Sternheimer factor

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). 

A detailed review and summary of the experimental data as well as the results of calculations of the efg in the heavy lanthanide metals at low temperatures has been given by Pelzl (1972). It was found that in the metal the radial averages r of the 4f electrons appropriate to the quadrupole interaction are 10% smaller than in ionic compounds. In comparison with the magnetic hyperfine interaction (section 2.1.1.1) the additional reduction arises from increased closed shell shielding (1 Rq) in the metallic case. In addition, the conduction electrons increase the antishielding of the lattice efg due to their greater density outside the atomic sphere via the factor (1 + F) and to an increased Sternheimer factor (1 - 7 ) in the metal. 

A difference in between nuclear V inner Sternheimer factor... 

In metallic materials there might be an additional contribution from conduction electrons in a band of non-s character. Field gradients from conduction electrons still present many open questions, one of which is the choice of an appropriate Sternheimer factor. 

For nuclei that have perfect cubic site symmetry (e.g., those in an ideal rock salt, diamond, or ZB lattice) the EFG is zero by symmetry. However, defects, either charged or uncharged, can lead to non-zero EFG values in nominally cubic lattices. The gradient resulting from a defect having a point charge (e.g., a substitutional defect not isovalent with the host lattice) is not simply the quantity calculated from simple electrostatics, however. It is effectively amplified by factors up to 100 or more by the Sternheimer antishielding factor [25],... 

For some quadrupolar nuclei with a very small quadrupolar moment, the dipole-dipole mechanism contributes significantly to relaxation, e.g. 7Li. 87Rb has a very large quadrupolar moment and Sternheimer anti-shielding factor, and thus, quadrupolar relaxation dominates completely the same is true of 23Na and 39K. The Sternheimer anti-shielding factor describes how sensitive the NMR relaxation of a nucleus is to its electronic environment.37... 

Here ay is the second-order Stevens factor, is the Sternheimer antishielding factor and a2 is a screening constant. 

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. 

There are several approximate methods often useful in understanding the trends in the quadrupole parameters in a related series of molecules containing the same quadrupolar nucleus. One. due to Townes and Dailey, is essentially a localized orbital approach, in which attention is focused on changes in the orbital populations of the atom containing the quadrupolar nucleus, and polarization of the core electrons (the so-called Sternheimer polarization factor) is assumed to vary negligibly from one molecule to another. In the case for example,... 

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... 

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