The quasi-quantum treatment of rotationally inelastic scattering from a hard shell potential : its derivation and practical use
The QQT is a quasi-quantum mechanical treatment of the collision between molecules. Instead of a partial wave expansion approach, it uses a kind of Feynman path integral method that exploits the path length differences originating from the different orientations of an anisotropic molecule. As a result, the QQT provides valuable physical insight while requiring very little computational effort. The current paper gives a systematic derivation of the QQT and explains its underlying principles. The expression for the scattering amplitude is shown to be selfconsistent, without any normalisation factors, when the rotational energy level spacing is negligible. The constant curvature approximation that is presented makes the QQT conceptually even more simple, and its effect on the calculated differential cross-sections (DCSs) turns out to be small. As examples we present QQT calculations of the DCSs for NeÂ–CO(1S ) and HeÂ–NO(2 ?), at collision energies of, respectively, 511 cm -1 and 514 cm -1. The anisotropy of the hard shell potential energy surface for NeÂ–CO in terms of the incoming de Broglie wavelength is about twice as large as for HeÂ–NO. This leads to state-to-state DCSs that have up to three maxima of comparable amplitude, instead of only one large maximum as is found for HeÂ–NO. The QQT results for these two applications are compared with results from close coupling calculations.
Ballast, A, Gijsbertsen, A, Linnartz, H, & Stolte, S. (2008). The quasi-quantum treatment of rotationally inelastic scattering from a hard shell potential : its derivation and practical use. Molecular Physics, 106, 315–331. doi:10.1080/00268970701803109