Nuclear Magnetic Relaxation of Three and Four Spin Molecules in a Liquid

Abstract

The semiclassical density-matrix theory of relaxation is employed to calculate the relaxation of the $z$ component of nuclear magnetization of molecules in a liquid for the cases in which the molecules contain either three or four equidistant identical nuclei of spin ½ arranged, respectively, at the corners of an equilateral triangle or a tetrahedron. The relaxation is assumed to be due to the time dependence of the intramolecular dipole-dipole interactions that result from the classical rotational diffusion of the molecules. It is found that, if the initial state of the spin systems is characterized by a spin temperature, the relaxation consists of the sum of two terms which decay exponentially with different time constants.