McMillan Tc公式的解析推导(Ⅲ)

本文把作者在前面两篇文章导出的T_c公式推广成下面形式:T_c=αω_log(ω_log/ω_c)^{(μ*/(λ-μ*))exp{-(1+λ)/(λ-μ*)},并从线性Eliashberg方程出发,导出了计算α的方程组。α一般是λ和μ*的函数。在弱耦合极限下,由上述方程组解得,α=2γ/π,其中lnγ=C=0.5772是Euler常数。这个结果表明了,前面两篇文章得到的T_c公式在弱耦合极限下是正确的。作者进而在Einstein谱和μ*=0情形,用数值计算方法从定α的方程组算出当λ=0.23,0.25,0.38和0.48时,a的数值。结果表明,至少在0.23≤λ≤0.45区间中,α变化很小,近似等于1/1.30。此时,本文的T_c公式实际上就是Allen及Dynes修改后的经验的McMillan T_c公式。 关键词：}

AN ANALYTIC DERIVATION FOR THE MCMILLAN Tc FORMULA (Ⅲ)

The T_c formula obtained in the previous two papers of this series is generalized to the following form: T_c=αω_log(ω_log/ω_c)^{(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 T_c 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 T_c formula obtained by us reduce practically to the empirical McMillan T_c formula in the version proposed by Allen and Dynes.}