the energy dependence of the above cross sections. INTRODUCTIONThere has been a great deal of activity in recent years in theoretical studies of vib-rotationally inelastic molecular collisions. A wide range of approaches to the subject have been formulated and applied, including angular momentum decoupling schemes [I], effective potential techniques [2] and semi-classical methods [3], to name but a few. However, at present, calculations of proven accuracy, such as those of the coupled-state method [1] can be carried out only for the lightest systems (e.g. He + H2) which have a relatively small number of open rotational channels at the energies of interest. There remains a need for approximate methods that can easily be applied to heavier molecules.Such methods will have useful applications even if confined to the order-ofmagnitude range of accuracy. Recently an analytical model for rib-rotational transitions was given by Gerber [4]. Based on the distorted-wave approximation for the vibrationally inelastic transitions and on the sudden approximation for the rotational states involved, this model requires very little computational effort. Moreover, an improved version of the model, developed by Eno and BalintKurti [5], proved to be of remarkable accuracy. Unfortunately, the model is confined to a special class of potential functions which restricts considerably its applicability.