  The properties and the isospin dependence of the liquid-gas phase transition
in hot asymmetric nuclear matter have been investigated within the framework of
the finite temperature Brueckner-Hartree-Fock approach extended to include the
contribution of a microscopic three-body force. A typical Van der Waals
structure has been observed in the calculated isotherms (of pressure) for
symmetric nuclear matter implying the presence of the liquid-gas phase
transition. The critical temperature of the phase transition is calculated and
its dependence on the proton-to-neutron ratio is discussed. It is shown that
the three-body force gives a repulsive contribution to the nuclear equation of
state and reduces appreciably the critical temperature and the mechanical
instable region. At fixed temperature and density the pressure of asymmetric
nuclear matter increases monotonically as a function of isospin asymmetry. In
addition, it turns out that the domain of mechanical instability for hot
asymmetric nuclear matter gradually shrinks with increasing asymmetry and
temperature. We have compared our results with the predictions of other
theoretical models especially the Dirac Brueckner approach. A possible
explanation for the discrepancy between the values of the critical temperature
predicted by the present non-relativistic Brueckner calculations including the
three-body force and the relativistic Dirac-Brueckner method is given.
