Semiclassical Transition Probabilities for Rotationally Inelastic Scattering

Degeneracy averaged partial cross sections for rotationally inelastic scattering are calculated using semiclassical methods. Assuming a classical linear trajectory simple expressions are derived for the sudden limit, the classical limit, and first‐order limit. A single uniform approximation is obtained which converges to all three limits. The partial inelastic cross section $Q_j{\prime }_{\mathrm{\leftarrow j}}$ is given by ${\mathrm{D\Sigma C}}^2{\text{(jλj′;000) A}}_{\lambda }\mathrm{(d)}$ , where $D$ and $d$ are reduced parameters, $C$ is the Clebsch–Gordan coefficient, and $A_{\lambda }$ is a set of integrals depending on the potential form; the $A_{\lambda }$ 's are calculated for the ion–dipole and anisotropic van der Waals potentials and in the sudden limit for the dipole–dipole potential.