Anti-Stokes neighborhood

To determine the 2n moments by a finite part of a spectrum, it is possible to approximate the inelastic cross section using (2.34). The function q(Z) changes on a constant ih h > 0). This constant and the moments may be determined with coincidence between the experimental curve and the constructed approximation. If the function (r) conserves sign up to distances that are comparable with the molecular diameter, the line of losses will appear only in the Stokes (anti-Stokes) neighborhood of the respective molecular term. In this case Ig e) is nonzero only on the negative (positive) half-axis, and the function q Z) = ih/ — Z (= ih/ /Z), h>0,is an appropriate choice. 

From (3.17), it follows that in the neighborhood of a critical point (x = 0), the correlational contribution scales in relation to the gas limit, near the impact cordinate A in the Stokes neighborhood and also in the asymptotic region of the anti-Stokes neighborhood of a single resonance ... 

Following Eqn. (3.24) the spectral line is similar to that of a one-component system in that it is strongly asymmetric and the rate of change of Ig e) in the Stokes and anti-Stokes neighborhoods is different. Analysis of (3.24) shows that EELS near the resonances has a complex behavior and depends strongly on the distance from the critical point, the values of the spectral intervals of energy loss close to the impact core A, and concentrations of the molecules of species 1 and 2. 

Note that if all (-> 0, the anti-Stokes neighborhood disappears and, in neglecting correlational effects (gf- 1), we obtain l g°Hs) -F... 

Thus in the Stokes neighborhood of a dipole-forbidden resonance formed by long-range interparticle correlations, the correlational structure of EELS takes changes close to the phase separation critical point. In the asymptotic anti-Stokes neighborhood, the correlational behavior is independent of the critical point behavior. 

In the neighborhood of the Van Hove singularities (fi > 0, vh) this scaling behavior disappears. Finally, the anti-Stokes impact core neighborhood is practically constant. The limit transition x-> 0(7 -< T,)... 

Finally, the anti-Stokes impact core neighborhood is practically constant and depends only on the thermodynamic state of the system. In the limit 3(.(i.2) 0 the scaling behavior of N e) is close to that of the second type of Van Hove points V(6) 1 -I-(2 /C g ). 2> 2 J. Note that the... 

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