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13. Summary and Typical Uncertainties

The modifications described herein lead to significant qualitative and quantitative improvement, particularly above 30-60 keV energies, near absorption edges, or at 0.03 keV to 5 keV energies. With limitations, the current scheme is able to extend to energies below 0.01 keV. More confidently, it also covers the region above 30 keV towards MeV energies, unlike most tabulations. The current tabulation is complementary to recent experimental syntheses. Examples are given where this formalism is in qualitative agreement with experiment, as opposed to results of the syntheses or of earlier theoretical tabulations. The theory of detailed corrections is summarized briefly.

There are regions of collective, valence, or band structure indicated in Ref. [16] which are not accounted for in the revised formalism presented here, while there are regions near edges and at higher energies accurate to within a few percent in the current calculations which are not adequately represented by Ref. [16] (or other methods). Where the preferred model is not obvious, the model variation may be used as an uncertainty. In many cases, the preferred model may be established by comparison to experimental data or by understanding the nature of processes occurring in the given energy regime. Typically errors of the current revision reduce to 1% at high energies away from edges, if photoabsorption is dominant. Uncertainty may reach 10-20% within 30% of edges, where scattering becomes significant, or in the 0.03-1 keV range (dependent on Z); and can be larger for energies less than 0.03 keV, regions of (collective) valence resonances, and in the near edge region for particular edges with bonding effects. There are tendencies for all schemes to fail below 0.1 keV (approaching a factor of two or more error).

The tabulation presented here resolves many of the difficulties encountered with previous tabulations, while some aspects remain to be treated in greater depth in the future, perhaps including aspects of collective behavior and near-edge effects. Improvement in application would follow use of better frel and f0 values, possibly allowing extension to higher energies and momentum transfers.

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