Collapse of Ring Diagrams and Nuclear-Matter Phase Transitions

We study a ring-diagram approach for nuclear matter where the particle-particle and hole-hole ring diagrams are calculated to all orders via a random-phase-approximation equation. This equation is found to have complex eigenvalues within a small temperature-density region, and our results suggest that this occurrence of complex eigenvalues may be a useful signal for nuclear-matter phase transitions. With a slightly modified Gogny interaction, our ring-diagram nuclear-matter calculations give ${\rho }_0=0.17\mathrm{}{\mathrm{fm}}^{-3\mathrm{}}$, $\frac{E_0}{A}=-15.9\mathrm{}$ MeV, $K=127\mathrm{}$ MeV, and the liquid-gas critical temperature $T_c=7.6\mathrm{}$ MeV.