  We present a family of exactly-solvable generalizations of the
Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or
SU(1,1) quasi-spins with a single boson field. They are obtained from the
trigonometric Richardson-Gaudin models by replacing one of the SU(2) or SU(1,1)
degrees of freedom by an ideal boson. Application to a system of bosonic atoms
and molecules is reported.
