Theory of current states in a very dirty SNS junction at temperatures near zero

Contact of two identical superconductors through the layer of a normal metal is studied. It is assumed that the free run distance in the pure superconductor $l$ is much smaller than $\xi_0$, the cogerentness distance in the pure superconductor and the thickness of the normal layer is much larger than $(\xi_0l)^{1/2}$, the correlation distance in the polluted superconductor. Under these assumptions the asymptotical expressions for the Josephson current are obtained in the neighbourhood of zero temperature and the estimate for the critical current at the zero temperature is given.