Nuclear quadrupolar relaxation in monatomic liquids

Abstract

A general theory is described for nuclear quadrupolar spin-lattice relaxation in monatomic liquids. The theory is valid for either liquid rare gases or liquid metals when appropriate forms are taken for the local electric field gradient (EFG). It is shown that the relaxation rate may be approximated in terms of an integral over the "elastic" limit $S(k,0)$ of the dynamic liquid structure factor multiplied by a weighting factor $I(k)$ determined by the spatial variation of the EFG. Calculations of $I(k)$ for Ne and Ga identify the ranges of $k$ values responsible for quadrupolar relaxation in these liquids. For Ne, the dominant modes fall in the range ${K}_{0}\ensuremath{\lesssim}k\ensuremath{\lesssim}2{K}_{0}$, where ${K}_{0}$ is the position of the main peak in the static liquid structure factor. For Ga, and for metals in general, $I(k)$ is largest near twice the Fermi wave vector ($2{k}_{F}$) if the EFG is determined from the asymptotic form of a screened ionic potential. For both liquid rare gases and liquid metals, these relatively high $k$ values indicate that collective motions play an important role in the nuclear relaxation process. As a corollary it is shown that magnetic dipolar relaxation in monatomic liquids can be described as a special case of the general theory with appropriate changes of the coupling constants. Numerical calculations of the relaxation rate for ${\mathrm{Ne}}^{21}$ and ${\mathrm{Ga}}^{69}$ near their respective melting points and the temperature dependence of the ${\mathrm{Ne}}^{21}$ rate are in good agreement with experiment.