Electric quadrupole interaction description

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

An instructive description of the first-order perturbation treatment of the quadrupole interaction in Ni has been given by Travis and Spijkerman [3]. These authors also show in graphical form the quadrupole-spectrum line positions and the quadrupole-spectrum as a function of the asymmetry parameter r/ they give eigenvector coefficients and show the orientation dependence of the quadrupole-spectrum line intensities for a single crystal of a Ni compound. The reader is also referred to the article by Dunlap [15] about electric quadrupole interaction, in general. 

Figure 8.53. Relationship between space-fixed (unprimed) and molecule-fixed (primed) axes for the description of the electric quadrupole interaction.

The expressions given above provide the theoretical formalism for the description of all forms of polarized Raman scattering through first-order in the magnetic dipole and electric quadrupole interaction of light with matter. This is sufficient to describe the various forms of ROA within the assumptions given above. 

Comparison can be made with the predictions of this simple molecular orbital model. The Fermi contact constant, for example, is expected to be small because the molecular orbital containing the unpaired electron has predominantly 2p atomic character. The observed contact interaction corresponds to only 6%, v character. The dipolar interaction is also in good agreement with this simple description. The electric quadrupole coupling is much more difficult to describe in simple terms because it involves all electrons. 

There are two other fairly common causes of apparent breakdown of the electronic selection rules. First, collisions with other atoms or molecules, or the presence of electric or magnetic fields, may invalidate selection rules based on state descriptions of the unperturbed species. Secondly, although the transition may be forbidden for an electric-dipole interaction, it may be permitted for the (much weaker) magnetic-dipole or electric-quadrupole transitions. 

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