A refined version of the ‘‘shape consistent’’ effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin–orbit operators for the elements Rb through Xe. Particular attention was given to the partitioning of the core and valence space and, where appropriate, more than one set of potentials is provided. These are tabulated in analytic form. Gaussian basis sets with contraction coefficients for the lowest energy state of each atom are given. The reliability of the transition metal AREPs was examined by comparing computed atomic excitation energies with accurate all-electron relativistic values. The spin–orbit operators were tested in calculations on selected atoms.
A b initio averaged relativistic effective core potentials (AREP) and spin–orbit (SO) operators are reported for the elements Cs through Rn. Two sets have been calculated for certain elements to provide AREPs with varying core/valence space definitions thereby permitting the treatment of core–valence correlation interactions. The AREPs and SO operators are tabulated as expansions in Gaussian-type functions (GTF). GTF valence basis sets for the lowest energy state of each atom are tabulated. The reliability of the AREPs and SO operators is gauged by comparing calculated atomic excitation energies and SO splitting energies with all-electron relativistic values. Calculated atomic excitation energies are found to agree to 0.12 eV and SO energies to 3.4%.
We report precise measurements of differential x-ray scattering cross sections in Ne and He from 11 -22 keV and develop a method for obtaining predictions of comparable accuracy (1%). The measurement of ratios (total scattering in Ne to He and Compton to Rayleigh scattering in Ne) facilitates comparison to theories. We find evidence for the need to include nonlocal exchange, electron correlation, and dynamic effects for an accurate description at low Z and conclude that no single current theory is sufficient. [S0031-9007(98)06921-X] PACS numbers: 32.80.Cy, 07.85. -mThe use of x rays has been of fundamental importance in a number of fields, from demonstrating the validity of the quantum theory of radiation [1] to determining macromolecular structures such as DNA [2]. Recent advances in experimental techniques, such as the use of modern synchrotron sources that permit accurate experiments with well-defined initial conditions, coupled with similar advances in theory, such as the development of computer codes that calculate the relativistic S-matrix, now make it possible to perform precision investigations necessary to probe details in the description of atomic x-ray scattering. Among the phenomena that have recently been investigated are the need for multipoles in describing photon-atom interactions [3] and the effects of electron correlations on atomic processes ([4], and references therein). In this Letter we describe the need for nonlocal effects in describing x-ray scattering, even at relatively high energies, and confirm the need for inclusion of electron correlation and dynamic effects. In obtaining these results, we performed the first experimental decomposition of Compton scattering from Rayleigh scattering in free atoms. We also describe experimental and theoretical methods to obtain absolute scattering cross sections at an accuracy of ഠ1%. Our results have broad implications for calculations of elastic and inelastic photon scattering from light elements, which are widely used to determine crystallographic structures and electron momentum distributions.Relativistic S-matrix calculations of elastic photon scattering have been available for some time [5]. These have mainly been tested by high energy x-or g-ray scattering on solid targets composed of heavy elements [6] where they are superior to other, simpler techniques, leading to their wide acceptance as a benchmark [7]. Only recently [8] has a similar theory been successfully applied to Compton scattering. This theory has not been as extensively tested against measurements. In both cases, the emphasis has been on an accurate description of the photon-atom interaction. The main approximations are made in the description of the atom, which is assumed to be spherically symmetric and with the electron-electron interactions included only within the independent particle (IPA) and local exchange approximations.Simpler predictions for these cross sections can be obtained by calculating form factors (FF) for Rayleigh scattering, and Compton profiles, using the impu...
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