IMPROVEMENTS IN COMPUTATION OF FORM-FACTORS

Tables for form factors and anomalous dispersion are of wide general use in the UV, X-ray and gamma-ray communities, and have existed for a considerable period of time. The generality of these works has entailed numerous simplifications compared to detailed relativistic S-matrix calculations. However, the latter calculations do not appear to give convenient tabular application for the range of Z and energy of general interest, whereas the former tables have large regions of limited validity throughout the range of Z and energies, and in particular have limitations with regard to extrapolation to energies outside tabulated ranges. Intermediate theoretical and procedural assumptions limit the precision and applicability of available tabulations and procedures. This paper identifies regions of Z and energy where these assumptions fail and the improvement which can be achieved by their avoidance, both in tabulated ranges and by extrapolation. Particular concern involves the application of the dispersion relation to derive Re(f) from photoelectric absorption cross-sections. Revised formulae can lead to significant qualitative and quantitative improvement, particularly above 30-60 keV energies, near absorption edges, or at 30-3000 eV energies. Current experimental syntheses are not superceded by this approach, but examples are given where predictions underlying revised theoretical tables am in qualitative agreement with experiment as opposed to results in available syntheses. Recent theoretical developments involving small corrections to earlier form factors are of limited usefulness if the relatively large corrections discussed herein are not included.