Nuclear spin, magnetic

We attempt to describe NMR Imaging in a simplified manner using only three essential equations that explain why we see a signal and what it looks like. The first equation describes the nuclear spin magnetization, thus the strength of the NMR signal (and indeed much more) ... 

Equation 1 was derived assuming that the nuclear spin magnetizations are at thermal equilibrium values prior to the start of the presaturation. In practice, due to time constraints on the instrument, this condition may not usually be reahzed and the nuclear spin magnetization can generally be in a quasiequilibrium state prior to presaturation. If (tj + t) is the delay between two consecutive 90° observe pulses, where t is the presaturation period and fa is the time delay before presaturation (this includes the data acquisition time for the previous pulse), then the appropriate expressions for STD and for control NMR spectra are given by ... 

In the chemical exchange mechanism, the nuclear spin magnetization migrates together with the spin, which changes the site i j) but not polarization (a,/3) ... 

Evidence that the proton lies midway between the fluorine atoms in the crystal KHF has been provided by entropy measurements,28 study of the polarized infrared spectrum,29 neutron diffraction,80 and nuclear spin magnetic resonance.81 The uncertainty in the location of the proton at the midpoint between the fluorine atoms is reported to be 0.10 A for the neutron diffraction study and 0.06 A for the nuclear magnetic resonance study. 

The interaction between the electron and nuclear spin magnetic moments is the sum of the terms (8.105) and (8.109). Our discussion is limited to liquids. For liquids, the rapid rotation of the molecules causes... 

Natural abundance (%) Nuclear spin Magnetic moment /j,a Sensitivity Receptivity relative to 13C... 

Electron spin magnetic moment)-(nuclear spin magnetic moment) dipolar interaction energy ... 

The remaining important magnetic interactions to be considered are those which arise when a static magnetic field B is applied. The Zeeman interaction with a nuclear spin magnetic moment is represented by the Hamiltonian term... 

The remaining important interactions which can occur for a 2 or3X molecule involve the presence of nuclear spin. Interactions between the electron spin and nuclear spin magnetic moments are called hyperfine interactions, and there are two important ones. The first is called the Fermi contact interaction, and if both nuclei have non-zero spin, each interaction is represented by the Hamiltonian term... 

L)(I) hyperfine interaction between the electron orbital and nuclear spin magnetic moments,... 

Derivation of nuclear spin magnetic interactions through the magnetic vector potential... 

We now show how the many-electron Hamiltonian developed in the previous chapter may be extended to include magnetic interactions which arise from the presence of nuclear spin magnetic moments. Equation (3.140) represents the Hamiltonian for electron i in the presence of other electrons we present it again here ... 

This is a very important result. The first term in the last line of (4.13) represents the so-called Fermi contact interaction between the electron and nuclear spin magnetic moments, and the second term is the electron-nuclear dipolar coupling, analogous to the electron-electron dipolar coupling derived previously in (3.151). The Fermi contact interaction occurs only when the electron and nucleus occupy the same position in Euclidean space, as required by the Dirac delta function S(-i Rai). This seemingly... 

The second term in (4.15) above yields terms representing coupling between the rotational and vibrational motions of the nuclei and the nuclear spin magnetic moments. These terms will become more explicit when we later transform to new coordinates, analogous to those used in section 3.11. 

There remain two other important magnetic interactions involving the nuclear spin magnetic moments, which cannot be derived from the present analysis, although their presence is reasonably self evident by analogy with corresponding electron spin terms which we have derived earlier. They are the nuclear Zeeman interaction,... 

It is possible to obtain the nuclear spin magnetic interaction terms by starting from the Breit equation. We recall that the Breit Hamiltonian describes the interaction of two electrons of spin 1 /2, each of which may be separately represented by a Dirac Hamiltonian ... 

The nuclear spin magnetic dipole interactions are listed in equation (4.18) in a space-fixed coordinate system of arbitrary origin. The two forms of the electric quadrupole... 

In case (a) coupling two main possibilities arise. The first, which is expected to arise very rarely, if at all, implies that the magnetic interaction of the nuclear spin magnetic moment with the electronic orbital and spin moments is sufficiently strong to force the nuclear spin to be quantised in the molecular axis system. The basis kets may be expressed in the form rj, A S, S, A, 2 2, Iz, 2 2, N, J) this scheme is known... 

In these expressions the index i runs over electrons and a runs over nuclei. The Fermi contact term describes the magnetic interaction between the electron spin and nuclear spin magnetic moments when there is electron spin density at the nucleus. This condition is imposed by the presence of the Dirac delta function S(rai) in the expression. The dipole-dipole coupling term describes the classical interaction between the magnetic dipole moments associated with the electron and nuclear spins. It depends on the relative orientations of the two moments described in equation (7.145) and falls off as the inverse cube of the separations of the two dipoles. The cartesian form of the dipole-dipole interaction to some extent masks the simplicity of this term. Using the results of spherical tensor algebra from the previous chapter, we can bring this into the open as... 

The fourth term in (8.2) describes the dipole-dipole interaction between the nuclear spin magnetic moments. For two equivalent protons this term takes the form,... 

The major interaction between die nuclear spin magnetic moments in H2 and D2 is the dipolar interaction, equation (8.10). We should at least mention the existence of an electron-coupled scalar interaction this is very small compared with the dipolar interaction, and plays a very minor role in the gas phase measurements. In liquids, however, the dipolar interaction averages to zero, and the scalar coupling becomes the important observable interaction between nuclear spins. The power and range of applications of high-resolution n.m.r. in liquids depends ultimately upon the scalar shielding and spin-spin interactions. 

The dipolar hyperfine interaction is a through-space interaction of the electron and nuclear spin magnetic moments. As such, it is similar to the nuclear spin-nuclear spin dipolar interaction discussed earlier in connection with the H2 molecule in its ground electronic state. We shall meet the dipolar hyperfine interaction in many examples described later, so at the risk of seeming somewhat pedantic and repetitive, we here... 

At this stage of the theoretical analysis there are no matrix elements off-diagonal J this relatively simple situation will change when we consider nuclear spin magnetic and electric interactions. 

There are no nuclear spin magnetic moments in the predominant isotopic form of SO (i.e. 32S160), so that hyperfine interactions are absent. The orbital angular momentum vector L is coupled to the rotational angular momentum vector R to form the total angular momentum J. For a A state the projection of the value of L on the internuclear... 

Pauli spin vector Dirac spin vector electron spin magnetic moment nuclear spin magnetic moment rotational magnetic moment electric dipole moment Ioldy Wouthuysen operator gradient operator Laplacian... 

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