A relationship between nuclear spin relaxation in the laboratory and rotating frames for dipolar and quadrupolar relaxation

Abstract

Density operator theory of nuclear spin relaxation due to fluctuating magnetic dipole or electric quadrupole interactions is based on a differential equation for the density operator which, in the weak collision limit, depends on the spectral density functions of the dipolar or quadrupolar fluctuations. It is shown that the differential equation for relaxation in the rotating frame may be expressed in a similar form to that for relaxation in the laboratory frame. Expressions for magnetization recoveries in the rotating frame can then be simply deduced from the laboratory frame expressions by replacing the spectral density functions in the laboratory frame results by linear combinations of spectral density functions. The method is applied to single-exponential relaxation for the dipolar mechanism and to single- and multiple-exponential relaxation for the quadrupole mechanism for both longitudinal and transverse magnetization recoveries.