  The orbital upper critical field $H_{c2} $ is evaluated for isotropic
materials with arbitrary transport and pair-breaking scattering rates. It is
shown that unlike transport scattering which enhances $H_{c2} $, the pair
breaking suppresses the upper critical field and reduces the dimensionless
ratio $h^*(0)=H_{c2}(0)/T_c(dH_{c2}/dT)_{T_c} $ from the Helfand-Werthamer
value of $\approx 0.7$ to 0.5 for a strong pair-breaking. $h^*(T)$ is evaluated
for arbitrary transport and pair-breaking scattering.
  A phenomenological model for the pair-breaking suppression by magnetic fields
is introduced. It shows qualitative features such as a positive curvature of
$H_{c2}(T) $ and the low temperature upturn usually associated with multi-band
superconductivity.

Superconductivity