0-pi transition in SFS junctions with strongly spin-dependent scattering

We develop theory of proximity effect in a superconductor - GMR alloy - superconductor trilayers, which takes into account strong spin dependence of electron scattering of compositional disorder in a diluted ferromagnetic alloy. We show that in such a system the critical current oscillations as the function of the thickness of the ferromagnetic layer, with the period of $v_{F}/2I$, decay exponentially with the characteristic length of the order of the mean free path.