Dynamic form factor

In summary, the movement of a high-energy electron in a solid may be described by a set of three Equations (1), (4) and (6). From these equations we may conclude that for high-energy electron diffraction the problem of multiple elastic and inelastic scattering by a solid is entirely determined by two functions, i.e. (1) the Coulomb interaction potential averaged over the motion of the crystal particles (V(r)> and (2) the mixed dynamic form factor S(r, r, E) of inelastic excitations of the solid. 

The above transition probabilities can be written in terms of one-sided time-correlation functions. For this purpose we define the dynamic form factor 5 B(k, od) as... 

If one returns to u space by Fourier transforming, one obtains the self-dynamical form factor S,(k, < >), the real part of. which is... 

Figure 12. The half-widths of the Lorentzian lines contributing to the real part of the self- dynamical form factor...

Dynamical form-factor for Earth Geocentric gravitational constant Constant of gravitation Ratio of mass of moon to that of Earth... 

Detailed an2ilysis of the problem of light scattering in a one-atomic liquid (Mountain, 1966 Stanley, 1971 Crossignajii et al., 1975 Berne and Pecora, 1976 Flygare, 1978) leads to the dynamic form factor... 

On substituting these correlation functions into Equation 57 with subsequent Fourier transformation, an expression for the dynamic form factor i.s deduced (Berne and Pccora, 1976) ... 

Formulations in Liouville space, which Introduce superoperators through commutation relations, are very useful in the derivation of compact expressions for double-differential cross sections, for example taking the form of generalized Lorentzian distributions. They can also lead to cumulant expansions as shown here for dynamical form factors, but for more general situations. They also provide a way of treating thermal averages over initial distributions in a consistent way, where all the initially populated states are incorporated simultaneously in the calculations. 

---