Anomalous Scattering Factors

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ASF Calculation

Atomic symbol or number (H-Es, or 1-99)

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photon energy (keV, 0-10000)

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minimum energy (keV, min. 0)
maximum energy (keV, max. 10000)
energy increment (0 => default grid)

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This form provides access to an extensive library of anomalous scattering factors calculated using relativistic Hartree-Fock-Slater wavefunctions. These data are available for all elements Hydrogen (Z=1) through Einsteinium (Z=99) and all photon energies 0-10,000 keV. A variable energy grid is used to ensure that two-point linear interpolation yields accurate intermediate results. These data include the high-energy limit corrections tabulated by Kissel and Pratt (1990) and the contribution of bound-bound atomic transitions.

Our anomalous scattering factors are provided in one of three forms:

  1. Anomalous scattering factors f',f'', defined relative to the nonrelativistic high-energy limit, are useful with the conventional form factor f(q). The f',f'' values shown here utilize the physics phase convention (see Pratt et al., 1995), wherein the sign of f'' differs from that commonly used in the crystallographic literature.

    The anomalous scattering factors of Cromer and Liberman (see, for example, Cromer and Liberman, J. Phys. Chem. 53, 1891-1989, 1970) are widely used in the crystallographic community. If we designate these factors as f'CL, f''CL, the sign relationship of these values to our factors is

    f'CL ~ f' ,
    f''CL ~ -f'' .

  2. Anomalous scattering factors g',g'', defined relative to the relativistic high-energy limit, are useful with the modified relativistic form factor g(q) (see Kissel et al., 1995). These factors are related to f',f'' by

    g' = f' - f'HEL ,
    g''= f'' ,

    where f'HEL represents the high-energy limit of f' (see, for example, Kissel and Pratt, 1990).

  3. The anomalous scattering factors f1,f2 (see, for example, Henke et al., At. Data Nucl. Data Tables 54, 181-342, 1993), are related to our anomalous scattering factors, and those used in the crystallographic literature by

    f1 = N + f'CL = N + f' = N + g' + f'HEL ,
    f2 = f''CL = -f'' = -g'' ,

    where N is the number of bound electrons.

For more information on anomalous scattering factors, see

"Validity of Form-Factor, Modified-Form-Factor and Anomalous-Scattering-Factor Approximations in Elastic Scattering Calculations," by Lynn Kissel, B. Zhou, S. C. Roy, S. K. Sen Gupta and R. H. Pratt, Acta Crystallographica A51, 271-288 (1995).

"New relativistic S-matrix results for scattering - beyond the usual anomalous factors/beyond impulse approximation," by R. H. Pratt, Lynn Kissel and P. M. Bergstrom, Jr., in RESONANT ANOMALOUS X-RAY SCATTERING, edited by G. Materlik, C. J. Sparks and K. Fischer (Elsevier Science, Amsterdam, 1994).

"Corrections to Tabulated Anomalous Scattering Factors," by Lynn Kissel and R. H. Pratt, Acta Crystallographica A46, 170-175 (1990).

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Information date: August 8, 2000 lk