AN ANALYTIC DERIVATION FOR THE MCMILLAN Tc FORMULA (Ⅲ)

Abstract
The Tc formula obtained in the previous two papers of this series is generalized to the following form: Tc=αωlog(ωlog/ωc)(μ*/(λ-μ*))exp{-(1+λ)/(λ-μ*)}, and a set of equations to be used to calculate the function a, is derived from the linear Eliashberg equation. a is a function of λ and μ* in general. In the weak coupling limit, we obtain a = 2γ/π from the set of equations mentioned above, where Inγ = C = 0.5772 is the Euler constant. Hence the Tc formula obtained in the two previous papers is correct in the same limit. We further calculate numerically the value of a when λ=0.23, 0.25, 0.38 and 0.48 from the set of equations mentioned above for the case of the Einstein spectrum and μ*= 0. Our results show that at least, in the interval 0.23 ≤λ≤ 0.48, a is vary small and equal to 1/1.30 approximately. With this value of a, the Tc formula obtained by us reduce practically to the empirical McMillan Tc formula in the version proposed by Allen and Dynes.

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