Nuclear Zeeman energy

VP-16 phenoxyl radicals [detection, 234, 632-637 reduction reactions in aqueous solution, 234, 638-640 reduction reactions in cell and nuclear homogenates, 234, 641-642] Zeeman energy of spin states, 246, 538, 593 zero-field splitting, 246,550-551. 

Fig. 1.10. The Zeeman energies of a nuclear spin (/ = 2) as a function of the external magnetic field Bo.

From the dipolar interaction energy, the dipolar shift can be obtained by evaluating from Eq. (2.16) A d,p between two states differing by A A// = 1 and dividing it by the nuclear Zeeman energy hyiBo (Appendix IV) ... 

The partial recovery of the quantum phase coherence of nuclear dipoles originates from the non-commutative property of the Zeeman energy with the quantum operator which represents the residual interaction after rotating the spins. This rotation has no effect on the magnetisation dynamics when the residual interaction, hHR, is equal to zero. No... 

Figure 8.36. Energy level diagram showing the nuclear spin Zeeman energies for the 7Li and 79Br nuclei in LiBr. The nuclear g-factor for 7Li (3.256) is larger than that for 79Br (2.106). Each level shown is split into a further triplet by the rotational Zeeman interaction which removes the Mj threefold-degeneracy for J = 1.

In some physical situations, namely when the hyperfine energy is small compared to the nuclear Zeeman energy, then the hyperfine splitting is linear in (the projection magnitude of) matrix A for example, see Ref. 131. Then, provided that g is anisotropic (note Ref. 128 on this point), one can detect asymmetry of A directly from EPR line-position measurement see below. 

For simplicity, the electron and nuclear Zeeman energy terms can be expressed in frequency units giving ... 

The longitudinal relaxation also called spin-lattice relaxation is induced by a quasi-resonant exchange which occurs between the Zeeman energy of the spin system and the thermal energy of molecules which carry nuclear magnetic dipoles. The condition of quasi-resonant exchange of energy is used to calibrate the time scale of relaxation of molecular... 

Since nuclear Zeeman energies are so small, the populations of the a and f spin states differ very slightly. For protons in a 1-T field, AN/N 3x 10 . Althougli... 

Transitions between Zeeman energy levels, and hence nuclear magnetic relaxation, are caused by fluctuations (time variations) in the local interactions at the nucleus that can cause transitions. The transition rates between these energy levels that cause nuclear spin relaxation depend on two factors ... 

In an exterior magnetic field, the torque on the magnetic moment of the spinning nucleus, /aligning force of the intramolecular potential. The corresponding potential energy (nuclear Zeeman effect) is given by ... 

In our further treatment we will neglect part (h) as compared to part (i) and part ( ) as compared to part (k). The latter would lead to a nuclear contribution to the susceptibilities. In both cases the contributions of the neglected terms to the Zeeman energy may be estimated to be roughly a factor of w/Mp smaller than the contributions of the terms retained. By a similar argument, part (1) may be neglected as compared to part (k) due to the weighting with 1/Af as compared to jm. 

Fig. 2. Zeeman energy levels for electron spin 5 and nuclear spin / (a) scalar coupling, dominant relaxation transition S / (b) dipolar coupling, dominant relaxation transition S-1+. ...

The sensitivity of conventional nuclear magnetic resonance (NMR) is rather poor compared with other spectroscopic techniques like EPR or optical spectroscopy. This is a result of the small population difference between the nuclear Zeeman energy levels even in the highest magnetic fields currently available in the laboratory. At room temperature, and in a magnetic field of 9.4 T, the polarisation of the protons is less than 4 x 10. In order to overcome this inherent limitation, methods to improve the signal to noise ratio (SNR) in magnetic resonance experiments have been the subject of active research since the discovery of NMR. 

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