Nuclear electric-quadrupole interaction

The term in equation (4.54) represents the nuclear electric quadrupole interaction. 

The form of the nuclear electric quadrupole interaction in the effective Hamiltonian for a diatomic molecule is given in equations (7.158) and (7.161), with the latter applying only to molecules in n electronic states. The two parameters which can be determined from a fit of the experimental data are eqo Q and et/i Q respectively. Since the electric quadrupole moment eQ is known for most nuclei, an experimental observation gives information on q0 (and perhaps qi), the electric field gradient at the nucleus. This quantity depends on the electronic structure of the molecule according to the expression... 

Three more terms involving nuclear spin remain to be considered. The most important of these is the nuclear electric quadrupole interaction, which we take to have... 

We now come to the nuclear electric quadrupole interaction, and draw upon the results derived earlier for D2 in its ground state. The present problem is marginally more complicated because of presence of electron spin. We note first that if the quadrupole interaction is given by (8.249), i.e. 

The nuclear electric quadrupole interaction was described in detail in chapter 4, where we showed that it could be represented by the scalar product of two second-rank tensors ... 

The nuclear electric quadrupole interaction in equation (9.9) was introduced in chapter 4 it describes the sum of all the electric interactions between the protons in the nucleus and the electrons in the molecule, averaged over the positions of the latter ... 

The nuclear electric quadrupole interaction (QI) results from the coupling between Q and the EFG at the nuclear site. The EFG is a symmetric tensor quantity of zero trace and may be described by five independent parameters. When in its principal axis system (PAS), the off-diagonal matrix elements equal zero, and two parameters can fully describe the diagonal elements. The diagonal elements of a tensor in its PAS (Pn, P22/ and 1 33 in this case) are called the principal components. In practice, the SSNMR spectrum is usually described by the nuclear quadrupolar coupling constant, Cq, and quadrupolar asymmetry parameter, rj which are related to the principal components of the EFG tensor as follows ... 

The nuclear interactions observed in ENDOR are three the nuclear Zeeman, electron-nuclear hyperfine, and (for I > i) the nuclear electric quadrupole interactions. The Hamiltonian H including these nuclear interactions in an external magnetic field B is given as... 

The term in equation (4.54) represents the nuclear electric quadrupole interaction. We note that the nuclear spin vibration interaction, anticipated in equation (4.15), is actually identically zero. This is because the only vibrational mode for a diatomic molecule is that associated with bond stretching. Such motion does not generate any angular momentum and so does not produce a magnetic field with which the nuclear spin can interact. 

For the nuclear electric quadrupole interaction, the situation is rather different. Corrections similar to those just discussed, but arising from second-order terms involving the square of the magnetic hfs constants, change the value of P by about 2% for isotope 147, and 5% for 149. After these corrections, a ratio (147/149) of... 

The Pr ground state nuclear spin levels consist of three levels split by the second-order hyperfine interaction and the relatively small nuclear electric quadrupole interaction. In non-zero magnetic fields each of these levels is additionally split due to the enhanced Zeeman interaction (see Fig. 4), The Hamiltonian of this system has been given by Teplov. ... 

Statement is however in disagreement with NMR-measurements which seem to indicate, from the nuclear electric quadrupole interaction constant, that Yb in YbAl2 is divalent (Jaccarino et al., 1960). 

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