Dynamics of cross relaxation in nuclear magnetic double resonance

Abstract

A theory, based on the formalism of memory functions, is developed to describe the rate of thermal mixing ${T}_{\mathrm{IS}}^{\ensuremath{-}1}$ between two spin species, one abundant and one dilute, in double-resonance experiments on solids. Cross-polarization spectra (dependence of ${T}_{\mathrm{IS}}^{\ensuremath{-}1}$ on departure of rf field strength from conditions for resonant mutual spin flip) are computed for Ca${\mathrm{F}}_{2}$ in two experimental limits: one where the abundant species is spin locked and the other where it is demagnetized in the rotating frame. Results for the latter case are successfully compared with experimental data of McArthur et al. Modifications expected from introduction of a third (abundant) species are discussed. An alternative theory, based on information theory, is also presented.