Transport Coefficients of Degenerate Plasma

An improved nonrelativistic calculation, based on the quantum Lenard-Balescu transport equation, is performed for the thermal and electrical conductivity of a plasma of highly degenerate, weakly coupled electrons and nondegenerate, weakly coupled ions. Dynamic shielding in the random-phase approximation is treated correctly, and both electron-ion (ei) and electron-electron (ee) collisions are included in the thermal conductivity. The argument that ee collisions are negligible, because the Pauli exclusion principle limits their effect to (kTEF)² less than that of ei collisions, is refuted in the case of the thermal conductivity. For temperatures of about 10⁸^∘{}K and densities of 10²⁶ to 10³⁰ electrons/cc, appropriate to red-giant stellar cores, ee collisions reduce the thermal conductivity by 25 to 50%. However, ee collisions are insignificant in terrestrial solids. The thermal conductivity κ is given by 1κ=1κₑᵢ+1κₑₑ, where κₑᵢ and κₑₑ are conductivities determined by ei and ee collisions. κₑᵢ∝Tn[ln(1λᵢ)+Cₑᵢ], where λᵢ²1 is the ion weak-coupling parameter, and the correction Cₑᵢ involves dynamic shielding. If λ²1 is the electron weak-coupling parameter, and γ≡4λEFkT1, then κₑₑ∝λ³n7/3T^-1, instead of the usual logarithmic form. If γ1, then κₑₑ∝T²n1/3[ln(1γ)+Cₑₑ], with the temperature dependence contrary to Fermi-liquid theory.