The "incoherent or 'Compton' crosssection" σ_{incoh} is likewise not always incoherent but represents the inelastic scattering contribution to the total interaction coefficient. This also depends upon the atomic form factor. The atomic photoabsorption crosssection τ_{PE} or σ_{PE} is directly related to the imaginary component of the form factor.
Simple addition of crosssections: Simple addition of crosssections from scattering and photoabsorption depends on the relative phases of scattered waves being incoherent, and may in some cases be quite inappropriate. In general the amplitudes should be summed including any relative phases. However the simple summation of the crosssections represents a common and often very good approximation.
Contributions of highenergy terms in the mediumenergy xray regime: The remaining terms in (eq 8) represent large contributions only for MeV energies and above, and as such are not the concern of the current discussion. They represent the pair production crosssection in the nuclear field (κ_{n}), the pair production crosssection in the atomic electron field (or triplet crosssection, κ_{e}), and the photonuclear crosssection σ_{p.n.}. An excellent review of these crosssections is given elsewhere [2]. Below MeV energies all interaction coefficients depend directly and implicitly upon the real and imaginary components of the atomic form factor. The graphs below depict the mass attenuation coefficients and the values of the form factors themselves, since it is critical to present not only quantities in use but also the fundamental parameters underlying the used quantities.
Dependence of f′ and f″ on angle: There have been concerns regarding a possible angular dependence (or scattering vector dependence) of the anomalous dispersion (i.e., energydependent) components f′ and f″ of the form factor (eq 4) and (eq 7). The current status of this query is well represented by Creagh and McAuley, who summarize that there is no dependence of either quantity upon scattering vector [17]. Hence all angular dependence of the form factor for an isolated atom is contained in f_{0}.
The justification for the separability of the angular and energydependent components as given in (eq 4) is a related issue. If the two dependencies upon angle (in f_{0}) and energy (in f′) are truly independent, then the components are clearly separable. However, it has been argued that this separation may not be valid for large energies and large momentum scattering vectors [18].
Because of this, some authors define a modified form factor (MFF)
Smatrix and general formalisms: Recent Smatrix computations have predicted new structure in angular dependences of Rayleigh scattering [1820]. A recent report and review for incoherent scattering factors has summarized much important information in this area [21]. There is no doubt that higher order corrections, particularly relating to the relativistic correction factor, are important and observable in principle. However, it is often not realized that the relativistic formulations of Cromer and Liberman [2225] (and most derivations since) are based on the following Smatrix (scattering matrix) equations for the superposition of the final states f (including ionized atoms, excited states, and elastic and inelastic scattered states) in a transition from the initial state i:
(eq 9) 
(eq 10) 
The scattering amplitudes T_{fi} in general are complex [26,27]. Most investigations have been restricted to coherent, forward scattering, and where changes in photon polarization do not occur.
All general theories make the isolated atom approximation and the IPA (independent particle approximation). Any variation between computations based on these theories are due to other limitations, not to the use of isolated atom or IPA. Experimental work relating to solids with very different nearedge structure from isolated atoms may be unable to be compared directly to these theoretical results. This can be used to investigate the redistribution of electron density in the formation of bonding in the solids, and can lead to improved XAFS calibration (see section 8.15). In some cases, this gives significant variation between one experiment and another. The comparison of different theoretical and computational schemes within these assumptions is unaffected by these solid state effects; and the conclusions below are largely independent of these concerns.
These approximations are usually combined with the electric dipole approximation to yield final computable results. In this sense all computations have made the same broad approximations. As seen below, most limitations in Chantler [16], Scofield [28], and Saloman and Hubbell [29] can be attributed to convergence problems rather than to higherorder corrections.
