Analytical solution to Solomon equations for three-spin groupings

Analytical solutions are provided for a set of three simultaneous first-order differential equations which describe either cross relaxation among three groupings of spin-1/2 nuclei (regardless of the number of spins within each grouping) or the complete longitudinal relaxation of a system of two spins-1/2, including CSA-dipolar interference terms (which couple the longitudinal spin order to conventional longitudinal magnetizations). In spite of their complexity, the expressions so obtained afford a time savings by a factor of 50 when used in a computer program. The efficiency of the method is illustrated by the fit of experimental data, exhibiting an unusual evolution due to both intra- and intermolecular dipolar couplings. (C) 1996 Academic Press, Inc.