  We use coherent states as trial states for a variational approach to study a
system of a finite number of three-level atoms interacting in a dipolar
approximation with a one-mode electromagnetic field. The atoms are treated as
semi-distinguishable using different cooperation numbers and representations of
SU(3). We focus our analysis on the quantum phases of the system as well as the
behavior of the most relevant observables near the phase transitions. The
results are computed for all three possible configurations ($\Xi$, $\Lambda$
and $V$) of the three-level atoms.
