Spinodal instabilities in nuclear matter in a stochastic relativistic mean-field approach

Spinodal instabilities and early growth of baryon density fluctuations in symmetric nuclear matter are investigated in the basis of the stochastic extension of the relativistic mean-field approach in the semiclassical approximation. Calculations are compared with the results of nonrelativistic calculations based on Skyrme-type effective interactions under similar conditions. A qualitative difference appears in the unstable response of the system: the system exhibits most unstable behavior at higher baryon densities around ${\rho }_b=0.4{\rho }_0$ in the relativistic approach while most unstable behavior occurs at lower baryon densities around ${\rho }_b=0.2{\rho }_0$ in the nonrelativistic calculations

Figure 1

Growth rates of unstable modes as a function of wave numbers in the spinodal region at baryon densities ${\rho }_{\mathrm{b}}=0.2{\rho }_0$ and ${\rho }_{\mathrm{b}}=0.4{\rho }_0$ at temperature $T=5$ MeV: (a) relativistic calculations, and (b) nonrelativistic calculations.

Figure 2

Growth rates of the most unstable modes as function of baryon density in the spinodal region at temperature $T=5$ MeV in relativistic calculations (solid line) and in nonrelativistic calculations (dashed line).

Figure 3

Boundary of the spinodal region in the baryon density-temperature plane for the unstable mode with wavelengths $\lambda =9$ fm in relativistic calculations (solid line) and in nonrelativistic calculations (dashed line).

Figure 4

Spectral intensity ${\tilde{\sigma }}_{\mathrm{b}}(\overrightarrow{k},t)$ of the baryon density correlation function as a function of wave number at times $t=0$, $t=20$ fm/$c$ and $t=40$ fm/$c$ at temperature $T=5$ MeV in relativistic calculations at densities (a) ${\rho }_{\mathrm{b}}=0.2{\rho }_0$ and (b) ${\rho }_{\mathrm{b}}=0.4{\rho }_0$.

Figure 5

Same as Fig. 4 in nonrelativistic calculations.

Figure 6

Baryon density correlation function ${\sigma }_{\mathrm{b}}(x,t)$ as a function of distance $x=|\overrightarrow{r}-{\overrightarrow{r}}^{\text{'}}|$ between two space points at times $t=0$, $t=20$ fm/$c$ and $t=40$ fm/$c$ at temperature $T=5$ MeV in relativistic calculations at densities (a) ${\rho }_{\mathrm{b}}=0.2{\rho }_0$ and (b) ${\rho }_{\mathrm{b}}=0.4{\rho }_0$.

Figure 7

Same as Fig. 6 in nonrelativistic calculations.