Strong-coupling theory of the upper critical magnetic fieldHc2

In this paper a strong-coupling theory of the upper critical magnetic field ($H_{c2}$) is developed within the framework of the Werthamer-Helfand-Hohenberg theory. We include Pauli paramagnetic limiting and momentum scattering of the conduction electrons at randomly distributed impurity sites. The developed theory is tested against experimental data available for niobium and ${\mathrm{V}}_3$Si. It is shown that for isotropic cases the presented theory gives excellent agreement with experiment over the complete temperature range. It is remarkable that it was not necessary in both cases to include spin-orbit scattering. It can be concluded that in most cases spin-orbit scattering was only used to compensate for strong-coupling effects in the older Bardeen-Cooper-Schrieffer–related theories.