The exchange and correlation contribution to the electron - electron scattering part of the thermal resistivity in alkali metals

Abstract

We have calculated the pressure-dependent electron - electron scattering part of the thermal resistivity, , for three alkali metals, Li, Na and K, using a Fermi liquid model. Within this model, the electron - electron interaction is given by self-energy derivatives. A first-order perturbation expansion of the self-energy gives the commonly used GW-approximation. We have compared this with a -approximation, where is a vertex correction. By using a sum rule, we show that the -approximation should be preferred in calculating the electron - electron interaction. We use four different static dielectric functions, describing the exchange and correlation, in the screening potential W, namely the RPA function, the SSTL function, an LDA function and a Hubbard modified version of the LDA function, HUB. We have also calculated the exchange and correlation contribution including dynamic dielectric functions, within the GW-approximation. The results for the sum rule indicate that the dynamic approximation that we use is not suitable for calculating the electron - electron interaction. The thermal resistivity is calculated in the pressure region 0 - 120 kbar for Na and K, and in the region 0 - 100 kbar for Li. The LDA dielectric function gives results for for Li and K that are 10 to 20 times higher than the other dielectric functions, and also compared to experimental results. This has its origin in the approximation for the function, which breaks down for small enough densities, when the electron density parameter is . The SSTL and Hubbard functions show quite similar behaviour for all three of the metals, except for at higher pressures in K ( kbar), where the SSTL function causes a more rapid increase in . The RPA function, finally, gives a similar behaviour to the SSTL and Hubbard functions in for Na and K, while it results in a lowering of of for Li. We have also calculated the quasiparticle mass and the magnetic susceptibility, and compared these with experiment. Even in these cases it is the LDA function that gives the largest deviations from experiments.