Figure 1

Pressure as a function of the baryon density (in units of the nuclear saturation density ${\rho }_0$) for the symmetric nuclear matter at zero temperature for three different EOSs and $\Delta$ coupling ratios (absence of $\Delta$ contribution in the monotonic curves). The shaded region corresponds to the limits obtained from the analysis of Ref. [26].Reuse & Permissions

Figure 2

The energy per baryon versus baryon density at zero temperature and GM3 parameter set with (a) without $\Delta$; (b) non-interacting $\Delta$ ($r_s=r_v=0$); (c) $r_s=1.3$, $r_v=1$, (d) $r_s=1.41$, $r_v=1$), (e) $r_s=1.45$, $r_v=1$, (f) $r_s=1.5$, $r_v=1$.Reuse & Permissions

Figure 3

The same as Fig. 2 but for different parameter sets and fixed $r_s=1.3$ and $r_v=1$.Reuse & Permissions

Figure 4

The $\Delta$ effective mass ratios versus the baryon density with $r_s=r_v=1$ (upper curves) and with $r_s=1.32$ and $r_v=1$ (lower curves) for different temperatures. The parameter set used in the calculation is NL$\rho \delta$.Reuse & Permissions

Figure 5

The energy per baryon versus baryon density for symmetric nuclear matter at different values of temperature and TM1 parameter set. The solid lines correspond to the $\Delta$ coupling ratios $r_s=r_v=1$ and the dashes lines correspond to $r_s=1.3$ and $r_v=1$.Reuse & Permissions

Figure 6

Variation of the baryon density, with respect to temperature, corresponding to the position of the second minimum of the energy per baryon for different parameter sets (see text for details).Reuse & Permissions

Figure 7

The relative nucleon (solid lines) and $\Delta$ (dashed lines) density versus the baryon density with $r_s=r_v=1$ (upper panel) and with $r_s=1.32$ and $r_v=1$ (lower panel) for different values of temperature (in MeV). The parameter set used in the calculation is NL$\rho \delta$.Reuse & Permissions

Figure 8

Variation of baryon density, as a function of temperature, for which $\Delta$-isobar density is equal to nucleon density, for different parameter sets. The scalar coupling ratios for each EOS are the values $r_s=r_s^{\mathrm{II}}$ reported in Table .Reuse & Permissions

Figure 9

Variations of the strangeness chemical potential ${\mu }_S$ (upper panel) and electric charge chemical potential ${\mu }_C$ (lower panel) with respect to the baryon chemical ${\mu }_B$ at different values of temperature (in MeV) and different $\Delta$ coupling constants. The parameter set is GM3 and $r_v=1$.Reuse & Permissions

Figure 10

Baryon density (in units of the nuclear saturation density ${\rho }_0$) as a function of the baryon chemical potential ${\mu }_B$ at different values of temperature (in MeV). The parameter set is GM3 and $r_v=1$.Reuse & Permissions

Figure 11

Pressure as a function of the baryon chemical potential ${\mu }_B$ at different values of temperature (in MeV). The parameter set is GM3 and $r_v=1$.Reuse & Permissions

Figure 12

Relative difference of the pressure as a function of the baryon chemical potential ${\mu }_B$ at different values of temperature with the exclusion (no $\Delta$) and the inclusion ($r_s=1.3$ and $r_v=1$) of the $\Delta$-isobar degrees of freedom. (a) $\Delta P(Z/A,{\mu }^{*})\equiv P(Z/A=0.5)-P(Z/A=0.4)$ and the symbol ${\mu }^{*}$ means that an effective chemical potential for all hadrons has been considered (see text for details); (b) the same as panel (a) but mesons have a bare chemical potential (free boson gas); (c) $\Delta P(Z/A=0.4,\mu ,{\mu }^{*})\equiv P(\mu )-P({\mu }^{*})$ at fixed $Z/A=0.4$, where the pressure $P(\mu )$ is calculated by considering a bare chemical potential for mesons and the pressure $P({\mu }^{*})$ is calculated by using an effective chemical potential for all hadrons; (d) same as panel (c) but at fixed $Z/A=0.5$. The circles, the squares, and the triangles represent the values of the baryon chemical potential corresponding to ${\rho }_B={\rho }_0$, 2 ${\rho }_0$, and 3 ${\rho }_0$, respectively.Reuse & Permissions

Figure 13

Ratios of net densities ${\Delta }^{++}/p$ as a function of the baryon chemical potential for different temperatures, $r_s$, and parameter sets (a, TM1; b, NL$\rho \delta$; c, GM3).Reuse & Permissions

Figure 14

Variation of the $K^{+}/{\pi }^{+}$ and $K^{-}/{\pi }^{-}$ ratios with respect to temperature at different values of baryon chemical potential and different parameter sets (a, TM1; b, NL$\rho \delta$; c, GM3). The $\Delta$ coupling ratios are fixed to $r_s=r_v=1$.Reuse & Permissions

Figure 15

Variation of the $K^{+}/K^{-}$ ratio with respect to temperature at different values of baryon chemical potential and for different $\Delta$ coupling ratios (TM1 parameter set).Reuse & Permissions

Figure 16

Variation of the $K^{+}/K^{-}$ ratio with respect to baryon chemical potential at fixed temperature $T=100$ MeV. The value $r_m$ corresponds to the average value between $r_s^{\mathrm{II}}$ and $r_s^{\max }$ listed in Table  for the two different parameter sets.Reuse & Permissions

Figure 17

Variation of $K^{+}/{\pi }^{+}$ ratios with respect to baryon density at $T=80$ MeV (lower curves) and $T=120$ MeV (upper curves). For the dash-dotted curves the symbol $\mu$ indicates that all mesons have bare chemical potentials (see text for details).Reuse & Permissions

Figure 18

The same as Fig. 17 but for $K^{+}/K^{-}$ ratios.Reuse & Permissions

Figure 19

Particle-antiparticle and $K^{+}/{\pi }^{+}$ ratios as a function of the $\overline{p}/p$ ratio for different temperatures. The $\Delta$ coupling ratios are fixed to $r_s=r_v=1$. The ratios of ${\Xi }^{+}/{\Xi }^{-}$ at $T=80$ and $120$ MeV are not reported because they are very strictly to the $\overline{\Lambda }/\Lambda$ ones.Reuse & Permissions