Relaxation of spins due to field inhomogeneities in gaseous samples at low magnetic fields and low pressures

We have developed a theory for the effect of magnetic-field inhomogeneities on the spin relaxation of gases in cells with negligible relaxation at the walls. There is a characteristic pressure $p^{\mathrm{*}}$ at which the time ${\tau }_d$ required for an atom to diffuse across the cell is equal to the time ${\tau }_l$ required for the spin to precess by one radian in the mean magnetic field. For ‘‘high pressures,’’ p≫$p^{\mathrm{*}}$, the longitudinal spin-relaxation time $T_1$ is inversely proportional to the pressure. This is the classic pressure dependence discussed in the literature. The new results reported in this paper are that at ‘‘low pressures,’’ p≪$p^{\mathrm{*}}$, the pressure dependence changes and the longitudinal relaxation time becomes directly proportional to the pressure; that is, motional narrowing occurs. We show that the transverse relaxation time $T_2$ will ordinarily be proportional to the pressure at both low and high pressures, but with different coefficients. There is also a small, pressure-dependent shift of the Larmor frequency associated with the field inhomogeneity.