McMillan T_c公式的解析推导(Ⅰ)μ~*=0情形

AN ANALYTIC DERIVATION FOR THE MCMILLAN T_c FORMULA (I) CASE OF μ* = 0

作者在μ*=0情形,从Eliashberg方程解析地导出如下的Tc公式: Tc=αω10gexp{-b（1+cλ/λ）}式中α=2γ/π,b=c=1;Inγ=C=0.5772是Euler常数。 这个Tc公式只有在Tc=0.36/α（k）以下才是正确的,α是个大于1并随材料而异的常数。我们推测,当Tc超过上述范围后,Tc公式的函数结构很可能不同于McMillanTc公式,至少α,b和c等参量不再是些不依赖于材料的常数了。

In the case of μ* = 0, the following Tc formula is derived analytically from the Eliashberg equationwhere, α = 2γ/π, b = c =1 and In γ = C = 0.5772 which is the Euler constant.The formula obtained by the authors holds only when Tc is less than 0.36/ α (K), where a is a constant larger than 1 and differs from one material to another. We conjecture, it is very likely that, when Tc is larger than 0.36/a, the functional structure of the Tc formula differs from that of McMillan's or at least the parameters a, b, and c are no longer constants independent of materials.