Exactly-solvable models for atom-molecule hamiltonians

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.