Atomic form factors, incoherent scattering functions, and photon scattering cross sections

TLDR

The authors provide comprehensive tables of atomic form factors, incoherent scattering functions, and total Rayleigh and Compton scattering cross sections for elements 1–100 across a wide range of momentum transfers and photon energies, derived from state‑of‑the‑art theoretical calculations and including radiative and double‑Compton corrections, with additional data for hydrogen and H₂. The tabulated scattering data are compared graphically to experimental photon‑scattering angular distributions, validating the calculations.

Abstract

Tabulations are presented of the atomic form factor, F (α,Z), and the incoherent scattering function, S (x,Z), for values of x (=sin ϑ/2)/λ) from 0.005 Å−1 to 109 Å−1, for all elements A=1 to 100. These tables are constructed from available state-of-the-art theoretical data, including the Pirenne formulas for Z=1, configuration-into action results by Brown using Brown-Fontana and Weiss correlated wavefunctions for Z=2 to 6 non-relativistic Hartree-Fock results by Cromer for Z=7 to 100 and a relativistic K-shell analytic expression for F (x,Z) by Bethe Levinger for x≳10 Å−1 for all elements Z=2 to 100. These tabulated values are graphically compared with available photon scattering angular distribution measurements. Tables of coherent (Rayleigh) and incoherent (Compton) total scattering cross sections obtained by numerical integration over combinations of F2(x,Z) with the Thomson formula and S (x,Z) with the Klum-Nishina Formual, respectively, are presented for all elements Z=1 to 100, for photon energies 100 eV (λ=124 Å) to 100 MeV (0.000124 Å). The incoherent scattering cross sections also include the radiative and double-Compton corrections as given by Mork. Similar tables are presented for the special cases of terminally-bonded hydrogen and for the H2 molecule, interpolated and extrapolated from values calculated by Stewart et al., and by Bentley and Stewart using Kolos-Roothaan wavefunctions.