Magnetic dipole and electric quadrupole

The ground state as well as the 6.2 keV excited state of Ta possesses sizeable electric quadrupole and magnetic dipole moments (cf. Table 7.1 at the end of the book) which, in cooperation with the extremely narrow line width, generally yield well-resolved Mossbauer spectra even in cases with relatively weak interactions. 

What about parity in electric-quadrupole and magnetic-dipole transitions The quantities (3.58) are even functions. Hence for electric-quadrupole transitions, parity remains the same. Magnetic-dipole transitions involve angular momentum operators. For example, consider Lz = -ih(xd/dy — yd/dx). Inversion of coordinates leaves this operator unchanged. Hence for magnetic-dipole transitions, parity remains the same. 

The origin with respect to which the electric quadrupole and magnetic dipole operators are defined is indicated by the superscript. jiPp is the /3 component of the velocity operator. The connection between the quadrupole moment referred to or - for example the centre of nuclear masses - and the EQC is... 

In a subsequent paper, Munn [98] showed that the frequency-dependent local-field tensors accounted for the shift of the poles of the linear and nonlinear susceptibilities from the isolated molecular excitation frequencies to the exciton frequencies. The treatment also described the Davydov splitting of the exciton frequencies for situations where there is more than one molecule per unit cell as weU as the band character or wave-vector dependence of these collective excitations. In particular, the direct and cascading contributions to x contained terms with poles at the molecular excitation energies, but they canceled exactly. Combining both terms is therefore a prerequisite to obtaining the correct pole structure of the macroscopic third-order susceptibility. Munn also demonstrated that this local field approach can be combined with the properties of the effective or dressed molecule and can be extended to electric quadrupole and magnetic dipole nonlinear responses [96]. 

The higher-order bulk contribution to the nonlinear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fundamental electric field at the same point. To leading order, we may represent these non-local terms as being proportional to a nonlinear response incorporating a first spatial derivative of the fundamental electric field. Such terms correspond in the microscopic theory to the inclusion of electric-quadrupole and magnetic-dipole contributions. The form of these bulk contributions may be derived on the basis of symmetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SHG in a cubic material excited by a plane wave ((o) ... 

The electric quadrupole and magnetic dipole interactions both generate multiple-line spectra, and consequently can give a great deal of information. All three interactions can be expressed as the product of a nuclear term which is a constant for a given Mossbauer y-ray transition and an electronic term which can be varied and related to the chemistry of the resonant absorber being studied. 

The interaction between the electrons and the nucleus causes a very small perturbation of the nuclear energy levels in comparison with the energy of the nuclear transition. Such interactions are called hyperfine interactions. The main hyperfine interactions are the following electric monopole, electric quadrupole, and magnetic dipole interactions between the nucleus and the electrons (shell electrons, ligands, etc.). Such interactions can be sensitively monitored by Mbssbauer spectroscopy. The measurement of hyperfine interactions is the key to the utilization of Mbssbauer spectroscopy in a wide range of applications. 

In the general case of combined electric quadrupole and magnetic dipole interactions the peak positions can only be calculated numerically. 

In the case of the electric quadrupole and magnetic dipole interactions, the individual peaks have characteristic intensities relative to each other, which can confirm the assignment of the peaks to the appropriate nuclear transitions, and, in addition to the information provided hy 6, A, and A, it helps assigning the various subspectra of the M5ssbauer spectrum to lattice sites. The relative intensities can also furnish information on the orientational relationships in the sample/lattice (Schatz et al. 1996). 

Next, we will not consider terms higher than the second, i.e. the dipole term. This is in accordance with the electric quadrupole approximation, which is based on the fact that the effects of electric quadrupole and magnetic dipole terms are of the same order of magnitude and smaller than the electric dipole terms. They should therefore be treated together, as we do here, while second-order magnetic moments should be treated together with third electric moments, which we have not discussed either. The remaining (dipole) term... 

The additional electric quadrupole and magnetic dipole contributions from the bulk can be separated from the real surface contributions only under special conditions for example, if one modifies the surface layer in the form of an evaporated thin film and if one extracts the bulk contributions by calculating the interface contributions (Koopmans et al. 1993). The bulk contributions are proportional to the field gradient, meaning that a zone of about A/27T 5... 10 nm contributes to the total signal intensity. 

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