Calculation of the transition temperature T c of superconductors

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 T c . For small T c ( T c ≪ 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 ω log is taken as pre‐factor, a correction which was already proposed earlier. For large T c the (λ < ω 2 ) 1/2 behaviour of Allen and Dynes is found. Numerical results are presented for 0.5 < λ < 8, where the α 2 F (ω)‐shapes are taken corresponding to Hg, Pb, In, and Nb.