Q, nuclear quadrupole moment

Q Nuclear quadrupole moment in units of femtometers squared (1 fm = 10 barn). Because the determination of quadrupole moments requires knowledge of the electron configuration... 

E energy of the level, Tt/2- half-life, a internal conversion coefficient, a natural abundance, / nuclear spin, Q nuclear quadrupole moment, b barn, /i nuclear magnetic moment, fin nuclear magneton, Co - nuclear absorption cross section. Wo- natural line width expressed as Doppler-speed interval. Absence of sign in the Q and n values means that the sign is undetermined (Cohen and Taylor 1987 Raghavan 1989 Pyykko 2001, 2008 NuDat 2009). 

Q nuclear quadrupole moment between source and absorber... 

Bq = magnetic flux density D = dipolar coupling constant D = effective dipolar coupling constant h = Planck s constant I = spin- nucleus / = coupling constant = field gradient tensor Q = nuclear quadrupole moment s = doublet splitting ... 

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... 

The experimentally observed quadrupole splitting AEq for Fe in inorganic compounds, metals, and solids reaches from 0 to more than 6 mm s [30, 32]. The range of AEq for other Mossbauer isotopes may be completely different because of the different nuclear quadrupole moment Q of the respective Mossbauer nucleus, and also because the EFG values may be intrinsically different due to markedly different radial distributions of the atomic orbitals (vide infra). As Q is constant for a given isotope, variations in the quadrupole coupling constants eQV can only arise from... 

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

The quantity pv C is the unpaired w-electron spin density at the carbon atom to which the hydrogen atom in question is bonded p c is defined as 1 times the fractional number of unpaired it electrons on the carbon atom, with the sign being determined by whether the net unpaired spin at the carbon atom is in the same or opposite direction as the spin vector of the molecule. The term -electron spin density is somewhat misleading in that pn is not an electron probability density (which is measured in electrons/cm3), but rather is a pure number. The semiempirical constant Q (no connection with nuclear quadrupole moments) is approximately —23 G. 

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 ... 

The spacing of the different energy levels studied by NQR is due to the interaction of the nuclear quadrupole moment and the electric field gradient at the site of the nucleus considered. Usually the electric quadrupole moment of the nucleus is written eQ, where e is the elementary charge Q has the dimension of an area and is of the order of 10 24 cm2. More exactly, the electric quadrupole moment of the nucleus is described by a second order tensor. However, because of its symmetry and the validity of the Laplace equation, the scalar quantity eQ is sufficient to describe this tensor. 

It is known from nuclear structure theory that nuclei with I > 1 also have an electric quadrupole moment Q, which is a measure of the asphericity of the nucleus. Nuclear quadrupole moments affect the rate of magnetic dipole relaxation, and nuclei with Q 0 are candidates for NQR measurements (see Table 3.3). 

Nuclear quadrupolar interaction arises from the coupling between the nuclear quadrupole moment Q and the EFG at the nuclear position. The EFG varies in space and is described by a traceless second-rank tensor. The EFG tensor is diagonal and its three principal components are VXXr Vyy and Rzz with the definition of VZZ > Vyy > VX < Such a principal-axis system for the EFG tensor is defined with the direction of the external magnetic field, as illustrated in Figure 3(A). It is convenient to express such quadrupolar interactions by using the following two parameters ... 

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