Sommerfeld screening parameters for S1/2terms in X-ray spectra

The screening of the nuclear charge by other electrons in the atom is customarily allowed for by introducing two screening parameters sigma 1 and sigma 2 in the Sommerfeld relativistic two-body energy equation. The values of sigma 1 and sigma 2 for the S 1/2 levels (L 1 , M 1 etc.), along with probable errors, have been calculated for the atomic number range Z=17 to Z=103. The method used for the calculation involves no series expansion and consequent truncation errors. Also, more precise energy value data have been used for the calculations. It is shown for the first time that the sigma 1 curves for the N 6,7 and O 2,3 levels cross each other around Z=77, and that, sigma 2 >2 for the L 1 level and the value of sigma 2 does not increase progressively with n but sigma 2 (N 1 )< sigma 2 (M 4,5 ) and sigma 2 (O 2,3 )< sigma 2 (N 6,7 ), which necessarily implies that sigma 2 (O 1 )< sigma 2 (N 6,7 ). Possible reasons for these new results have been discussed.