Quadrupolar Relaxation ofXe131in Xenon Gas

A theoretical study is made of the spin-lattice relaxation of ${\mathrm{Xe}}^{131}$ ($I=\frac{3}{2}$) nuclei in pure xenon gas due to collision-induced nuclear electric quadrupole interactions. The calculation treats a pair of colliding Xe atoms as a rotating "diatomic molecule," whose nuclear electric quadrupole interaction couples the nuclear spin and rotational angular momenta. This interaction permits the nuclei to relax by exchanging energy with the rotational motion of the colliding atoms. The quadrupole interaction in such a "diatomic molecule" is computed by considering the effects of exchange and Van der Waals interactions in deforming the spherical electronic charge clouds of the free atoms. It is found that the exchange interaction makes the dominant contribution to the quadrupole interaction. Averaging the single-collision transition probabilities over all types of collisions gives the following result for the spin-lattice relaxation time $T_1:\frac{1}{T_1}=0.046\mathrm{}\rho$ ${\sec }^{-1\mathrm{}}$, where $\rho$ is the density in amagats. This is in good agreement with the observed result: $\frac{1}{T_1}=0.039\mathrm{}\rho$ ${\sec }^{-1\mathrm{}}$.