Transition toΔmatter from hot, dense nuclear matter within a relativistic mean field formulation of the nonlinearσandωmodel

Abstract

An investigation of the transition to $\ensuremath{\Delta}$ matter is performed based on a relativistic mean field formulation of the nonlinear $\ensuremath{\sigma}$ and $\ensuremath{\omega}$ model. We demonstrate that in addition to the $\ensuremath{\Delta}$-meson coupling, the occurrence of the baryon resonance isomer also depends on the nucleon-meson coupling. Our results show that for the favored phenomenological value of ${m}^{*}$ and $K$, the $\ensuremath{\Delta}$ isomer exists at baryon density $\ensuremath{\sim}2$--3${\ensuremath{\rho}}_{0}$ if $\ensuremath{\beta}$=1.31 is adopted. For universal coupling of the nucleon and $\ensuremath{\Delta}$, the $\ensuremath{\Delta}$ density at baryon density $\ensuremath{\sim}2$--3${\ensuremath{\rho}}_{0}$ and temperature $\ensuremath{\sim}0.4$--0.5 fm${}^{\ensuremath{-}1}$ is about normal nuclear matter density, which is in accord with a recent experimental finding.