Integral cross sections, collisional

In Eqs. (14.3) and (14.4) fil is the ns-(n — l)p dipole matrix element. Eq. (14.3) makes it apparent that the requirement for driving the transition is that the time integrated interaction be one. Solving Eq. (14.4) for b2, ignoring factors of n, gives the cross section crR for the resonant collisional energy transfer. Explicitly,... 

A final aspect of these radiation collisions, shown experimentally by Thomson et a/.,17 is that the cross section integrated over all the collisional resonances increases with the rf field. Since the mth collisional resonance has a cross section of o = oR Jm KEmvJ/oj) and 2m J2m(x) = 1, in general, 2 om > crR.17... 

Potential energy surfaces of weakly bound dimers and trimers are the key quantities needed to compute transition frequencies in the high resolution spectra, (differential and integral) scattering cross sections or rate coefficients describing collisional processes between the molecules, or some thermodynamic properties needed to derive equations of state for condensed phases. However, some other quantities governed by weak intermolecular forces are needed to describe intensities in the spectra or, more generally, infrared and Raman spectra of unbound (collisional complexes) of two molecules, and dielectric and refractive properties of condensed phases. These are the interaction-induced (or collision-induced) dipole moments and polarizabilities. 

Figure 12. The initial- and final- state energies, Wi and Wf in a high frequency rf field. Only two cycles of the rf field are shown. Each time Wi = Wf a collisional interaction occurs and the relative amplitude of ipi and ipf change. If — 4>+ = 27T N, then the transition amplitudes over successive cycles add constructively and a resonance in the cross section is observed. For the maxima in the cross section 4> and 4>+ must separately be equal to integral multiples of 2tr.

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