Relativistic atomic form factors and photon coherent scattering cross sections

Tabulations are presented of relativistic Hartree-Fock atomic form factors F (x,Z), for values of x (=sin(ϑ/2)/λ from 0.01 to 109 Å−1, for all elements Z=1 to 100. For Z=1, F (x,Z) is given by the exact expression of Pirenne. For Z=2 to 98, x=0.01 to 2.0 Å−1, the tabulated values are those of Cromer and Waber given in the International Tables for X−Ray Crystallography (Vol. IV, 1974), based in part on the work of Doyle and Turner. For Z=21 to 92, x=2.2 to 6.0 Å−1, the present tables are based on the values of Doyle and Turner and additional values (Z=44,60,68, and 74) as given by O/verbo/. For Z=3 to 20.x=2.2 to 45 Å−1, Z=21 to 92,x=62 to 45 Å−1 the tables are interpolated from values given for 36 elements by O/verbo/, extended to x=109 Å−1 using O/verbo/’s corrections to the Bethe-Levinger K-shell expression. The remainder of the table is filled in by interpolation and extrapolation, guided for high x-values by the Bethe-Levinger result. Tables of relativistic coherent (Rayleigh) scattering cross sections, obtained by numerical integration of the Thomson formula weighted by F2(x,Z), are presented for all elements Z=1 to 100, for photon energies 100 eV (λ=124 Å=12.4 nm) to 100 MeV (λ=0.000 124 Å=12.4 fm). Departures from the nonrelativistic coherent scattering cross sections tabulated in J. Phys. Chem. Ref. Data 4, 471 (1975) are less than 1% for Z20. However for a high-Z element such as lead, for example, the relativistic coherent scattering cross section is systematically higher by less than 0.4% below 1 keV, by 8% at 100 keV and by 13% above 1 MeV.