Inelastic Vibrational and Rotational Quantum Collisions

Abstract

Scattering theory and related scattering measurements have made dramatic strides in the last few years. There are a number of excellent reviews in various areas of this field [2.1–5]. The entire field of atom-molecule scattering theory has been rather thoroughly treated in the excellent book Atom-Molecule Collision Theory, edited by BERNSTEIN [2.6]. This book covers many areas, from the computation of interaction potentials through numerical techniques for both classical and quantum mechanical calculations and approximation methods. Since another review is not needed at this time, I intend to concentrate here on ideas and methods which I believe will lead to an understanding of the details of energy transfer in collisions and eventually to understanding chemical reactions. I do not intend to cover all or even a majority of the considerations which will contribute to such an understanding. On the contrary, I shall mainly concern myself with the accurate calculation of rotational and vibrational energy transfer in atom-molecule collisions. Accurate calculation does not necessarily imply the solution of the close coupled equations. In fact, if we limit ourselves to solution of the close coupled equations, we restrict the problems which we may study to a pitful few. It is, of course, important that this select group of problems be solved accurately as benchmarks for future work and to serve as a source of experience on which to develop intuition. The central problem, however, is to devise approximations which will allow us to handle larger systems accurately. A system of approximations is needed which will allow us to describe each feature of a collision in which we have an interest in the desired accuracy. There are a few approximations, developed in recent years, which represent a step in the right direction. The most fruitful approach at present appears to be the dimensionality reducing approximations pioneered by RABITZ [2.7].KeywordsAsymptotic RegionFixed Coordinate SystemUnperturbed SolutionRelative Angular MomentumBody Fixed Coordinate SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.