Spin relaxation due to magnetic-field inhomogeneities: Quartic dependence and diffusion-constant measurements

In a recent perturbative treatment of the effects of magnetic-field inhomogeneities on nuclear spin relaxation of gases, the lowest-order contributions to the relaxation rate were predicted to be proportional to the square of the field inhomogeneity. However, recent experiments show that under magnetic-resonance conditions the observed relaxation rates can have comparable contributions from both the square and the fourth power of the field inhomogeneity. For a fixed magnetic-field inhomogeneity, the quartic contribution will always dominate at sufficiently high pressures. There are no noticeable contributions proportional to higher powers of the field inhomogeneity under the experimental conditions we have explored. In this paper we extend the perturbative theory of spin relaxation in inhomogeneous magnetic fields to account for these quartic effects. We present measurements in which spin relaxation in inhomogeneous magnetic fields is used to determine the diffusion constant of Xe in 760 Torr of either He or ${\mathrm{N}}_2$ at 80 °C to be 0.791±0.032 and 0.21±0.03 ${\mathrm{cm}}^2$/sec, respectively. Using our measured diffusion constants, we show that our theory describes well the observed quartic effects.