Dynamic Structural Factor in Thermal Regime

When the energy of incident pai ticle is not too large, the potential surfaces may be assumed to be plane. It means that K(r) = Vo(z). In this approximation by virtue of (1.3.6) one obtains 

For the sake of brevity, only the simplest case of plane rotating oscillator has been considered here. Nevertheless, more involved situations like polyatomic molecules modelled with non-rigid asymmetric tops with the account of intramolecular vibrational-vibrational and vibrational-rotational couplings, may be studied in the framework of the same formalism (Dubrovskiy et al. 1983 Bogdanov et al. 1985b). Some of the cases where cross effects determine the physical picture of scattering are discussed below (Sect. 2.4). 

For both Morse and Born-Mayer potentials —Vq z) = 2Wi z). Hence for the Bom-Mayer potential 

At present it is not clear enough wheather ImB really contributs to the scattering probability, because when the trajectory is continuous, the imaginary part of Pi often can be neglected. To clarify this question, it is necessary to study the generalized Langevin equations for the classical trajectory. 

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