  We analyse a p+ip-wave pairing BCS Hamiltonian, coupled to a single bosonic
degree of freedom representing a molecular condensate, and investigate the
nature of the BEC-BCS crossover for this system. For a suitable restriction on
the coupling parameters, we show that the model is integrable and we derive the
exact solution by the algebraic Bethe ansatz. In this manner we also obtain
explicit formulae for correlation functions and compute these for several
cases. We find that the crossover between the BEC state and the strong pairing
p+ip phase is smooth for this model, with no intermediate quantum phase
transition.
