Renormalization effects on the upper critical field for weak electron-phonon coupling

We calculate the temperature dependence of the upper critical field in the presence of Pauli paramagnetism, spin-orbit coupling, and weak electron-phonon interaction. It is shown that renormalization accounts for a modification of the BCS-type theory of Werthamer, Helfand, and Hohenberg. This modification is accomplished by the renormalization procedure suggested earlier by Orlando et al.