A method for the calculation of Sommerfeld's screening parameters σ₁and σ₂for experimentally unresolved spin doublets

Abstract

It is well known that the Sommerfeld screening parameters U , and u2 for a spin doublet of levels can only be calculated if the individual energies of the two members of the doublet are known. In several cases, the resolution of the experimental method for finding the energies has proved insufficient and so only the energy of the unresolved doublet of levels has been reported. A new method has been developed for calculating these parameters for a spin doublet of levels by using the unresolved experimental energy values given by Bearden and Burr. The results of our calculations are presented. It is found that the energy values calculated by using these parameters in the Sommerfeld energy expression are in very good agreement with the recently reported resolved experimental energy values of the individual components of different spin doublets.

A new method for the calculation of Sommerfeld screening parameter σ1 in x-ray spectra

“…A new method for obviating this difficulty was developed by Misra et al [7]. Inserting the values of ½ and ¾ obtained by this method in the Sommerfeld formula, individual energy values for the two members of such spin doublets were calculated and found to be in very good agreement with the resolved energy values which are obtained in the mean time by experiment [22].…”

“…However, as pointed by Misra et al [7] there certainly are some approximations inherent in these calculations as well as some hitherto unknown systematic effects which are responsible for the differences between the theoretical and experimental electron binding energy values. One must also remember that these theoretical studies relate to free atoms and that though there is very good agreement between their results and experiment in the case of simple atoms (that is atoms with closed shells or with one electron outside a closed shell), such is not the case for complicated atoms.…”