An investigation of the transition to $\Delta$ matter is performed based on a relativistic mean field formulation of the nonlinear $\sigma$ and $\omega$ model. We demonstrate that in addition to the $\Delta$-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 $\Delta$ isomer exists at baryon density $\sim 2$–3${\rho }_0$ if $\beta$=1.31 is adopted. For universal coupling of the nucleon and $\Delta$, the $\Delta$ density at baryon density $\sim 2$–3${\rho }_0$ and temperature $\sim 0.4$–0.5 fm${}^{-1}$ is about normal nuclear matter density, which is in accord with a recent experimental finding.

• Received 9 January 1997

DOI:https://doi.org/10.1103/PhysRevC.56.1570