Calculations of the electronic density of states and conductivity consistent with the generalized optical theorem

In order to study density of states (DOS) effects on the resistivity of liquid metals and alloys we derive a set of integral equations for these quantities so that this set satisfies the generalized optical theorem. The DOS is calculated up to second order in the scattering potential using renormalized propagators. The theory is applicable to weak scattering systems, for example, alkali and alkaline earth metals and, for example, to Li-Pb alloys for compositions where the mean free path is much larger that the average interatomic distance. From our numerical results we conclude that the Ziman equation for the resistivity should be multiplied by g2=N2(Esub(F))/N2sub(O)(Esub(F)) where N(Esub(F)) is the DOS at the Fermi level as calculated in our model and Nsub(O)(Esub(F)) is the free electron DOS. This solves the long standing problem of whether or not one should correct the Ziman equation by an effective mass correction. Our model is only valid for alloys consisting of atoms with a small difference in electronegativity. This is clearly shown in the results for the liquid Li-Pb system. Some of the existing resistivity theories for weak and intermediate scattering are examined in the light of our calculations. (author)