Relativistic Effects on the Hyperfine Interactions in Alkali Metals

A relativistic formulation of the hyperfine properties of metals has been developed and applied to study the Knight shifts $K_s$, relaxation times $T_1$, and Ruderman-Kittel $A_{12}$ and pseudodipolar $B_{12}$ interactions in the two alkali metals, rubidium and cesium. The calculations have been carried out using Dirac orthogonalized-plane-wave wave functions, and the relativistic expressions derived have been checked for correctness by proceeding to the nonrelativistic limit. The calculated values of $K_s$ for rubidium and cesium are 0.60% and 1.42%, as compared to 0.65% and 1.49% from experiment. The values of $T_{1}T$ for these metals are 1.293 and 0.128 deg sec, in good agreement with the experimental values of 1.235 and 0.130 deg sec, respectively. The relativistic values of $A_{12}$ for rubidium and cesium are found to be 24.45 and 189.64 cps, as compared to 50±5 and 200±10 cps from resonance experiments. The theoretical values of $B_{12}$ for the two metals are 0.45 and 2.65 cps, respectively, as compared to 11±2 cycles and 35±5 cps from recent steady-state NMR measurements. The relativistic results for all the properties, including ${\left(T_{1}T\right)}^{-1\mathrm{}}$, are substantially larger (7% to 60%) than predicted by nonrelativistic theory, leading to improved agreement with experiment. Possible reasons for the poor agreement between experiment and theory for $B_{12}$ in both metals are discussed.