Temperature and Purity Dependence of the Superconducting Critical FieldHc2. IV. Strong-Coupling Effects

The existing theory of the transition temperature of a strong-phonon-coupling superconductor in zero magnetic field is merged with that of the upper critical field $H_{c2\mathrm{}}$ of a weak-coupling type-II superconductor to arrive at formulas for the strong-coupling corrections to $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$. A numerical computation is carried out for a phonon model of pure niobium. The strong-coupling effects make up only a negligible portion of the discrepancy between the earlier weak-coupling theory of $H_{c2\mathrm{}}$ and experimental observation, the remainder of which must be ascribed to Fermi-surface a nisotropy.