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We present an analytical description of the phase transitions from a nucleongas to nuclear matter and from nuclear matter to quark matter within the samemodel. The equation of state for quark and nuclear matter is encoded in theeffective potential of a linear sigma model. We exploit an exact differentialequation for its dependence upon the chemical potential $\mu$ associated toconserved baryon number. An approximate solution for vanishing temperature isused to discuss possible phase transitions as the baryon density increases. Fora nucleon gas and nuclear matter we find a substantial density enhancement ascompared to quark models which neglect the confinement to baryons. The resultspoint out that the latter models are not suitable to discuss the phase diagramat low temperature.Comment: 27 pages, Int.J.Mod.Phys.A versio

Quark and Nuclear Matter in the Linear Chiral Meson Model