Core polarisation term

An appropriate potential for many cases is the frozen-core Hartree—Fock potential with the addition of a core-polarisation term. 

Since K depends on the wavefunction density at the nucleus, the effect is dominated by s-electrons which is certainly true in metals with unpaired s-electrons. If the Pauli susceptibility and electron density can be independently measured then the Knight shift will give an independent measure of the s-component of the conduction electron spin density. These shifts are positive and are much larger than chemical shift effects, some typical values being Li — 0.025%, Ag — 0.52% and Hg — 2.5%. In other metals the situation is more complicated when the s-electrons are paired but there are other electrons (e.g. p but especially d). As only s-electrons have significant density at the nucleus the effects of these other electrons are much smaller. The hyperfine fields of these electrons induce polarisation in the s-electrons that subsequently produce a shift, termed core polarisation. 

When a bicontinuous cubic lipid-water phase is mechanically fragmented in the presence of a liposomal dispersion or of certain micellar solutions e.g. bile salt solution), a dispersion can be formed with high kinetic stability. In the polarising microscope it is sometimes possible to see an outer birefringent layer with radial symmetry (showing an extinction cross like that exhibited by a liposome). However, the core of these structures is isotropic. Such dispersions are formed in ternary systems, in a region where the cubic phase coexists in equilibrium with water and the L(x phase. The dispersion is due to a localisation of the La phase outside cubic particles. The structure has been confirmed by electron microscopy by Landh and Buchheim [15], and is shown in Fig. 5.4. It is natural to term these novel structures "cubosomes". They are an example of supra self-assembly. 

The final term in this potential model is that due to polarisation effects. In the solid environment there is likely to be some distortion of electron clouds due to the surrounding electric field, and this must be taken into account when modelling the interactions of an essentially ionic system. The polarisability in this case is modelled using the shell model of Dick and Overhauser. Here the atom is considered to consist of a massless charged shell, for the valence electrons, and a charged core. The two components are linked via a harmonic spring, and displacement of the valence electrons takes place with respect to the following equation... 

The higher states can be treated with the same method. The derivation of the unperturbed electronic energy is not difficult there. Instead the calculation of the perturbation term is tedious, and even more the effect of the polarisation of the core. But extrapolation from the known behaviour for ii = 0 (helium) could be sufficient to a large extent because of the good first approximation of the eigenfunction. 

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