Screening doublets

A pair of terms having the same s and / but different L values is called as screening doublet (or irregular doublet). Lj-Ljj, Mj-Mu, MupMjy are examples of such screening doublets. 

From the first term of the Sommerfeld formula, one obtains the screening doublet law, which states that the difference between the square roots of the term values of a given doublet is constant, i.e. independent of Z. This term also gives the irregular doublet law which states that the difference between term values of an irregular (screening) doublet is a linear function ofZ. 

This equation, including succeeding terms, was obtained originally by Sommerfeld from relativistic considerations with the old quantum theory the first term, except for the screening constant sQ> has now been derived by Heisenberg and Jordan] with the use of the quantum mechanics and the idea of the spinning electron. The value of the screening constant is known for a number of doublets, and it is found empirically not to vary with Z. 

This increase should be observed for all screening constants, and in particular for the Sommerfeld fine-structure screening constants. The constancy of s reported for the Z-doublet throughout the periodic system (s = 3.50 Ai 0.08 from Z = 41 to Z = 92, Sommerfeld, Atom-bau pp. 447, 462) seems to contradict this. But actually this constancy proves the point. For s has been calculated with the complete formula,... 

The characteristic K line consists of a closely spaced doublet with a 2 1 intensity ratio between the K i and K 2 lines. This not a problem if a low spatial resolution recording medium, such as a fluorescent screen and image intensifier, is used but is a problem if high resolution nuclear emulsion plates are used. Then individual dislocation images are doubled because the diffracted beams from the two lines make different directiorrs in space, giving rise to a type... 

Applying this model, the 4f doublet of Th metal would appear to be a typical 5f-transition metal spectrum (i.e., with a split doublet where the 5 fs play the screening role of the d electrons in a d-transition metal). This is consistent with strong hybridization of 5f and (d, s) states as predicted by theory ... 

The ionization potential is determined by removing an electron from the highest occupied molecular orbital (HOMO). For an even n cluster, in a singlet state, the electron which is removed will see a greater nuclear charge than will an electron in the HOMO of an odd n cluster in a doublet state. This results because the nuclear charge for a closed shell orbital is only partially screened by the other electron in that orbital. In contrast, an odd electron in what is probably a more diffuse HOMO... 

C transitions to 2p 4f (and 4f ) 5d final states (Ce oxidation state). The doublets of the lines B and C are probably due to crystal field effects. As for XPS, we are able to calculate the 2p 4f 5d spectral weight from the C transitions. Note that in the case of X-Ray absorption, final state effects are of less importance due to the participation of the 5d photoelectron to the screening of the core hole. In good agreement with previously reported XPS and XAS spectra, the two methods give the same value of the spectral weights for pure CeC (ref. 15). 

In his paper in 1910 [125]. Sommerfeid applied his formula to interpret X-ray spectra and their fine structure. The doublet interval which is now known as Lu—Lul had been measured for a number of elements. Sommerfeid interpreted this as the difference in energy of an electron between the states n = 2, k = 1 and n = 2, k = 2, the electron in question moving under the influence of the nucleus but being partially screened from it by the other electrons in the atom. The screening effect he took into account by reducing the nuclear... 

The doublet-fragmentation time was measured by direct real-time observation of the doublets on flie screen and by analysis of a series of images acquired at 1-3 min intervals (25). The formation and disraption/coalescence of a doublet could thus be determined. 

Die Abschirmungskonstanten der relativistischen oder magnetischen Rontgenstrahlendubletts (German The screening constant of relativistic or magnetic X-ray doublets). Z. Physik 40 (1926) 344—350. 

---