G. G. Dussel

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) quasispins 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. The application to a system of bosonic atoms and molecules is reported.

Meaning of S-D dominance

The dominance of S and D pairs in the description of deformed nuclei is one of the facts that provided sustain to the Interacting Boson Approximation. In Ref.(J. Dukelsky and S. Pittel, Phys. Rev. Lett. 86, 4791, 2001.), using an exactly solvable model with a repulsive pairing interaction between bosons it has been shown that the ground state is described almost completely in terms of S and D bosons. In the present paper we study the excited states obtained within this exactly solvable hamiltonian and show that in order to obtain a rotational spectra all the other degrees of freedom are needed.