Calculation of Rotational and Vibrational Transitions for the Collision of an Atom with a Rotating Vibrating Diatomic Oscillator

A practical method is presented for computing the T‐matrix elements for a rotating, vibrating oscillator. A simple model is used which approximates the features of the $He–H2$ system. It is found that the rigidrotor approximation is in error even at energies well below the threshold for vibrational excitation. For computation of rotational transitions from the ground to the first accessible excited rotational state, many of the excited rotational transitions may be neglected but some of the excited vibrational transitions must be included. At high energies, it is shown that for any particular transition many of the states not strongly coupled to the states involved in the transition may be neglected. It is found that the computation of T‐matrix elements for vibrational transitions in the presence of rotational transitions is not prohibitively time consuming. In computing the total cross section, it is shown that a calculation including only the ground state gives remarkably good results.