Adiabatic invariance treatment of reactive collisions between ions and polar molecules at low temperatures

Abstract

A new semiclassical adiabatic invariance treatment of ion-molecule reactive collisions is proposed to investigate the influence of the molecular rotation on the cross-sections and rate constants at very low temperatures. Within the domain of validity of the adiabatic separation of the ion-molecule radial motion and the molecular rotation, the method is applicable to linear or symmetric-top molecules, for which the system is integrable. The correspondence principle is then used to partition the space of the classical action space into quantum “bins”, each of which corresponds to a specific quantum state. The procedure differs from the more usual Einstein-Brillouin-Keller (EBK) semiclassical quantization, where each quantum state is represented by a single point of action space. The results for the linear rigid rotor case, obtained using this modified semiclassical adiabatic invariance model, are in excellent agreement with the quantum mechanical methods, even for low rotational levels of the molecule, where the EBK semiclassical quantization fails.