The density matrix formalism of nuclear relaxation: a review

This is a review of the density matrix formalism of quantum statistical mechanics as it relates to nuclear relaxation. The single spin and coupled exchanging two spin systems are treated explicitly. We show the circumstances under which these models reduce to the more familiar expressions used to describe proton relaxation in tissue. The effect of radiofrequency (rf) pulses on the density matrix is presented as well as the density matrix description of the Carr-Purcell pulse technique and conditions under which even and odd echo trains will superpose or are independent of rf pulse rate.