Density reorganization in hot nuclei

The density profile of a hot nuclear system produced in intermediate-energy heavy ion collisions is studied in a microcanonical formulation with a momentum and density dependent finite range interaction. The caloric curve and density evolution with excitation are calculated for a number of systems for the equilibrium mononuclear configuration; they compare favorably with the recent experimental data. The studied density fluctuations are seen to build up rapidly beyond an excitation energy of $~8$ MeV/u indicating the instability of the system toward nuclear disassembly. Explicit introduction of deformation in the expansion path of the heated nucleus, however, shows that the system might fragment even earlier. We also explore the effects of the nuclear equation of state and of the mass and isospin asymmetry on the nuclear equilibrium configuration and the relevant experimental observables.

Figure 1

Calculated equilibrium density of ${}^{150}\mathrm{Sm}$ as a function of excitation energy per nucleon. Thick line corresponds to the calculations with the soft EOS ($K_{\infty }=238$ MeV); thin line, to those with the hard EOS ($K_{\infty }=380$ MeV); dashed line, to calculations without correlation effects for the softer EOS. Filled circles are the experimental data from Ref. [8]; open squares, from Ref. [6].

Figure 2

Calculated equilibrium densities as a function of excitation energy for $A=150$ isobars in the two definitions of density as explained in the text. Experimental points are same as in Fig. 1.

Figure 3

Equilibrium proton density profile for the system ${}^{150}\mathrm{Yb}$ at excitation energies of 6, 7, and 8 MeV per nucleon.

Figure 4

Same as in Fig. 2, but for the nuclei ${}^{40}\mathrm{Ca}$ and ${}^{40}\mathrm{S}$.

Figure 5

Mononuclear caloric curve for the system ${}^{150}\mathrm{Sm}$. Thick and thin lines refer to soft and hard EOS, respectively. Dashed line corresponds to the caloric curve calculated without correlation effects for the softer EOS. Experimental data points (filled circles) are from Ref. [39].

Figure 6

Mononuclear caloric curves showing isospin effects for $A=150$ isobars (top panel) and $A=40$ isobars (bottom panel). Experimental data are as in Fig. 5. Information on the mass dependence of the caloric curves can be gained by comparing the curves of the pair of nuclei ${}^{150}\mathrm{Sm}$ and ${}^{40}\mathrm{S}$ that have asymmetry $X~0.2$, with those of the nuclei ${}^{40}\mathrm{Ca}$ and ${}^{150}\mathrm{Yb}$ that are symmetric or nearly symmetric.

Figure 7

Expansion energy as a function of total excitation energy for $A=150$ isobars (top panel) and $A=40$ isobars (middle panel). EOS dependence of the expansion energy for ${}^{150}\mathrm{Sm}$ (bottom panel). Filled circles are experimental estimates [6].

Figure 8

Entropy profile at different fixed excitations as a function of the central density for the nuclei ${}^{150}\mathrm{Yb}$ and ${}^{150}\mathrm{Cs}$. Equilibrium configurations are marked by arrows, full ones for Yb, and broken ones for Cs.

Figure 9

Entropy profile at different fixed excitations as a function of temperature for the systems ${}^{150}\mathrm{Yb}$ and ${}^{150}\mathrm{Cs}$. Arrows have the same meaning as in Fig. 8.

Figure 10

Average temperature as a function of excitation energy in panels (a) and (c) for $A=150$ and $A=40$ isobars, respectively. Panels (b) and (d), corresponding variances in temperature.

Figure 11

Average values of the specific volumes and their variances for the different systems considered.

Figure 12

Entropy gain $\Delta S$ from deformation as a function of $E^{*}/A$ for the systems ${}^{150}\mathrm{Sm}$ and ${}^{150}\mathrm{Cs}$ in upper panels. Caloric curves with (full line) and without (dashed line) deformation in lower panels.