  The London penetration depth is evaluated for isotropic materials for any
transport and pair-breaking Born scattering rates. Besides known results, a
number of new features are found. The slope $|d\rho/d\theta |$ of the
normalized superfluid density $\rho=\lambda^2(0)/\lambda^2(\theta)$ at the
transition $\theta=T/T_c=1$ has a minimum near the value of the pair-breaking
parameter separating gapped and gapless states. The low-$T$ exponentially flat
part of $\rho$ for the s-wave materials is suppressed by increasing pair
breaking. For strong $T_c $ suppression by magnetic impurities the "Homes
scaling" $\lambda^{-2}(0) \propto \sigma T_c$ with $\sigma$ being the normal
conductivity gives way to $\lambda^{-2}(0) \propto \sigma T_c^2$. For the
d-wave order parameter, the transport and spin-flip Born scattering rates enter
the theory only as a sum, in particular, they affect the $T_c$ depression in
the same manner. We confirm that the linear low temperature behavior of $\rho$
in a broad range of the combined scattering parameter turns to the $T^2$
behavior only when the critical temperature is suppressed at least by a factor
of 3 relative to the clean limit $T_{c0}$. Moreover, in this range, $\rho
(\theta)$ is only weakly dependent on the scattering parameter, i.e. it is
nearly universal.
