Atomic Nuclei: Nuclear Relaxation Processes

When a magnetic field is applied, degenerate nuclear spin states begin to precess and orient themselves along the lower energy state or against the higher energy state according to Boltzmann's distribution. The magnetic moments precess around the z-axis, creating a net magnetization along that axis with no net contribution from transverse xy components.

Radiofrequency radiation excites nuclei, causing them to absorb energy. The random distribution of magnetic moments becomes slightly phase coherent, and the net magnetization vector tips toward the y-axis. Transverse components Mx and My are no longer zero, while Mz decreases from its equilibrium value.

Saturation occurs when continued radiofrequency excitation equalizes populations in the upper and lower spin states, decreasing the population difference. The absorption signal decreases because the excess population in the lower energy state is no longer maintained, reducing the net magnetization available for detection.

When the relaxation rate is greater than or equal to the excitation rate, the excess population in the lower energy state is maintained and a signal is observed. If excitation is faster than relaxation, saturation occurs and the signal diminishes. Relaxation must restore equilibrium populations for continuous signal detection.

During relaxation, excited nuclear spins return to equilibrium population distribution. Coherence is lost and the transverse xy components disappear. The net magnetization is restored to its equilibrium value along the z-axis, allowing the spin system to recover and be re-excited for subsequent measurements.

At equilibrium, precessing magnetic moments are randomly oriented around the z-axis. Although individual moments have xy components, they are randomly distributed in phase, causing their transverse contributions to cancel out. Only the z-axis component, where spins preferentially align with the lower energy state, produces net magnetization.

Upon radiofrequency excitation, the random distribution of magnetic moments becomes slightly phase coherent, meaning they begin to precess in a more synchronized manner. This coherence allows the net magnetization vector to tip away from the z-axis toward the y-axis, creating observable transverse magnetization components.