Gyromagnetic ratio nuclear

A(g) is the signal intensity observed with an applied gradient g, A(0) is the intensity in the absence of an applied gradient, y is the nuclear gyromagnetic ratio, and (5 and A are time intervals of the pulsed field gradient spin—echo sequence. 

These equations can be also expressed as functions of the strength H of the main magnetic field by using a relation of = yH, were y is the nuclear gyromagnetic ratio. Such expressions may be more useful for the usual broad-line NMR spectrometry in which the main field is slowly swept under a constant rotating subfield. 

In Eqs. (7-11), fi is the nuclear gyromagnetic ratio, g is the electron g factor, fiB is the Bohr magneton, rGdH is the electron spin - proton distance, co, and cos are the nuclear and electron Larmor frequencies, respectively (co=yB, where B is the magnetic field), and A/fl is the hyperfine or scalar coupling constant between the electron of the paramagnetic center and the proton of the coordinated water. The correlation times that are characteristic of the relaxation processes are depicted as ... 

Here yN is the nuclear magnetogyric ratio, gN is the nuclear gyromagnetic ratio, and fa is the nuclear magneton ... 

Table 3.3 Nuclear Spin /, Nuclear Gyromagnetic Ratio gN, Isotopic Abundance, Nuclear Electric Quadrupole Moment Q, and NMR Resonance Frequency v at 1 Tesla (10,000 Gauss) for Nuclei of Interest to NMR and NQRa...

For chemically interesting nuclei, Table 11.10 lists values of the nuclear spin quantum number I, the nuclear gyromagnetic ratio gN/ the nuclear electric quadrupole moment Q, and the nuclear magnetic resonance frequency v (Hz, for H0 = 1 tesla). 

The maximum S/N gain expected from cross-polarization relative to a solid-echo sequence is given by the ratio of the nuclear gyromagnetic ratios and the heat capacities of the two spin reservoirs [33,34]. Equation (3) describes the change of magnetization from a reference state, Mgo (the equilibrium magnetization obtainable in the spin-echo experiment), to a final equilibrium state,... 

A further interesting feature arises in the comparison of proton and deuteron hy-perfine constants for the same radical. One normally expects these constants to be in the ratio of the nuclear gyromagnetic ratios, so that deuteron constants are expected to be a factor 6.514 39 smaller than those for the corresponding proton. We may calculate this ratio for the four constants of OH (OD) and SH (SD) witii the following results ... 

The Fermi contact interaction is the major mechanism for J coupling. It is governed by the electron density at the nucleus (S,) and the nuclear gyromagnetic ratio according to the expression... 

Here, ye and are the electronic and nuclear gyromagnetic ratios, respectively, and is the Boltzmann constant. The Knight shift, K, also has a simple relationship with the electronic density of states at the Fermi level through the Pauli susceptibility, xpaedit... 

The gN values are dimensionless and characteristic of the type of nucleus. yN is the nuclear gyromagnetic ratio. Some values are listed in Table 1, together with the corresponding quantum numbers I and Mj, in which the quantum number Mj allows for the space-quantization of... 

The first term results from the Fermi contact interaction, while the second represents the long-range dipole-dipole interaction. In the equations above, ge is the free-electron g factor, /Xe the Bohr magneton, gi the nuclear gyromagnetic ratio, and /xi the nuclear moment. Moreover, the nucleus is located at position R, and the vector r has the nuclear position as its origin. Finally, p (r) = p (r) — p (r) is the electron spin density. The only nontrivial input into these equations is precisely this last quantity, i.e. Ps(r), which can be computed in the LSDA or another DFT approximation. The resulting Hamiltonian can be used to interpret the hyperfine structure measured in experiments. A recent application to metal clusters is reported in Ref. [118]. 

Here Yi is the nuclear gyromagnetic ratio, Q is the nuclear quadrupole moment, -e is the charge of an electron, is the component of the gradient of the ligand electric field, and T) = (Vja - Vyy)/Vzz is the asymmetry parameter of that gradient. 

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