Sternheimer effect

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. 

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],... 

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... 

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 operator and consequently the effective Hamiltonian are complex and have an imaginary (antihermitian) part that describes damping of the molecular excited states by interaction with the radiation field. Rather than using the eigenfunctions (3) of H m, it is then appropriate to choose the regular eigenfunctions of the total effective Hamiltonian (16) to represent the molecular excitations (Sternheim and Walker, 1972). 

In practice, one can first compute the bound state in the approximation of potential harmonics, with a fairly large Then the effect of nonpotential harmonics of low L, say can be estimated by solving Sternheimer-type equations. If... 

The effect was first mentioned by Goldhaber and Sternheimer [109], who speculated on the fine and hyperfine structure of exotic atoms consisting of an atomic nucleus and an fl . The splitting pattern would provide a measurement of the quadrupole moment as well as the magnetic moment of the ft . In ref. [109], a quadrupole moment Q = fm was assumed for numerical illustration, on the grounds that the has a mass comparable to that of the deuteron and hence might also have Q of the same order of magnitude. In fact much smaller values of Q are obtained from current quark models [108,110]. 

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. 

In practice, one does not examine naked nuclei, but nuclei in atoms. Because of the intervening electrons, the nuclei are submitted usually to a magnified efg (an Ji 2 perturbation). This screening due to the atomic electrons leads to an antishielding effect which was first calculated by Sternheimer (2-5). Since the original work of Sternheimer (2-5) ca. 30 years of work, in numerous papers, have been devoted to this topic. Fortunately, a recent review is available (6). The Sternheimer antishielding factors Yoo have been calculated recently by a fully self-consistent Hartree-Fock treatment for the alkali metal cations, and we shall quote these results (7) (Table 5). 

Perhaps the most serious limitation on both these approximate calculations is that the influence of both outer bound and coordinated charges must be scaled by a factor 7oo iu order to allow for the amplifying effect of inner electron motions on the externally applied field gradient. is called the Sternheimer antishielding factor, and lies typically between two and ten. Yet a further efg arises from the polarization of the inner orbitals by the electric quadrupole of I itself, but this term may readily be allowed for in any calculation. 

---