  The S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the
dimerized phase using analytic triplet-wave expansions and dimer series
expansions. The occurrence of two-triplon bound states in the S=0 and S=1
channels, and antibound states in the S=2 channel, is predicted by the
triplet-wave theory, and confirmed by series expansions. All bound states are
found to vanish at or before the critical coupling separating the dimerized
phase from the Neel phase. The critical behaviour of the total and
single-particle static transverse structure factors is also studied by series,
and found to conform with theoretical expectations. The single-particle state
dominates the structure factor at all couplings.
