Nuclear quadrupole electrical moment

Point charge and dipole electrostatic fields have been described in Chapter 4. There are more complex electrical systems created by irregularly distributed charges (refer to Appendix 3). It is shown in Appendix 3 that such a system can produce an electrostatic field, which can be described by the sum of terms differently dependent on the distance r 

Being charged, the nucleus has nonzero monopole contribution. Since nuclei possess the definite symmetry elements listed above, it cannot possess a dipole moment a dipole moment as a vector cannot coexist with the symmetry operations mentioned. This signifies that the nucleus does not possess a dipole moment. 

However, this does not prohibit a nucleus from having an electrical mnltipole moment of higher order quadrupole, in particular. In other words, the deflection of the nucleus from a spherical form brings about the existence of the qnadmpole moment eQ (refer to Appendix 3). Value eQ is measured in C m units (in SI). 

As shown in Appendix 3, the charged system elongated up to the z axes possesses a positive quadrupole moment, though for the flattened nucleus it is negative. 

This means that at 7=0, the quadrupole term is meaningless at 1=112, it cannot be measured and it is reliably measured at 7 l/2. 

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Isotope Natural abundance (%) Nuclear spin Electric quadrupole moment NMR frequency fora 23.5 kO field (MHz) Relative sensitivity... 

We often say that an electron is a spin-1/2 particle. Many nuclei also have a corresponding internal angular momentum which we refer to as nuclear spin, and we use the symbol I to represent the vector. The nuclear spin quantum number I is not restricted to the value of 1/2 it can have both integral and halfintegral values depending on the particular isotope of a particular element. All nuclei for which 7 1 also posses a nuclear quadrupole moment. It is usually given the symbol Qn and it is related to the nuclear charge density Pn(t) in much the same way as the electric quadrupole discussed earlier ... 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

Ru has a nuclear ground state with spin /g = 5/2 and a first excited state with 4 = 3/2" ". Electric quadrupole perturbation of Ru was first reported by Kistner [110] for Ru02 and ruthenocene this author has also evaluated the ratio of the nuclear quadrupole moments to be QJQ > 3. The sign and magnitude of the individual quadrupole moments are given in Table 7.1 (end of the book). 

In the literature [55], typical energies involved in the nuclear quadrupole moments -crystalline electric field gradient interactions range up to A E 2x 10-25 J. The measured AE seems to confirm the hypothesis that the excess specific heat of the metallized wafer is due to boron doping of the Ge lattice. 

To calculate the nuclear quadrupole moment from the measured quadrupole splitting, it is necessary to know the electric field gradient, q, at the Te nucleus as well as the asymmetry parameter, rj. These can be calculated in the Townes and Dailey approximation (4) by knowing the chemical bonding in Te. 

One method of determining nuclear quadrupole moment Q is by measuring the quadrupole coupling constant, given by eqQ/h, where e is the charge of the electron and q the electric field gradient due to the electrons at the atomic nucleus. The extraction of Q depends on an accurately calculated q. As a test of our finite-field relativistic coupled cluster approach, preliminary results for Cl, Br, and I are presented. 

The expressions for the various parts of the Hamiltonian (equation 1) are well documented and for our purpose and the following discussion it suffices to summarize the results for axially symmetric situations in angular frequency units with the equations 2-6, where and Ashielding tensor and the shielding anisotropy, respectively, D is the dipole coupling, eq or V is the electric field gradient at the nucleus, eQ is the nuclear quadrupole moment and the other symbols have their usual meaning ... 

For nuclei possessing an electric quadrupole moment, the electric field gradient at the atomic nuclei can be measured accurately by techniques such as nuclear quadrupole resonance, Mossbauer spectroscopy, nuclear magnetic resonance, and, for gaseous species, by microwave spectroscopy. The diffraction data permit an... 

Other effects frequently encountered in inorganic systems that can severely affect line shape involve relaxation processes arising from interactions of nuclear quadrupole moments with electric field gradients. For quad-rupolar nuclei (I 1), the quadrupolar contribution to the spin-lattice relaxation time Ti is given approximately by... 

Due to the electric quadrupole interaction, the Mi = 1/2 and Mi = 3/2 components of the 7 = 3/2 state of 57Fe split up, giving rise to the quadrupole splitting. Derived from the interaction of the nuclear quadrupole moment with the electric field gradient at the iron nuclei, AEq provides information about the asymmetry of the electron density around the iron nucleus. The electric field gradient at the iron nucleus can be calculated to obtain AEq (97). Since both 6 and AEq are related to the electron density at the nucleus, basis sets with an enlarged flexibility at the core region... 

The interaction between a nuclear quadrupole moment eQ and the electric field gradient q at that nucleus gives a term in the Hamiltonian... 

Nuclei with I > 1 have an electric quadrupole moment eQ (Section 5.8). As mentioned in Section 5.8, the presence of a nuclear quadrupole moment... 

PAC atomic probes (e.g., mIn or mHf) possess a nuclear quadrupole moment and a magnetic dipole. Even if no field acts on the PAC nucleus, the successive emission of the y-photons through an intermediate state exhibits an appreciable angular anisotropy between the emission directions. If the (isolated) nucleus is then brought into a perturbing field (e.g., on a specific lattice site which is next to a vacancy), the angular anisotropy becomes time-dependent due to the precession of the nuclear spin. For example, if the PAC nucleus in the crystal is exposed to a (static) electric... 

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