Growth of spinodal instabilities in nuclear matter

Early growth of density fluctuations of nuclear matter in the spinodal region is investigated employing the stochastic mean-field approach. In contrast to the earlier treatments in which only collective modes were included in the calculations, in the present work noncollective modes are also included, thus providing a complete treatment of the density correlation functions. Calculations are carried out for symmetric matter in a nonrelativistic framework using a semiclassical approximation.

Figure 1

The contour chosen to calculate the integral in Eq. (10). Dots $\pm i\Gamma {}_k$ indicate the collective poles of the integrand, and the dotted line along the entire real $\omega$ axis is the branch cut of the integrand.

Figure 2

Phase diagram in the density-temperature plane for different wavelengths corresponding to the potential given by Eq. (27).

Figure 3

Spectral intensity of the correlation function as a function of wave number at initial density $\rho =0.2{\rho }_0$ ${\mathrm{fm}}^{-3}$ at time $t=30$ fm/$c$ at temperatures $T=1$ MeV (a) and $T=5$ MeV (b). Dotted, dashed-dotted, and solid lines are results of pole, cut, and total contributions, respectively.

Figure 4

Spectral intensity of the correlation function as a function of wave number at initial density $\rho =0.2{\rho }_0$ ${\mathrm{fm}}^{-3}$ at time $t=50$ fm/$c$ at temperatures $T=1$ MeV (a) and $T=5$ MeV (b). Dotted, dashed-dotted, and solid lines are results of pole, cut, and total contributions, respectively.

Figure 5

Spectral intensity of the correlation function as a function of wave number at initial density $\rho =0.4{\rho }_0$ ${\mathrm{fm}}^{-3}$ at time $t=30$ fm/$c$ at temperatures $T=1$ MeV (a) and $T=5$ MeV (b). Dotted, dashed-dotted, and solid lines are results of pole, cut, and total contributions, respectively.

Figure 6

Spectral intensity of the correlation function as a function of wave number at initial density $\rho =0.4{\rho }_0$ ${\mathrm{fm}}^{-3}$ at time $t=50$ fm/$c$ at temperatures $T=1$ MeV (a) and $T=5$ MeV (b). Dotted, dashed-dotted, and solid lines are results of pole, cut, and total contributions, respectively.

Figure 7

Density correlation function as a function of distance between two space locations $x=|\vec{r}-\vec{r}{}^{\prime }|$ for initial density $\rho =0.2{\rho }_0$ ${\mathrm{fm}}^{-3}$ and temperatures $T=1$ MeV (a) and $T=5$ MeV (b) at times $t=20,30,40,50$ fm/$c$.

Figure 8

Density correlation function as a function of distance between two space location $x=|\vec{r}-\vec{r}{}^{\prime }|$ for initial density $\rho =0.4{\rho }_0$ ${\mathrm{fm}}^{-3}$ and temperatures $T=1$ MeV (a) and $T=5$ MeV (b) at times $t=20,30,40,50$ fm/$c$.

Figure 9

Density correlation function as a function of distance between two space locations $x=|\vec{r}-\vec{r}{}^{\prime }|$ for initial density $\rho =0.2{\rho }_0$ ${\mathrm{fm}}^{-3}$ and temperatures $T=1$ MeV (a) and $T=5$ MeV(b) at times $t=30,50$ fm/$c$. Solid and dotted lines are complete calculations and pole contributions, respectively.

Figure 10

Density correlation function as a function of distance between two space locations $x=|\vec{r}-\vec{r}{}^{\prime }|$ for initial density $\rho =0.4{\rho }_0$ ${\mathrm{fm}}^{-3}$ and temperatures $T=1$ MeV(a) and $T=5$ MeV(b) at times $t=30,50$ fm/$c$. Solid and dotted lines are complete calculations and pole contributions, respectively.