relaxation

In MRI and NMR spectroscopy, an observable nuclear spin polarization (magnetization) is created by an RF pulse or a train of pulses applied to a sample in a homogeneous magnetic field at the resonance (Larmor) frequency of the nuclei. At thermal equilibrium, nuclear spins precess randomly about the direction of the applied field but become abruptly phase coherent when any of the resultant polarization is created orthogonal to the field. This transverse magnetization can induce a signal in an RF coil that can be detected and amplified by an RF receiver. The RF pulses cause the population of spin-states to be perturbed from their thermal equilibrium value. The return of the longitudinal component of the magnetization to its equilibrium value is termed spin-lattice relaxation while the loss of phase-coherence of the spins is termed spin-spin relaxation, which is manifest as an observed free induction decay (FID).
For spin=½ nuclei (such as 1H), the polarization due to spins oriented with the field N- relative to the spins oriented against the field N+ is given by the Boltzmann distribution:







N

+



N

−




=

e

−



Δ
E


k
T







{\displaystyle {\frac {N_{+}}{N_{-}}}=e^{-{\frac {\Delta E}{kT}}}}
where ΔE is the energy level difference between the two populations of spins, k is the Boltzmann constant, and T is the sample temperature. At room temperature, the number of spins in the lower energy level, N−, slightly outnumbers the number in the upper level, N+. The energy gap between the spin-up and spin-down states in NMR is minute by atomic emission standards at magnetic fields conventionally used in MRI and NMR spectroscopy. Energy emission in NMR must be induced through a direct interaction of a nucleus with its external environment rather than by spontaneous emission. This interaction may be through the electrical or magnetic fields generated by other nuclei, electrons, or molecules. Spontaneous emission of energy is a radiative process involving the release of a photon and typified by phenomena such as fluorescence and phosphorescence. As stated by Abragam, the probability per unit time of the nuclear spin-1/2 transition from the + into the
- state through spontaneous emission of a photon is a negligible phenomenon.
Rather, the return to equilibrium is a much slower thermal process induced by the fluctuating local magnetic fields due to molecular or electron (free radical) rotational motions that return the excess energy in the form of heat to the surroundings.

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