Unreactive Interactions A BC

This model is widely used in the calculation of the probabilities of vibrational excitation. As for explicit r dependence of Ubc and Uabj it is controlled by the model accepted. In particular, the parabolic approximation for Ubc is frequently assumed (the free BC is simulated by the harmonic oscillator) and the exponential function is used for Uab- However, whatever the actual form of U, the approximation (10.6) permits the construction of a general pattern of the potential 

Let the initial vibrational energy of BC be zero. Then the approach of A and BC is represented on the surface by the rectilinear part of the trajectory running over the valley bottom. The vibrational excitation corresponds to the reflection of the mass point. The receding of A and of vibrationally excited BC is represented by the sinusoidal part of the trajectory which is connected by the countour line for the total energy. 

Consider now non-linear configurations. The dependence of the total potential U on the angle y is usually represented as the sum of spherically symmetric Vg and asymmetric Va contributions. The latter vanishes after averaging over all orientations. When the asymmetry is rather small, Va can be expressed by a rapidly converging sum over the Legendre polynomial (cos y). Thus 

There is at present a bulk of information on the interaction potentials for simple systems obtained both from ab initio calculations [413] and from experimental data on inelastic scattering in beams and on relaxation phenomena in gases [122, 581]. 

---