In an idealized system, all nuclei in a given chemical environment, in a magnetic field, precess with the same frequency. However, in real systems, there are minor differences in chemical environment which can lead to a distribution of resonance frequencies around the ideal. Over time, this distribution can lead to a dispersion of the tight distribution of magnetic spin vectors, and loss of signal (free induction decay). In fact, for most magnetic resonance experiments, this "relaxation" dominates. This results in dephasing.
However, decoherence because of magnetic field inhomogeneity is not a true "relaxation" process; it is not random, but dependent on the location of the molecule in the magnet. For molecules that aren't moving, the deviation from ideal relaxation is consistent over time, and the signal can be recovered by performing a spin echo experiment.
The corresponding transverse relaxation time constant is thus T, which is usually much smaller than T. The relation between them is:
where γ represents gyromagnetic ratio, and ΔB the difference in strength of the locally varying field.
Unlike T, T* is influenced by magnetic field gradient irregularities. The T* relaxation time is always shorter than the T relaxation time and is typically milliseconds for water samples in imaging magnets.