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 Kₛ, relaxation times T₁, and Ruderman-Kittel A₁₂ and pseudodipolar B₁₂ 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 Kₛ for rubidium and cesium are 0.60% and 1.42%, as compared to 0.65% and 1.49% from experiment. The values of T₁T 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 A₁₂ 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 B₁₂ 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 (T₁T)^-1, 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 B₁₂ in both metals are discussed.