Rotational energy transfer in collisions between orbitally non-degenerate open-shell systems

The theory is developed for the rotational energy transfer induced in an open-shell molecule by collision with an open-shell atom. The consequences of the exchange interaction between such systems are investigated and related to the behaviour of unpaired electron spins during inelastic collisions. The coupled equations for the closed shell case are first developed, and generalized equations derived for the matrix elements of a spin-independent potential. The spin-exchange interaction potential of open-shell species is then expressed in a form suitable for scattering theory and this leads to coupling matrix elements in a basis which includes electron spin. Nuclear spin is also included by a simple extension of the basis set. It is then argued that many open-shell collisions leading to rotational energy transfer will be sufficiently weak that the coupled equations can be treated by use of the restricted distorted-wave Born approximation. This method leads to the derivation of expressions for scattering cross-sections in both the spin-independent and spin-correlated cases. The influence of exchange forces is manifest in branching fractions for spin multiplets, which relate the cross-sections for the different ΔJ associated with each change in rotational quantum numbers. A general expression for the branching fractions in hyperfine multiplets is also derived. The discussion deals with the extent to which exchange forces will influence rotational energy transfer in practice. It shows how the results of experimental investigations such as those in the following paper might be interpreted. The way in which rotational propensity rules may be affected by exchange interactions is illustrated by reference to the model systems H + CN and H + NH2. In conclusion it is noted that open-shell open-shell collisions take place naturally both in the upper atmosphere and in interstellar space.