NIST Physical Measurement Laboratory XCOM Photon Cross Sections Database

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2. Database for Elements

A comprehensive database for all elements over a wide range of energies was constructed through the combination of incoherent and coherent scattering cross sections from Refs. [12] and [13], photoelectric absorption from Scofield [14], and pair production cross sections from Ref. [8]. For scattering and pair production, the same cross sections are used as in other recent tabulations in Refs. [6,8,11], whereas for photoelectric absorption there is a small difference (omission of a renormalization correction) which is discussed below.

The incoherent (Compton) scattering cross sections in Ref. [12] were obtained from a combination of the Klein-Nishina formula and nonrelativistic Hartree-Fock incoherent scattering functions. Radiative and double Compton-scattering corrections were also included. The coherent (Rayleigh) scattering cross sections in Ref. [13] were calculated from a combination of the Thompson formula and relativistic Hartree-Fock atomic form factors. The photoelectric cross sections were obtained by Scofield [14] by a phase-shift calculation for a central potential and a Hartree-Slater atomic model. Scofield's results extend only up to 1.5 MeV. At higher energies, where the photoelectric cross section is quite small, a semi-empirical formula from Ref. [2] connects Scofield's values at 1.5 MeV to the asymptotic high-energy limit calculated by Pratt [15]. Cross sections for pair production given in Ref. [8] are based on complicated combinations of formulas from Bethe-Heitler theory with various other theoretical models to take into account screening, Coulomb, and radiative corrections. Different combinations were used in the near-threshold, intermediate and high-energy regions to obtain the best possible agreement with experimental cross sections.

For elements with atomic numbers from 2 to 54, Scofield [14] presented correction factors for individual atomic subshells, with which the photo-effect cross sections can be renormalized so that they correspond approximately to a relativistic Hartree-Fock model rather than the Hartree-Slater model used in the original calculation. This renormalization is most significant for the outer atomic shells; the total cross section is lowered by no more than 10 percent at energies above 1 keV. Scofield did not actually apply the renormalization to the cross sections given in his tables. The renormalization was used, however, in the tabulations in Refs. [6,8,11]. Recent reviews [16,17] indicate that, on the whole, agreement with experiment is better when the renormalization is not done. We have therefore omitted the renormalization in the database for the XCOM program.

Introduction   |   Database for Elements   |   Interpolation and Combination   |   Using the Program   |   References

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