Inelastic and ballistic processes resulting from CsF–Ar collisions

Abstract

This paper continues the study of inelastic and ballistic collisions for the CsF–Ar system using the impulse approximation (IA). The IA expresses the atom–diatom potential as the sum of the two atom–atom potentials. The atom–atom interaction is approximated by a hard core potential, and the laboratory differential cross sections are calculated for an initial relative translational energy of 1.0 eV as a function of the laboratory recoil velocity of CsF. The calculated differential cross sections are in excellent agreement with the experimental measurements for all eight laboratory scattering angles for which the data are available. While the calculated results show no significant dependence on the initial relative velocity or on the initial vibrational quantum number of CsF, they do show a systematic variation with the initial rotational quantum number—the ballistic effect is more pronounced than that observed experimentally for initial quantum rotational numbers less than 30 and is not pronounced enough for rotational quantum numbers more than 100. Two mechanisms give rise to the ballistic peak. The first one is dominant when the laboratory scattering angle is equal, or nearly equal, to the laboratory angle of the centroid velocity. This mechanism transfers almost all of the relative translational energy into the internal energy of the diatom and magnifies the center-of-mass (c.m.) differential cross section almost a million times. This is due to a singularity in the Jacobian at very small c.m. recoil velocities, which physically means that a small solid angle in the laboratory frame can collect the signal from all 4π steradians in the c.m. frame. The second mechanism producing the ballistic peak, also determining the smallest and the largest laboratory scattering angles, is the rainbowlike singularity called edge effect. This mechanism becomes operative when the recoil velocity of the alkali halide in the c.m. frame is perpendicular to its recoil velocity in the laboratory frame. While the dynamics of the collision leads to a conversion of the proper amount of relative translational energy into internal energy of the diatom, the kinematic singularities mentioned above magnify the relevant c.m. differential cross sections leading to the observed ballistic effect. The ballistic effect, therefore, should be observable for any two collision partners under appropriate circumstances. The simple atom–diatom potential reproduces the experimental results very well, because (i) for inelastic scattering, the experimental observations correspond to large center of mass scattering angles for which the attractive part of the potential makes little contribution to the scattering process, (ii) for ballistic scattering, only the repulsive portion of the potential can cause a large amount of energy exchange between the relative translational and the internal degrees of freedom, and (iii) the calculated cross sections are insensitive to the details of the repulsive portion of the potential. A number of consequences of the theory, including the conclusion that the alkali halide beam in the experiments is rotationally unrelaxed, are discussed.