Sternheimer

Of course there arc other contributors to the value of q besides the valence electrons. Additional effects are due to molecular interactions,22 induced quadrupole moments (Sternheimer, R. M., Phys. Rev. 105, 158, (1957), etc.)... 

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],... 

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... 

From the above discussion it becomes clear that in order to eliminate the spin-orbit interaction in four-component relativistic calculations of magnetic properties one must delete the quaternion imaginary parts from the regular Fock matrix and not from other quantities appearing in the response function (35). It is also possible to delete all spin interactions from magnetic properties, but this requires the use of the Sternheim approximation [57,73], that is calculating the diamagnetic contribution as an expectation value. 

Consider first the effect of the atomic electrons. A filled or half-filled electron shell has a spherically symmetric electron distribution, and as such gives rise to no electric field gradient (except through external deformation, i.e., Sternheimer antishielding). Thus, of all the atomic electrons, only the... 

M. Flato, Z. Marie, A. Milojevic, D. Sternheimer, and J. P. Vigier (Eds.), Quantum Mechanics, Determinism, Causality, and Particles, ISBN 9-02-770623-9, North-Holland, Dordrecht, 1976. 

J. P. Vigier, M. Flato, D. and J. Sternheimer, and G. Wathaghin, On the masses on non-strange pseudo-scalar mesons and the generalized Klein-Gordon equation (1966). 

J. P. Vigier, D. Bohm, M. Flato, and D. Sternheimer, Conformal group symmetry on elementary particles, Nuovo Cimento 38, 1941 (1965). 

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

---