Incomplete Andreev reflection in a clean SFS junction

We study the stationary Josephson effect in a ballistic superconductor/ferromagnet/superconductor junction for arbitrarily large spin polarizations. Due to the exchange interaction in the ferromagnet, the Andreev reflection is incomplete. We describe how this effect modifies the Josephson current in the crossover from a superconductor/normal metal/superconductor junction to a superconductor/half metal/superconductor junction.