  The Dicke model is derived in the contraction limit of a pseudo-deformation
of the quasispin algebra in the su(2)-based Richardson-Gaudin models. Likewise,
the integrability of the Dicke model is established by constructing the full
set of conserved charges, the form of the Bethe Ansatz state, and the
associated Richardson-Gaudin equations. Thanks to the formulation in terms of
the pseudo-deformation, the connection from the su(2)-based Richardson-Gaudin
model towards the Dicke model can be performed adiabatically.
