Energy nuclear spin with magnetic field

Spin-lattice relaxation is the steady (exponential) build-up or regeneration of the Boltzmann distribution (equilibrium magnetisation) of nuelear spins in the static magnetic field. The lattice is the molecular environment of the nuclear spin with whieh energy is exchanged. 

Relaxation can be described in terms of the magnetization vector components. At resonance, the equilibrium magnetization M0 parallel to B0 decreases to Mz, due to the transitions between the nuclear magnetic energy levels caused by the alternating field B,. Following resonance, the equilibrium of the nuclear spins with their lattice and with each other is restored by relaxation. 

Figure 18-4. ENDOR energy level diagram for an electron Ms = 1/2 in the local magnetic field of a proton Mj = 1 /2. To observe an ENDOR transition, the external magnetic field H0 is positioned on an EPR line, in this case the transition from Ms = —1/2, Ml = +1/2 > to Ms = +1 /2, M, = + 1/2 >. Then a radio-frequency transmitter is scanned through the various NMR frequencies (typically 10-100 MHz). This diagram shows two ENDOR transitions of energy haq and hu2 that correspond to the hyperfine couplings of a nuclear spin with Mj = 1/2...

Spin relaxation in a nucleus is induced by random fluctuations of local magnetic fields. These result from time-dependent modulation of the coupling energy of the resonating nuclear spin with nearby nuclear spins, electron spins, quadrupole moments, etc. Any time-dependent phenomenon able to modulate these couplings can contribute to nuclear relaxation. The distribution of the frequencies contained in these time-dependent phenomena is described by a correlation function, characterized by a parameter Tc, the correlation time. Its reciprocal can be considered as the maximum frequency produced by the fluctuations in the vicinity of the nuclear spin. If more than one process modulates the coupling between the nuclear spin and its surroundings, the reciprocal of the effective correlation time is the sum of the reciprocals of the various contributions... 

Fig. 2+t. Energy levels of a nuclear spin with 7=1/2 in the absence and presence of a magnetic field of B. The NMR transition occurs at the radio frequency of v. 

Nuclei that interact with magnetic fields are said to possess nuclear spin. The exact number of different energy levels a nucleus can adopt is determined by this nuclear spin, /, of the particular isotope. The nuclear spin / can have various values such as 0,... 

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