  Quantum phase transitions and observables of interest of the ground state in
the Tavis-Cummings model are analyzed, for any number of atoms, by using a
tensorial product of coherent states. It is found that this "trial" state
constitutes a very good approximation to the exact quantum solution, in that it
globally reproduces the expectation values of the matter and field observables.
These include the population and dipole moments of the two-level atoms and the
squeezing parameter. Agreement in the field-matter entanglement and in the
fidelity measures, of interest in quantum information theory, is also found.The
analysis is carried out in all three regions defined by the separatrix which
gives rise to the quantum phase transitions. It is argued that this agreement
is due to the gaussian structure of the probability distributions of the
constant of motion and the number of photons. The expectation values of the
ground state observables are given in analytic form, and the change of the
ground state structure of the system when the separatrix is crossed is also
studied.
