  We present an analytical description of the phase transitions from a nucleon
gas to nuclear matter and from nuclear matter to quark matter within the same
model. The equation of state for quark and nuclear matter is encoded in the
effective potential of a linear sigma model. We exploit an exact differential
equation for its dependence upon the chemical potential $\mu$ associated to
conserved baryon number. An approximate solution for vanishing temperature is
used to discuss possible phase transitions as the baryon density increases. For
a nucleon gas and nuclear matter we find a substantial density enhancement as
compared to quark models which neglect the confinement to baryons. The results
point out that the latter models are not suitable to discuss the phase diagram
at low temperature.
