Relaxation in NMR is the process by which an excited magnetic state returns to equilibrium. After excitation of the magnetization by a radio frequency (RF) pulse it relaxes back to equilibrium by two different mechanisms. First there is a coherence loss of the magnetization in the x-y plane (spin-spin relaxation or transverse relaxation - T2) and then a recovery of the relaxation along the z-axis (spin-lattice relaxation or longitudinal relaxation – T1).  There are many factors that contribute to the relaxation processes such as homonuclear dipolar coupling, heteronuclear dipolar coupling, chemical shift anisotropy, spin rotation etc. 

The spin-lattice (T1) relaxation can be determined by using the inversion recovery pulse sequence, which is basically a sequence of 180-degree RF pulse, a delay followed by a 90-degree RF pulse. The delay (t) is varied from a small value to a large value and the signal intensity is I0[1 - 2exp(-t/T1)].  

T1 can be determined by repeating the experiment with several different delay values (known as vdlist), and by plotting peak intensity with respect to recovery delay time. The resulting curve is exponential with a rate of 1/T1. T1 can be measured by running single experiments, changing the delay until a null intensity is found. In the case where the signal intensity is zero, T1 is this delay divided by ln2 (T1 = tnull/ ln2); however, the accuracy of this measure of T1 is low. 

T2 relaxation is also known as spin-spin or transverse relaxation. T2 relaxation involves energy transfer between interacting spins through dipole and exchange interactions. In this process the energy transfer is between spins and their neighboring nuclei, which results in the decay of the magnetization in the xy-plane to zero: 

I=I₀[exp(−t/T2)] 

 T2 values are temperature independent and much less affected by the external magnetic field than T1 values. 

In principle, if the external magnetic field is completely homogeneous, it is possible to measure T2 relaxation time by applying a 90-degree RF pulse and measuring the decay of the FID. However, since the magnetic field is not completely homogeneous, the decay of the FID is also affected by magnetic field inhomogeneity, temperature gradients, etc. These effects cause a faster dephasing of the magnetization in the XY plane, and the decay constant of the FID is known as T2*. T2* values depend on the instrument while T2 values do not. T2* is usually shorter than T2. The linewidth of an NMR signal is inversely proportional to T2*, and it is possible to extract T2* directly from the peak linewidth. Short T2* results in a broad peak in the NMR spectrum.  

In order to calculate T2, the effect of field inhomogeneity must be removed, and this is achieved by using sequences that are based on spin echo (90-tau-180-tau-FID).  

Currently, T2 is measured by the Carr-Purcell-Meiboom-Gill sequence (CPMG). In this sequence there is an increasing number (vclist) of repeats of the d20-180-d20 block, which yields a signal intensity of I0exp(-t/T2), where t is the total evolution time, equal to 2xd20xvclist. d20 is a short delay (short enough to remove the effect of diffusion) and vclist is a variable loop counter list (all values must be even numbers to remove errors in the 180-degree pulse) 

  By plotting ln of the normalized signal intensity as a function of t, T2 can be extracted.