IMPROVEMENTS IN COMPUTATION OF FORM-FACTORS

Tables for form factors and anomalous dispersion are of wide general u se in the UV, X-ray and gamma-ray communities, and have existed for a considerable period of time. The generality of these works has entaile d numerous simplifications compared to detailed relativistic S-matrix calculations. However, the latter calculations do not appear to give c onvenient tabular application for the range of Z and energy of general interest, whereas the former tables have large regions of limited val idity throughout the range of Z and energies, and in particular have l imitations with regard to extrapolation to energies outside tabulated ranges. Intermediate theoretical and procedural assumptions limit the precision and applicability of available tabulations and procedures. T his paper identifies regions of Z and energy where these assumptions f ail 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 photo electric absorption cross-sections. Revised formulae can lead to signi ficant qualitative and quantitative improvement, particularly above 30 -60 keV energies, near absorption edges, or at 30-3000 eV energies. Cu rrent experimental syntheses are not superceded by this approach, but examples are given where predictions underlying revised theoretical ta bles am in qualitative agreement with experiment as opposed to results in available syntheses. Recent theoretical developments involving sma ll corrections to earlier form factors are of limited usefulness if th e relatively large corrections discussed herein are not included.