Resonances coupled-channel approach

In the reduced-dimensionality space the dynamics is treated exactly, e.g.. by the quantum coupled-channel approach. The remaining degrees of freedom are described in one of several approximate ways which will be reviewed below. The advantage of this approach is that it is feasible for systems of arbitrary complexity. In addition, it enables one to calculate cross sections, rate constants, etc. that are implicitly averaged over those degrees of freedom not explicitly treated dynamically, thus enabling a direct comparison to experiments which in most cases are not fully state-resolved. The degrees of freedom which are neither state-resolved experimentally nor treated dynamically will often be the same because they are usually the low-frequency motions such as rotation which are widely populated initially and finally in a collision. In the next section we shall review the elements of this theory for reactive systems with particular emphasis on resonances. 

This remark is associated with the amount of calculation performed and is not intended as a criticism. This work provides a valuable quantum mechanical analysis of a three-dimensional system. The artificial channel method (19,60) was employed to solve the coupled equations that arise in the fully quantum approach. A progression of resonances in the absorption cross-section was obtained. The appearance of these resonances provides an explanation of the origin of the diffuse bands found... 

This approach allows for a complete calculation of transport in the presence of vibrations and interacting with them. In this way, the effect of temperature (through phonon population, i.e. degree of excitation of the vibrations) and multiple excitations is taken into account. The inclusion of multiple electronic channels permits them to go beyond the above resonance models the molecule can have several orbitals contributing to the conductance and to the coupling with its vibrations [28]. 

The approach we follow here is based on a many-body theory of reactive scattering (1 ). Other approaches have been reviewed in the literature (14). For example, several of the available results on resonances have been obtained in wave-mechanical approaches that propagate and match wavefunctlons (15.16) or expand them in functions of suitable coordinates (17). Another approach which promises to provide accurate resonance cross sections is that of channel-coupling-array equations, also recently reviewed (18). The Feshbach theory of resonances has also been recently applied to molecular reactions (19. ). 

On the theoretical side, both quantal and semlclasslcal methods have been used to calculate resonance energies and widths, principally for colllnear reactions, although there are a few studies of 3D reactions. In quantal studies of 3D reactions, some close-coupling calculations on H+H2 have been reported (If), (li), but the large number of channels has necessitated approaches based upon the J -conserving (3),... 

---