Theory of Indirect Nuclear Interactions in Rubidium and Cesium Metals

A quantitative evaluation has been made of the Ruderman-Kittel and pseudodipolar parameters $A_{\mathrm{ij}}$ and $B_{\mathrm{ij}}$ for ${\mathrm{Rb}}^{85}$ and ${\mathrm{Cs}}^{133}$ nuclei in the respective metals using one-orthogonalized-plane-wave functions and calculated band structures. All the possible mechanisms that contribute to $A_{\mathrm{ij}}$ and $B_{\mathrm{ij}}$ have been considered. For $A_{\mathrm{ij}}$, about 90.54 and 92.25% of the total contribution for rubidium and cesium, respectively, are found to arise from the second-order effect of the contact hyperfine interaction. For $B_{\mathrm{ij}}$, the corresponding figures are 89.95 and 88.84%, arising from one order each in the electron-nuclear contact and dipole interactions. For each mechanism, the calculation involves an integration over the region of k space within the Fermi surface. The integrand is composed of three k-dependent factors, an expectation value over the wave functions, a density-of-states term, and a phase factor which depends on the distance between the nuclei. The final result depends sensitively on the $k$ dependence of these factors, and in some cases there is a cancellation between positive and negative contributions from different regions of k space. In the light of this, a critical analysis is made of earlier approximations, where some of the k-dependent factors were replaced by their values at the Fermi surface. Self-consistency and correlation effects are explicitly included, and produce less than 10% correction for $A_{\mathrm{ij}}$ and $B_{\mathrm{ij}}$ in both metals. Our calculated values for $A_{\mathrm{ij}}$ are 22.73 and 124.65, respectively, for rubidium and cesium, as compared to recent experimental values 51±5 and 200±10 cps. For $B_{\mathrm{ij}}$, the calculated values are 0.398 and 2.330, as compared to experimental values 11.80 and 35.00 cps. Possible sources for the discrepancies, and additional factors whose inclusion could lead to improved agreement with experiment, are discussed.