The ‘‘Fraunhofer theory’’ of rotational inelastic scattering of He on small molecules

Abstract

The well-known Fraunhofer approximation provides a simple and direct qualitative physical explanation for the diffraction oscillations and the oscillation phase shift phenomena observed in differential rotational state to state scattering cross sections for He on a number of small molecules. This approximation has been further developed to yield a simple analytical expression for the angular dependence of the inelastic cross sections. For the experimentally and theoretically well investigated systems He–N2 and He–CH4 the Fraunhofer formula is found to reproduce the measured cross sections to within better than a factor of 2. For the investigated collision energy Ecm ≊30 meV (≊3 kJ/mol) the deformed sphere interaction potential model used in the Fraunhofer approximation appears to be closely related to the zero crossing equipotential line of the full interaction potential. The relationship to the cluster model of molecules composed of atomic hard spheres is discussed. The dependence of the rotational excitation on the interaction potential is shown to be primarily a dependence on the equilibrium positions of the atoms in the molecule.