Nuclear spin density

Assuming that the lattice can, on the time scale relevant for the evolution of the nuclear spin density operator, be considered to remain in thermal equilibrium, a = a, and applying the Redfield theory to the nuclear spin sub-system allows us to obtain the following expressions for nuclear spin-lattice and spin spin relaxation rates ... 

The NMRI technique uses an induction coil surrounding the sample to image nuclear spin density that results from the nuclear spin system rearrangement. An initial magnetic pulsed field orients the nuclear spin system and then it relaxes back toward a random state. Because of the relaxation time and that tomographic reconstruction is needed to extract the 3-D details, there are time limitations (Altobelli et al., 1992) (currently of the order of 10-ms, at best). Consequently, the technique has been used mostly for steady or quasi-steady laminar flows because of the rather low data acquisition rate. However, modifications to allow turbulent and unsteady flows to be investigated have been reported and new... 

We next consider the effect of finite nuclear size on the nuclear spin Hamiltonian. The electric moments were derived by considering the Coulomb interaction of the nuclear charge density, expanded in a multipole series, with the electrons. By analogy, the magnetic moments are derived by considering the Gaunt interaction of the nucleus with the electrons. It is at this point that we must consider, at least as a formal entity, the nuclear wave function, and from it obtain a nuclear spin density that interacts with the electron spin density. 

In equation (bl. 15.24), r is the vector coimecting the electron spin with the nuclear spin, r is the length of this vector and g and are the g-factor and the Boln- magneton of the nucleus, respectively. The dipolar coupling is purely anisotropic, arising from the spin density of the impaired electron in an orbital of non-... 

Chemical shift relates the Larmor frequency of a nuelear spin to its ehemieal environment The Larmor frequency is the preeession frequency Vg of a nuclear spin in a static magnetic field (Fig. 1.1). This frequency is proportional to the flux density Bg of the magnetic field vglBg = const.)... 

Figure 1.1. Nuclear precession nuclear charge and nuclear spin give rise to a magnetic moment of nuclei such as protons and carbon-13. The vector n of the magnetic moment precesses in a static magnetic field with the Larmor frequency vo about the direction of the magnetic flux density vector Bo...

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 ... 

As mentioned in the start of Chapter 4, the correlation between electrons of parallel spin is different from that between electrons of opposite spin. The exchange energy is by definition given as a sum of contributions from the a and /3 spin densities, as exchange energy only involves electrons of the same spin. The kinetic energy, the nuclear-electron attraction and Coulomb terms are trivially separable. 

Spin Density Properties from the Electron Propagator Hyperfine and Nuclear Spin-Spin Couplings... 

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