Rotational and vibrational excitation in the scattering of atoms by diatomic molecules

The theory of rotational-vibrational excitation in collisions of atoms with diatomic molecules is developed through the use of a generalized phase shift. This is accomplished by first transforming the usual coupled equations to a new set based on a coupling scheme involving directly the vector changes in the angular momenta of the problem. The resulting set of coupled second-order equations is then transformed to a set (twice as large) of coupled first-order equations. The functions determined by these equations are inter-preted as complex amplitudes, and generalized phase shifts are defined in terms of the asymptotic form of the solutions. It is found that transitions among the vibrational states of the diatomic molecule arise because of offdiagonal elements of matrix elements of the interaction potential and also due to the overlap of vibrational wave functions associated with different rotational states of the molecule. It is probable that the latter is an important mechanism in the transitions among the highly excited rotational-vibrational states lying near the continuum.