Spin-Lattice Relaxation in the Rotating Frame: Weak-Collision Case

A comprehensive theoretical expression for the spin-lattice relaxation time in the rotating frame $T_{1\rho }$ is derived for the case of weak collisions. Starting from the laboratory-frame dipolar Hamiltonian and retaining both secular and nonsecular terms, the doubly-rotating-frame Hamiltonian is determined and the relaxation expression derived, using standard density-matrix techniques. In limiting cases the derived expression reduces to established forms, including the normal expression for $T_1$. An experimental measurement of the angular dependence of $T_{1\rho }$ is described and the data for the sample of tetramethyl-ammonium iodide shown. The theoretical curve is in good agreement with the experimental data.