Relaxation equations for the magnetic moment of a system of coupled spins

Redfield's equation [4] for the spin-density matrix is used to derive the macroscopic relaxation equations for the magnetic moment of a system of three nuclear spins coupled by dipole-dipole interaction. The relaxation is due to the Brownian rotation of the molecule in which the spin nuclei are randomly placed. The relaxation problem is solved for a system of spins at the vertices of an isosceles triangle; four exponentials are involved. A formula is derived for the number of relaxation equations governing the magnetic moment in the case of an arbitrary number of interacting spins.