  A model is introduced for two reduced BCS systems which are coupled through
the transfer of Cooper pairs between the systems. The model may thus be used in
the analysis of the Josephson effect arising from pair tunneling between two
strongly coupled small metallic grains. At a particular coupling strength the
model is integrable and explicit results are derived for the energy spectrum,
conserved operators, integrals of motion, and wave function scalar products. It
is also shown that form factors can be obtained for the calculation of
correlation functions. Further, a connection with perturbed conformal field
theory is made.
