Spin angular momentum gyromagnetic ratio

The magnitude of the magnetic moment jjln of a nucleus N is directly proportional to its spin angular momentum J, with the constant of proportionality defined as the gyromagnetic ratio (7n)- That is,... 

In this equation, u equals the magnetic dipole, equals the gyromagnetic ratio for spin X, and I equals the spin angular momentum. 

For the nuclei of each element, the magnetic moment, )X, is directly proportional to the spin angular momentum, I, the proportionality constant, 7, being known as the magnetogyric or gyromagnetic ratio, i.e. 

A factor of 2 in front of the spin angular momentum is the experimentally determined gyromagnetic ratio of the electron (actually this is 2.0023). It is more convenient to express this in terms of the total angular momentum J = L + S by introducing the Lande g-factor. 

S is the sum of the spin quantum numbers, to which each electron contributes /2 and g is the gyromagnetic ratio, i. e. the ratio of the magnetic moment to the angular momentum. For a free electron, g = 2. 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

This form makes it more obvious why y is referred to as the gyromagnetic ratio. Equation (11.16b) is valid both for angular momentum and spin, but of course the value is different for electrons and protons. The angular velocity Wy of the precession is foimd to be... 

The gyromagnetic ratio, y, is defined as the ratio of magnetic moment to angular momentum of the nucleus and impacts on the sensitivity of NMRS experiments. Assuming that the coupling between the individual spins is weak, the relative populations of the two levels are given by a Boltzmaim distribution ... 

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