Calculation of the transition temperature Tc of superconductors

Abstract
An iterative solution of the Eliashberg equations for isotropic superconductors is approximated by an analytical expression and gives as a result an equation for the superconducting transition temperature Tc. For small Tc (Tc ≪ mean phonon energy) a formula is derived, which agrees within a few per cent with the well‐known McMillan formula, if in this formula the mean logarithmic phonon energy ωlog is taken as pre‐factor, a correction which was already proposed earlier. For large Tc the (λ < ω2)1/2 behaviour of Allen and Dynes is found. Numerical results are presented for 0.5 < λ < 8, where the α2F(ω)‐shapes are taken corresponding to Hg, Pb, In, and Nb.