Low-Field Relaxation and the Study of Ultraslow Atomic Motions by Magnetic Resonance

Abstract

Conventional resonance enables one to study motion of atoms by measurement of linewidth when the mean time $\ensuremath{\tau}$ between jumps is less than $\frac{1}{\ensuremath{\Delta}\ensuremath{\omega}}$, where $\ensuremath{\Delta}\ensuremath{\omega}$ is the rigid lattice linewidth, or by measurement of the spin-lattice relaxation time, ${T}_{1}$, when $\ensuremath{\tau}\ensuremath{\sim}\frac{1}{{\ensuremath{\omega}}_{0}}$, where ${\ensuremath{\omega}}_{0}$ is the Larmor frequency. We describe a new technique applicable when $\ensuremath{\tau}<{T}_{1}$. It is therefore applicable to the study of very slow motion. The method is analogous to measuring ${T}_{1}$ with ${\ensuremath{\omega}}_{0}=0$. However, we are able to keep ${\ensuremath{\omega}}_{0}$ in the megacycle region by performing the experiments in the reference frame rotating at the Larmor frequency. Analysis of the technique requires solution of the problem of the effect of infrequent motion on the nuclear relaxation time when the applied static field is comparable to the local field. The relaxation time is then comparable to $\ensuremath{\tau}$, indicating that jumps are strong "collisions" for the spins. The case of strong "collisions" is not treated in the conventional treatment of Bloembergen, Purcell, and Pound. We solve the problem by use of the concept of spin temperature and the sudden approximation. Explicit formulas are given for the nuclear relaxation in the laboratory for weak static fields, and in the rotating frame for alternating fields of the order of or less than the local field. We treat both diffusional motion and molecular reorientation.