5. Dirac-Slater atomic potentials (data_SCF)

The starting point of all our numerical calculations is the model of relativistic single-electron transitions in a local, central potential. We have utilized a modified version of the relativistic Dirac-Slater HEX code (Liberman et al., 1971) to evaluate our atomic potentials. Although HEX was used as the basis for these SCF calculations, initiated over 25 years ago, a fresh start today would utilize a more modern code such as DAVID (Liberman and Zangwill, 1984). A copy of the source for RSCF is included in the code folder of the RTAB database for those who wish to duplicate or extend our work.

An important characteristic of the all our (as opposed to the work of other authors) elastic scattering data in the RTAB database is that it is consistently computed in the same Dirac-Slater potential. That is, form factors, anomalous scattering factors, photoeffect cross sections, bound-bound oscillator strengths, and S-matrix elements are all computed starting from the same Dirac-Slater potential. As a consequence, comparisons of predictions in different approximations are not unnecessarily complicated by differences in the underlying atomic model. As shown in Figure 1, there is considerable resonance structure in our evaluation of elastic scattering. As a consequence of using the same potential for computing the S-matrix and anomalous-scattering-factor approximations, the resonances shown in Figure 1 occur at exactly the same energy in both approximations. This useful feature will be exploited when we subsequently discuss interpolating on the S-matrix values.

The exceptions to this use of a single underlying potential model is the work of other authors (redistributed with their permission) that we've included in the RTAB database for completeness and convenience of potential users. The non-relativistic form factors due to Hubbell et al. (1975) (in 'data_NF'), and the differential scattering cross sections computed from these form factors (in 'tables_NF'), do not result from our Dirac-Slater potential. Also, the anomalous-scattering-factor code and database of Cromer and Liberman (in 'other/CromerLiberman83'; Cromer, 1983), and Henke et al. (1993) (in 'other/Henke93') do not result from our potential. The photoeffect cross sections of Scofield (1973) (in 'other/Scofield73') were computed in a Dirac-Slater potential, although not identically the one provided in the RTAB database.

The potential files are contained in a folder named 'data_SCF' and have filenames of the form 'ZZZ_scfIM' where

ZZZ is a 3 digit integer indicating the atomic number
'_scf' indicates that the file contains self-consistent-potential data,
'I' is an integer indicating the ioniticity ('0' => neutral atom),
'M' is a string indicating details of the atomic model used, some examples are,
- 'sl' => Slater exchange coefficient with Latter tail (potential goes to as 1/r at large distances),
- 'kl' => Kohn-Sham exchange coefficient (2/3 the Slater value) with Latter tail,
- 'cK' => Coulomb potential, electron in K shell.

For example, '082_scf0sl' indicates the potential for neutral Lead (Pb, Z=82) with a Slater-exchange coefficient and Latter-tail approximation.

The Dirac-Slater potentials are stored as UFO library-structured files containing four logical files: 'PARAMETERS' contains the input parameters to the RSCF code used to generate this file; 'SUMMARY' contains a summary report on the results of the calculation; 'CONFIG' contains a report on the electronic configuration of the atom used in the calculation; and 'V' contains the potential as [r,V(r),Q(r)] tuples,

Figure 1. The resonant structure of elastic scattering through 90° for Lead (Pb, Z=82), observed in our SM and ASF calculations, is usually ignored in simpler approximations.

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Information date: Sep. 2, 2000 lk