Resonant scattering of conduction electrons by impurities in the alkali metals

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Abstract
When alkali metals are the solvents, the spin-flip scattering cross-section σ and the change Δ X in the magnetic susceptibility are functions of the valence z1 of the impurity and are such that σ is smaller and Δ X is much larger for z = 5, 6 than the corresponding values for smaller z'. The latter effect is due to a decrease in the density-of-states at the Fermi energy and the former is due to a decrease at the Fermi energy in the p-electron density around the impurity. We show that these two effects are connected by the derivative (η) kF of the p-wave phase-shift, and that (η) kF must be negative to explain the experimental results. This can only be explained by the occurrence of an ‘incomplete’ resonance in n 1 (k) for some value of k < kF ; the hypothesis that the p-valence electrons are bound to the impurity is shown to be inconsistent with the occurrence of giant diamagnetism. When there is a virtual bound state, the impurity looks like a virtual atom, with most of the p-electron screening density occurring at the resonance energy. A new self-consistent calculation of the impurity potential for Te in Li is presented. The results are in qualitative agreement with our theoretical conclusions and with the experimental results.