Low-frequency conductivity in the average-atom approximation

The quantum-mechanical average-atom model is reviewed and applied to determine scattering phase shifts, mean-free paths, and relaxation times in warm-dense plasmas. Static conductivities σ are based on an average-atom version of the Ziman formula. Applying linear response to the average-atom model leads to an average-atom version of the Kubo–Greenwood formula for the frequency-dependent conductivity σ(ω). The free–free contribution to σ(ω) is found to diverge as 1/ω2 at low frequencies; however, considering effects of multiple scattering leads to a modified version of σ(ω) that is finite and reduces to the Ziman formula at ω = 0. The resulting average-atom version of the Kubo–Greenwood formula satisfies the conductivity sum rule. The dielectric function ε(ω) and the complex index of refraction n(ω) + iκ(ω) are inferred from σ(ω) using dispersion relations. Applications to anomalous dispersion in laser-produced plasmas are discussed.