Application of the adiabatic-nuclei approximation to energy-loss cross sections for collisions with molecules

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Abstract
A general expression is derived for the energy-loss, or stopping, cross section for particles incident on linear or symmetric-top molecules, within the context of the adiabatic-nuclei approximation for vibration and rotation, or only rotation. The derivation is an alternative to that of Shimamura, and confirms his proof that the cross section is, when summed over all final rotor states, independent of the initial rotor state. It involves a sum rule for Clebsch-Gordan coefficients that, if not newly derived here, is certainly unfamiliar. The expression relating body-frame (fixed-nuclei) and laboratory-frame cross sections for linear and symmetric-top molecules is generalized to the asymmetric-top molecule, and it is shown that for this case the cross section for transitions between any rotational states can be written as a simple linear combination of the cross sections for the ground rotational state only in special circumstances. Application of Shimamura's theorem to this case leads to a general expression, applicable to all three classes of molecules, that is ideally suited to use with the results of standard fixed-nuclei scattering calculations. Applications near threshold and/or for polar molecules are discussed and illustrated for electron collisions with CO.