Sternheimer corrections

The Breit, Zwanziger and Sternheim corrections [22,14,15] lead to a result... 

Surveying the history of the theory of optical lanthanide spectroscopy, we can discern several main features the usefulness of Lie groups, following their introduction by Racah (1949) the relevance of the method of second quantization, as demonstrated by the use of annihilation and creation operators for electrons and the inability of the Hartree-Fock method and its various elaborations to provide accurate values (say to within 1%) of such crucial quantities as the Slater integrals F (4f,4f) and the Sternheimer correction factors R , for a free ion. The success of the formal mathematics is in striking contrast to the failure of the machinery of computation. This turn of events has happened over a period of time when... 

X 10 e.s.u. Some d-hybridization may also be involved, but d orbitals make a negligible contribution to the field gradient (4). The correction for the Sternheimer effect is also negligible in the Townes... 

Quantum mechanical calculations of 33S nuclear quadrupole coupling constants are not an easy matter (not only for the 33S nucleus, but for all quadrupolar nuclei). Indeed, the electric field gradient is a typical core property, and it is difficult to find wave functions correctly describing the electronic distribution in close proximity to the nucleus. Moreover, in the case of 33S, the real importance of the Sternheimer shielding contribution has not been completely assessed, and in any case the Sternheimer effect is difficult to calculate. 

The term (i - R) is the Sternheimer factor that corrects for the polarization of the ferric core by the EFG of the odd d electron, and (i - y) is the Sternheimer factor that takes into consideration the polarization of the ion s core electron by the external crystaline EFG (i7, 18). 

In those days electric field gradients could not be evaluated to a high degree of accuracy and correction factors for relativistic effects and polarization of the atomic core (Sternheimer shielding) had to be applied transferring this inaccuracy to the final NQM values. 

This term of the energy produces a polarization of the inner electrons which results in a deviation from spherical symmetry of the field experienced by the valence electrons. The effect of this is an appreciable change of the quadrupole coupling constant. Sternheimer - showed that the effect of the polarization of the inner shell electrons on the quadrupole coupling constant can be taken care of by multiplying the same constant by a correction factor 1 — f , which may be obtained by perturbation methods. 

The example of Na illustrates the problem in locating in the literature accurate values of the quadrupole moment Q and of the Sternheimer antishielding factor Yoo After undertaking a critical survey, I feel that values of Q close to 0.15 barn (0.15 X 10-28 2) are erroneous. Taking the experimental values obtained for the atom in the 3p or 4p state (13,14) and correcting for the antishielding contribution yields values of Q 0.10 X 10-28 ra (15), in excellent accord with results from calculation (16). 

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