Dependence of the second upper critical field on coupling strength

We have calculated the second upper critical magnetic field ${\mathit{H}}_{\mathit{c}2}$(T) in the clean and dirty limit for a number of known strong-coupling superconductors based on tunneling-derived kernels. The microscopic theory is used to derive a simple semiphenomenological analytic form for the strong-coupling corrections that involve the single parameter ${\mathit{T}}_{\mathit{c}}$/${\mathrm{\omega }}_{\mathit{l}\mathit{n}}$, namely the ratio of critical temperature (${\mathit{T}}_{\mathit{c}}$) to characteristic phonon energy (${\mathrm{\omega }}_{\mathit{l}\mathit{n}}$). The parameters in the derived form are fixed through consideration of our numerical data for real materials.