The Sommerfeld screening parameter σ2 and theoretically calculated energies of atomic inner shells

Abstract

Using the recent theoretical atomic energy values of Huang et al. (1976), the values of the Sommerfeld screening parameter sigma 2 have been calculated for those spin doublet levels where calculations could not formerly be performed owing to the lack of experimental energy values. The method used was described earlier by Burr and Carson (1974) and involves no errors arising from the truncation of the series expansion of the Sommerfeld-Dirac relativistic energy expression. It is found that: (i) sigma 2 is a function of Z for all the spin doublets studied; (ii) the sigma 2 values calculated smoothly fit in the gaps in the sigma 2 against Z curves drawn by Burr and Carson; (iii) the sigma 2 values which show excessive scattering in the sigma 2 against Z curves drawn by Burr and Carson have been recalculated and are found to fit much better in the sigma 2 against Z curves; (iv) there exists a dip in the sigma 2 values in the regions of inner-shell filling (3d,4d, 4f,5d etc.) for all the doublets studied; (v) the sigma 2 values become negative for Z=22-25 (3d filling region) for the M2M3 spin doublet; and (vi) comparison of the sigma 2 against Z curves obtained by using the experimental energy values on the one hand, and the Huang et al. theoretical energy values on the other hand shows that the dips are quite pronounced in the latter case.