Magnetic core polarization

The magnetic parameters of aquo-Mb obtained from Fig. 44 are collected in Table 15.1. The theoretical A values for the heme and histidine nitrogen, which are about 50% smaller than the observed values, have been determined by Mun et al.242), using an extended Hiickel-type calculation. According to these authors, the agreement between theoretical and experimental values could perhaps be improved further by considering electron core polarization effects. 

However, the ratio of Hint to the effective magnetic moment of the host atom is almost constant for the three alloys, as is to be expected if conduction electron polarization is the cause of the internal fields. Accurate theoretical estimates of the contributions to Hint from conduction electron polarization and from core polarization have not been made yet. 

That happens because all windings share the same magnetic core, despite the fact that they are not physically (galvanically) connected to each other. Similarly, all the dotted ends also go low at the same time. Clearly, the dots are only an indication of relative polarity. Therefore, in any given schematic, we can always swap the dotted and non-dotted ends of the transformer, without changing the schematic in the slightest way. 

Conduction electrons in broad bands of s- and p-like character contribute to all three quantities (sp). The Landau orbital diamagnetism (L) of these electrons is frequently considered only in the free-electron approximation, and taken care of by introducing a factor of two thirds in front of jp, whilst represents only the core diamagnetism. More localized non-s-like electrons in narrow bands give temperature-dependent contributions. In addition to the spin part (d) of the susceptibility, which is noticeable at the nucleus via core polarization (and finally Fermi-contact interaction) or via dipolar interaction (dip), van Vleck type induced orbital contributions of the magnetic susceptibility lead to orbital (orb) contributions of K and l/T, and eventually also to quadrupolar contributions (Q) of l/Ti- In this chapter we will use the symbol a, (instead ofH , ) for the hyperfne coupling constant(s) (with units of Oep. or Oe/electron) in the equation... 

In ferromagnetic materials the magnetic field experienced by the nucleus is much larger than in the paramagnetic materials discussed above. This hyperfine field can be determined experimentally by sweeping the resonance frequency in zero external field. There are several contributions to These comprise contributions due to core polarization of the inner s shell by the net d-spin or f-spin density and contributions due to conduction electron polarization by the atomic moment associated with the nucleus under consideration (/fj and a contribution due to conduction electron polarization caused by the atomic moments of the surrounding atoms H ). This latter contribution is often referred to as the transferred hyperfine field. Adding up, one therefore has... 

Europium metal, like ytterbium at the end of the lanthanide series, loses only 2 electrons to the conduction band, and so retains a half filled 4f shell. Thus the observed C must be caused by core polarization effects i.e. since L 0, the magnetic field produced at the nucleus of the Eu ion is due mainly to polarization of electrons in closed shells by the spin moments of the 4f electrons. In the other rare earths this interaction is completely masked by the much larger field due to the orbital angular momentum of the 4f electrons. 

Figure 14. Nilsson diagram for odd neutrons close to N = 82. The Fermi levels for N = 83, 85, and 87 indicate a successive filling of the/)/2 shell. On the right, the experimental magnetic dipole and electric quadrupole moments are compared with the results from particle-rotor calculations assuming deformations of e = 0.10 and 0.15. The trend of the quadrupole moments reproduces the increase of coupling to the collective motion, while the discrepancy in the trend for the magnetic moments is understood as a change of core polarization.

We have extended the Bohr-Weisskopf theory, based largely on the nuclear single particle model with the inclusion of core polarization in the evaluation of the effect of finite size of the nuclear magnetization. This model was found quite successful in ac-... 

It is clear that it is impossible to obtain a reversal in sign of A for these cesium isotopes from a relation e = const.as the magnetic moments increase monotonically. A physical explanation for the reversal given when these data were obtained was a possible break in the variation of the nuclear size at the shell closure with magic number N = 82. This now appears to be supported by recent isotope shift measurements in cesium Fig. 4. The core polarization (configuration mixing) model did allow us this sign reversal. 

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