Abstract
A new method for solving the Eliashberg equations in the Matsubara representation is presented, and an approximate equation for the transition temperature, T c, is determined. The T c-equation is tested using numerical solutions of the Eliashberg equations and unlike the McMillan equation, it gives valid solutions for all electron-phonon coupling strengths, λ, and for different shapes of the electron-phonon interaction spectrum, α 2 F( ω). The recent controversy over the asymptotic limit of T c at very large λ is resolved.
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