Excess population nuclear spin states

The product of escape from the cage (3) is formed with an excess population of nuclear spin state a. Figure A1.6 shows the upper state with enhanced population. With this inverted polarization, the spin system will emit energy and a negative peak will be observed. There is a net effect in the direction of emission, E. 

Our NMR theory is almost complete, but there is one more thing to consider before we set about designing a spectrometer. We indicated previously that at equilibrium in the absence of an external magnetic field, all nuclear spin states are degenerate and, therefore, of equal probability and population. Then, when immersed in a magnetic field, the spin states establish a new (Boltzmann) equilibrium distribution with a slight excess of nuclei in the lower energy state. 

In the absence of magnetic field, the populations of the two nuclear spin states (n+, the spin-up number and , the spin-down number per unit volume) are equal. When a magnetic field is applied, there is a slight excess of nuclei in the lower spin state. The populations follow the Boltzmann distribution law ... 

If the excited state is populated in excess of that required by the Boltzmann distribution, energy is emitted on relaxation to the normal distribution, and an emission signal (negative peak) is observed. If it is the ground state that is populated in excess, the probability for energy absorption is increased, and enhanced absorption is observed. Several discussions are available that provide a detailed account of the mechanism by which interacting radical pairs affect the population of the nuclear spin states of product. 

The fact that saturation is often not observed must mean that there are non-radiative processes by which p nuclear spins can become a spins again and hence help to maintain the population difference between the two sites. The nonradi-ative return to an equilibrium distribution of populations in a system (eqn 13.9) is an aspect of the process called relaxation. If we were to imagine forming a system of spins in which all the nuclei were in their p state, then the system returns exponentially to the equilibrium distribution (a small excess of a spins over p spins) with a time constant called the spin-lattice relaxation time, T, (Fig. 13.25). 

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