The microscopic theory of the nuclear matter equation of state at finite temperature is developed within the Bloch–De Dominicis diagrammatic expansion. The liquid gas phase transition of symmetric nuclear matter is identified, with a critical temperature $T_c\approx 20\hspace{0.5em}\mathrm{MeV},$ using the Argonne $v_{14}$ as the bare $\mathrm{NN}$ interaction and a phenomenological three-body force adjusted to give the correct saturation point. Pure neutron and asymmetric matter, relevant to supernovae explosions, are also studied. It is found that the liquid-gas phase transition disappears at asymmetries $a>\mathrm{}\mathrm{0.9.}\mathrm{}$ At the bounce-off of the supernova collapse, temperatures of several tens of MeV are reached and we find that the compressibility steeply increases at such temperatures. Finally, we find that the equation of state gives a “limiting temperature” of finite nuclei consistent with the experimental observation in compound nucleus reactions. A careful analysis of the diagrammatic expansion reveals that the dominant terms are the ones that correspond to the zero-temperature Bethe-Brueckner-Goldstone diagrams, where the temperature is introduced in the occupation numbers only, represented by Fermi distributions, thus justifying this commonly used procedure of naively introducing the temperature effect.

• Received 8 June 1998

DOI:https://doi.org/10.1103/PhysRevC.59.682