  A Quantum Phase Transition (QPT) in a simple model that describes the
coexistence of atoms and diatomic molecules is studied. The model, that is
briefly discussed, presents a second order ground state phase transition in the
thermodynamic (or large particle number) limit, changing from a molecular
condensate in one phase to an equilibrium of diatomic molecules-atoms in
coexistence in the other one. Usual markers for this phase transition are the
ground state energy and the expectation value of the number of atoms (or,
alternatvely, the number of molecules) in the ground state. In this work, other
markers for the QPT as the Inverse Participation Ratio (IPR) and, particularly,
the R\'enyi entropy are analysed and proposed as QPT markers. Both magnitudes
present abrupt changes at the critical point of the QPT.
