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We report measurements of the dectrical resistivity, Hall coefficient, magnetoresistance, thermoelectric power, infrared reflectivity, and c-axis lattice parameter of single crystals of titanium disulfide Ti&+"S& with varying degrees of nonstoichiometry. The strong correlations we find between different measurements made on the same sample allow us to conclude that titanium disulfide is a semiconductor rather than a semimetal. Even though this fact is established, our most stoichiometric samples continue to exhibit metallic behavior, and the source of these conduction electrons is unknown. In addition, none of the scattering mechanisms examined here is capable of explaining the unusual temperature dependence of the electrical resistivity which varies as T' at low T and as T~a bove 100 K where y ranges from 1.85 for the least stoichiometric samples to 2.2 for the most stoichiometric.

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The interaction between two-electron quasiparticles is approximated in terms of the dielectric and vertex functions of the uniform electron gas. These functions must satisfy the compressibility sum rule, and this fact makes the interaction at metallic densities much stronger than the Thomas-Fermi screened Coulomb interaction. A problem arises in applying this theory to real metals because the compressibility of the electron gas at densities appropriate to rubidium and cesium is negative. This anomaly is removed by taking into account the real metal effect of core polarization, The effective interaction is used to calculate the electron-electron scattering rate and its contribution to the thermal resistivity. The result is consistent with the single experimental measurement presently available on sodium (new results on potassium, rubidium, and cesium became available after this paper was completed; these are reported in Table III), whereas the Thomas-Fermi interaction predicts a thermal resistivity that is too small by a factor of 7. The scattering rates and thermal resistivities of all the alkali metals are calculated to enable comparison with future experimental values. I. INTERACTIONThis work was motivated by the experiments of Cook, Van der Meer, and I aubitz' who carefully measured both the electrical and thermal resistivities of sodium from 40 to 360 K and used an ingenious method' to extract from their data the contribution of electron-electron scattering to the thermal resisitivity. Kukkonen and Smith' calculated this quantityusing the Thomas-Fermi screened Coulomb interaction and obtained a result that was smaller than experiment by a factor of 7. One aim of this paper is to resolve this discrepancy. This paper is organized as follows. In Sec. II we obtain an approximate electron-electron interaction U"(q) in terms of z(q) and A(kz, q), the dielectric and vertex functions and z(kF), the quasiparticle renormalization factor, of the uniform electron gas,where V(q) =4''/q . This interaction is appropriate for electrons with opposite spins. The vertex function takes into account the Pauli principle in that the screening cloud around an electron is due both to its charge and to the Pauli principle. Since we are discussing the interaction of twoelectron quasiparticles, there is a vertex function associated with each of them. [We note that the Thomas-Fermi interaction considers both z(k~) and A(kz, q) to be unity. ] We make no attempt to do an independent calculation of the dielectric and vertex functions; rather, we examine and test the consequences of several existing calculations.There are constraints on the model interaction [Eq. (1)] because the q = 0 limits of both the dielectric and vertex functions are exactly related to the compressibility of the electron gas. Requiring that the compressibility obtained from the groundstate energy is identical to that obtained from an appropriate @=0 limit of the dielectric function is called the compressibility sum rule. The dielectric functions of Hubbard' (as modifie...