Core polarisation

Figure 2 Systematic trends of the oscillator strengths of the 3s2 S0- 3s3p P 0 transitions in the magnesium isoelectronic sequence. RQDO (pol) are the core-polarisation-corrected RQDO f-values. Both CIV3 and GRASP f-values correspond to the length form of the transition integral...

Table 5.3. One-electron separation energies for the lower-energy states of sodium (units eV). Experimental data (EXP) are from Moore (1949). The calculations are FCHE, frozen-core Hartree—Fock and POL, frozen-core Hartree—Fock with the phenomenological core-polarisation potential (5.82)...

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

Scattering from alkali-metal atoms is understood as the three-body problem of two electrons interacting with an inert core. The electron—core potentials are frozen-core Hartree—Fock potentials with core polarisation being represented by a further potential (5.82). 

Fig. 9.4. Elastic asymmetry for electron—sodium scattering at 1.0 and 1.6 eV (Bray and McCarthy, 1992). Circles, Lorentz et al. (1991) full curves, 15-state coupled channels with core-polarisation in the bound states broken curve, the same reaction calculation omitting core polarisation.

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. 

If such a wavepacket were formed in H, then the wavepacket would remain intact, with a fixed orientation in space, until some incoherent process (either spontaneous emission (see chapter 4) or collisions, discussed above) destroys the coherence. This arises because conservation of angular momentum for the excited electron applies strictly in this case. However, the experiment is performed in an alkali atom, which possesses a core, and there is a back reaction of the excited electron on this core (core polarisation), which depends on the degree of penetration of the excited electron into the core, i.e. on the quantum defect, which itself is a function of the angular momentum. Thus, the wavepacket precesses under the influence of a small potential due to the quantum defect of the alkali. It is found to follow a classical trajectory determined by the core polarisation potential. 

Core-polarisation and conduction-electron polarisation effects can be studied as can exchange polarisation of diamagnetic atoms in magnetic hosts. The lattice dynamics of the metal lattice are examined via the temperature dependence of the /-factor. Many metals approximate closely to the Debye model, and a Debye temperature has some significance. Impurity doping can... 

The chemical isomer shift in Fe-Al alloys increases regularly with increase in Al nearest neighbours probably indicating transfer of electrons to the Fe 3d-band which would also cause the reduction in core polarisation observed... 

This implies that the magnetic field at the iron is produced by the short-range core-polarisation effects, and that the conduction-electron polarisation is negligible because of there being little 4 density at the Fermi surface. This is consistent with the successful interpretations of the hyperfine field values using a 3(/-model only. 

Co doped MgO and CaO show both Fe and Fe-+ charge states. Application of an external magnetic field induces hyperfine structure, analysis of which confirms that both cations have a core-polarisation of —254<5 j> kG... 

A systematic study of the Eu/Yb and Eu/Ba alloys has been made [52, 53]. In the ytterbium system, the Curie temperature falls from 90 to 5 K and the saturation field also falls from 265 to 160 kG as the ytterbium content increases from 0 to 92 at. %. The relationships are linear apart from a discontinuity at 50 at. % where there is a phase change. Similarly for barium the Curie temperature falls from 90 to 40 K and the field from 265 to 206 kG as the barium content rises to 50 at. %. However, the chemical isomer shift is not significantly altered. The sign of the magnetic field is known to be negative from neutron diffraction data. Calculations suggest that a contribution of —340 kG to the field in europium metal arises from core polarisation, that +190 kG comes from conduction-electron polarisation by the atoms own 4/-electrons, and that —115 kG comes from conduction-electron polarisation, overlap, and covalency effects from neighbouring atoms. 

To summarise, the pure valence correlation (double excitations) tends to lower the spin-orbit splitting while the valence spinors relaxation (single excitations) tends to increase the splitting. Concerning the role of the core orbitals, the whole core polarisation, core-core and core-valence correlations taken into account via a semi-empirical CPP tend to enhance this splitting. ... 

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