Tensor nuclear quadrupole

In contrast, the second term in (4.6) comprises the full orientation dependence of the nuclear charge distribution in 2nd power. Interestingly, the expression has the appearance of an irreducible (3 x 3) second-rank tensor. Such tensors are particularly convenient for rotational transformations (as will be used later when nuclear spin operators are considered). The term here is called the nuclear quadrupole moment Q. Because of its inherent symmetry and the specific cylindrical charge distribution of nuclei, the quadrupole moment can be represented by a single scalar, Q (vide infra). 

The tensor of the nuclear quadrupole moment Q has nine elements... 

RBa2Cu40g (R = Sm, Y, Er) Nuclear-quadrupole coupling parameters at the rare-earth metal and copper sites from Cu ( Zn) and Ga( Zn) Mossbauer emission spectroscopy, EEG tensor in comparison with point charge model, shows that holes in lattices are localized primarily at chain-oxygen sites... 

Y2Ba4Cu7025 Nuclear quadrupole interaction at copper sites, EFG tensor at all sites is calculated using the point charge model, conclusion that holes in the Y2Ba4Cu70i5 lattice are localized predominantly at positions of chain oxygen... 

Oxirane is an important Lewis base in the present context. The O atom carries two equivalent n-pairs of electrons, as it does in H20, but oxirane has the advantage over water in that it is possible to determine both angles 0 and 9 for its complexes with HC1 and ClF because the non-zero off-diagonal element Xab(Cl) of the Cl nuclear quadrupole coupling tensor is available. The corresponding Lewis base in which an S atom carries two equivalent n-pairs is thiirane. Each of the pair of complexes (CL S- -HC1 and (CL S- -ClF has Cs symmetry and here it is the off-diagonal element Xac(Cl) that is non-zero... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

Quadrupole coupling, isomer shift Quadrupole tensor, nuclear Zeeman splitting, g values, coupling constants, relaxation times... 

The highly rhombic nuclear quadrupole tensor of the Cu(II) ion indicates that the total electron density at the copper site deviates considerably from any idealized symmetry. 

The nuclear quadrupole tensor of the Cu(II) ion is discussed in terms of the formalism outlined in Sect. 5.2.1. Kita et al.158) treated the Stemheimer antishielding factor (1 - as an adjustable parameter. The rhombicity of the measured quadrupole tensor was found to originate from the charge distribution on the ligands, the field gradient due to the copper valence electrons being nearly axially symmetric. 

ENDOR experiments can be performed in liquid solution, in which only the isotropic hfc s (Ajso) are detected. They are proportional to the spin density at the respective nucleus. Erom the assigned isotropic hfc s a map of the spin density distribution over the molecule can be obtained. In frozen solutions and powders the anisotropic hf interactions can also be determined. Eurthermore, the method allows the detection of nuclear quadrupole couplings for nuclei with 1 1. For dominant g anisotropy as found in many metal complexes the external magnetic field can be set to several specific g values in the EPR, thereby selecting only those molecules that have their g tensor axis along the chosen field direction. In such orientation-selected spectra only those hf components are selected that correspond to this molecular orientation ( single crystal-like ENDOR ). 

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 ... 

Nuclear Quadrupole Coupling Tensors in Some Aluminosilicates... 

Classically, the electric field gradient at a nucleus is produced by the arrangement of charges (i.e., other nuclei and electrons) about that nucleus 66). If the nucleus is quad-rupolar, as in the case of 27A1, then the interaction of its nuclear quadrupole moment, eQ, with the largest component of the EFG tensor, V33, is defined as the quadrupolar coupling constant, CQ ... 

X the 33S nuclear quadrupole coupling constant (expressed in frequency units), and r] the asymmetry parameter of the electric field gradient tensor (0[Pg.21]

An electrostatic quadrupole moment is a second-rank tensor characterized by three components in its principal-axis system. Since the trace of the quadrupole moment tensor is equal to zero, and atomic nuclei have an axis of symmetry, there is only one independent principal value, the nuclear quadrupole moment, Q. This quadrupole moment interacts with the electrostatic field-gradient tensor arising from the charge distribution around the nucleus. This tensor is also traceless but it is not necessarily cylindrically symmetrical. It therefore needs in general to be characterized by two independent components. The three principal values of the field-gradient tensor are represented by the symbols qxx, qyy and qzz with the convention ... 

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