Scattering approximation

In the first Bom approximation, the interaction between the photons and the scattering system is weak and no excited states are involved in the elastic scattering process. Furthermore, there is no rescattering of the scattered wave, that is, the single-scattering approximation is valid. In the Feynman diagrams (Fig. 1.2), there is only one point of interaction for first-Born-approximation processes. 

Complete formal analysis of the recoil corrections in the framework of the relativistic two-particle equations, with derivation of all relevant kernels, perturbation theory contributions, and necessary subtraction terms may be performed along the same lines as was done for hyperfine splitting in [3]. However, these results may also be understood without a cumbersome formalism by starting with the simple scattering approximation. We will discuss recoil corrections below using this less rigorous but more physically transparent approach. 

The kernels with two transverse exchanges in Fig. 4.4 give the following contribution to the energy shift in the scattering approximation... 

Due to the simplicity of the photon polarization operator the calculation based on the scattering approximation [8] is so straightforward that we can... 

P. L. Frattini, and G. G. Fuller, Conservative dichroism of a sheared suspension in the Rayleigh-Gans light scattering approximation, J. Coll. Inter. Sci., 119, 335 (1987). 

Inasmuch as molecular weights obtained from light scattering approximate Mw more closely than Mn, the necessary substitutions for Ott/dc from Eq. (4.35) and Mn are made in Eq. (4.34) to give... 

Torres-Verdin C., and T. M. Habashy, 1994, Rapid 2.5-dimensional forward modeling and inversion via a new scattering approximation. Radio Science, 29, No. 4, 1051-1079. 

Using the single scattering approximation and assuming that the atoms are very small (so that the incident wavefront is effectively plane) it is found that the oscillatory component of the EXAFS is given by 123,125... 

A full theoretical treatment of the scattering problem would involve solution of the Schrodinger equation for the system, with the potential energy expressed in terms of equation (8). This approach, however, is impossible at present since the atom-surface interaction is too strong for treatment to be reliable within the Born or other weak-scattering approximations but considerable progress has been made using both... 

We also begin in the elastic scattering approximation, which has the advantage of being very simple in this approximation, radiative channels are neglected, and all the observed spectral fluctuations are due to particle widths, i.e. to the decay of the excited state via autoionising channels. Radiative widths are included at a later stage, once the basic effects have been illustrated. 

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