  We present a theoretical study of the density of states and supercurrent in
diffusive superconductor-normal metal-superconductor (SNS) junctions. In
particular, we study the influence on these two equilibrium properties of both
an arbitrary transparency of the SN interfaces and the presence of spin-flip
scattering in the normal wire. We show that the minigap that is present in the
spectrum of the diffusive wire is very sensitive to the interface transmission.
More mportantly, we show that at arbitrary transparency the minigap replaces
the Thouless energy as the relevant energy scale for the proximity effect,
determining for instance the temperature dependence of the critical current. We
also study in detail how the critical current is suppressed by the effect of
spin-flip scattering, which can be due to either magnetic impurities or, under
certain circumstances, to an external magnetic field. Our analysis based on the
quasiclassical theory of diffusive superconductors can be very valuable to
establish quantitative comparisons between experiment and theory.
