Properties of cold nuclear matter are studied within a generalized Nambu-Jona-Lasinio model formulated on the level of constituent nucleons. The model parameters are chosen to reproduce simultaneously the observed nucleon and pion masses in vacuum as well as saturation properties of nuclear matter. The strongest constraints on these parameters are given by the empirical values of the nucleon effective mass and compression modulus at nuclear saturation density. A preferable value of the cut-off momentum, determining density of active quasinucleon states in the Dirac sea, is estimated to about 400 MeV/c. With the most reasonable choice of model parameters we have found a first order phase transition of the liquid-gas type at subsaturation densities and the gradual restoration of chiral symmetry at about 3 times the saturation density. Fluctuations of the scalar condensate around its mean-field value are estimated and shown to be large in the vicinity of chiral transition.
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