A semiclassical model for the vibrational excitation of spherical-top molecules in collisions with ions

A simple theory is presented to explain the previously observed single-mode vibrational excitation of the spherical-top molecules CH₄, CF₄ and SF₆ in collisions with H⁺ and Li⁺. The theory is based on a three-dimensional forced-oscillator model which has been modified to take account of many independent harmonic oscillators. For small-angle collisions the linear driving forces are the dipole-, polarizability- and quadrupole-derivatives taken from IR, Raman spectroscopy and simple estimates, respectively. To explain the results at larger angles near and beyond the rainbow it has been necessary to introduce short-range repulsive forces between the ions and the outer atoms of the molecule. For small angles both the predicted first moment of the energy transfer and the time-of-flight spectra agree quantitatively with the experimental results. At large angles, for which only the first moment of the energy is available, good qualitative agreement is obtained after a slight adjustment of the potential parameters. The energy transfer as a function of time is calculated and shows a different oscillatory behavior for the proton and Li⁺-ion systems. Also the effect of intra-mode coupling is investigated and shown to have only a small effect on the overall energy transfer. The paper closes with a discussion of the implications of these experiments and the possible role of rotational excitation. The field strengths in these ion scattering experiments are shown to be greater than in the strongest focused Q-switched laser pulses.