Strong-coupling expansions for multiparticle excitations: Continuum and bound states

We present a new linked cluster expansion for calculating properties of mul tiparticle excitation spectra to high orders. We use it to obtain the two-p article spectra for systems of coupled spin-half dimers. We find that even for weakly coupled dimers the spectrum is very rich, consisting of many bou nd states. The number of bound states depends on both geometry of coupling and frustration. Many of the bound states can only be seen by going to suff iciently high orders in the perturbation theory, showing the extended chara cter of the pair attraction.