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Photon Anomalous Scattering Factors

For Elements Z = 1 through 100

Over the Energy Range 1 eV to 10 MeV

Data is Available in a Simple Tabulated Text Format

Anomalous scattering factors are those of Cullen [2] computed using the relativistic dispersion relation as detailed in Pratt, et al. (1994) [3] in conjunction with the EPDL97 photoionization and photoexcitation data. Since the relativistic photoelectric cross section varies as 1/E at high energies, the relativistic dispersion integral is not convergent without considering other contributing effects. As Pratt, et al. [3] note, contributions from bound-electron pair production contribute to the same order and must be included for convergence of the integral. We estimate this contribution to the dispersion integral using analytic semi-relativistic expressions due to Costescu, et al. (1994) [4]. For more details on our utilization of bound-electron pair production (wherein the electron of the pair is created in a bound state of the atom) in evaluation of the relativistic dispersion relation, see Kissel, et al. (1995) [1].

The resulting anomalous scattering factors vary from a value of -Z at zero photon energy to a non-zero high energy limit as defined by Kissel and Pratt (1990) [5]. The accuracy of the convergence of our numerical anomalous scattering factor to -Z at low energy provides us with an important check on our numerical procedures as this limit is a statement of the relativistic Thomas-Reiche-Kuhn sum rule (see, Kissel, et al. 1995, for more details [1]). Note, using the convention defined here, the high energy limit is equal to the values defined by Kissel and Pratt, and is negative.

Anomalous scattering factors are included from 1 eV to 10 MeV. At higher energies they become progressively smaller and approach the limit of Kissel and Pratt [5], and have progressively less effect on the coherent cross section. By 10 MeV they have essentially no effect on the coherent cross sections and are not considered above 10 MeV.

[1] L Kissel, et al., "The Validity of Form-Factor, Modified Form-Factor and Anomalous-Scattering-Factor Approximations in Elastic Scattering Calculations," Acta Cryst. A51, pp 271-288 (1995).

[2] D.E. Cullen, "Program SCATMAN: A Code Designed to Calculate Photon Coherent Scattering Anomalous Scattering Factors and Cross Sections," Lawrence Livermore National Laboratory, UCRL-ID-103422, November 1989

[3] R.H. Pratt, L. Kissel and P.M. Bergstrom, Jr., "New relativistic S-Matrix results for scattering - beyond the usual anomalous factors/ beyond impulse approximation," in Resonant Anomalous X-Ray Scattering, G. Materlik, C.J. Sparks and K. Fischer, eds. (Elsevier Science Publishers, Amsterdam, 1994), pp 9-33.

[4] A. Costescu, et al., " Retardation and Multipole Effects in Rayleigh Scattering by Hydrogen-like Ions at Low and X-Ray Photon Energies," Phys. Rev. A 50, 1390-1398 (1994).

[5] L. Kissel and R.H. Pratt, "Corrections to Tabulated Anomalous Scattering Factors," Acta Cryst. A46, pp 170-175 (1990).