### 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.