Chemical and mechanical instability in warm and dense nuclear matter

Abstract

We investigate the possible thermodynamic instability in a warm and dense nuclear medium ($T\ensuremath{\leqslant}50$ MeV and ${\ensuremath{\rho}}_{0}\ensuremath{\leqslant}{\ensuremath{\rho}}_{B}\ensuremath{\leqslant}3\phantom{\rule{0.16em}{0ex}}{\ensuremath{\rho}}_{0}$) where a phase transition from nucleonic matter to resonance-dominated $\ensuremath{\Delta}$ matter can take place. The analysis is performed by requiring the global conservation of baryon and electric charge numbers in the framework of a relativistic equation of state. Similarly to the liquid-gas phase transition, we show that the nucleon-$\ensuremath{\Delta}$ matter phase transition is characterized by both mechanical instability (fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the charge concentration) in asymmetric nuclear matter. We then perform an investigation and a comparative study on the different nature of such instabilities and phase transitions.