Tracing the evolution of the symmetry energy of hot nuclear fragments from the compound nucleus towards multifragmentation

The evolution of the symmetry energy coefficient of the binding energy of hot fragments with increasing excitation is explored in multifragmentation processes following heavy-ion collisions below the Fermi energy. In this work, high-resolution mass spectrometric data on isotopic distributions of projectile-like fragments are systematically compared to calculations involving the statistical multifragmentation model (SMM). Within the SMM picture, the present study suggests a gradual decrease of the symmetry energy coefficient of the hot primary fragments from 25 MeV at the compound nucleus regime towards 15 MeV in the multifragmentation regime. The isotopic distributions of the hot primary fragments are found to be very wide and extend towards the neutron drip line. These findings are expected to have important implications in the modeling of the composition and the evolution of hot and dense astrophysical environments, such as those of core-collapse supernova.

Figure 1

Average $Z/A$ vs $A$. (a) BigSol data; (b), (c), (d) MARS data. Solid points: data. Thin solid line (SL): line of stability. Thin dotted line (EAL): evaporation attractor line. Thick lines: DIT/SMM05 calculations. Dotted lines, top to bottom: with $C_{\mathrm{sym}}=25,20,15$ MeV, respectively. Thick solid line: with $C_{\mathrm{sym}}(E^{*}/A)$ given by the thick line in Fig. 2. Arrows: multifragmentation vs compound nucleus regime.

Figure 2

Thick solid line: form 2–4 of $C_{\mathrm{sym}}(E^{*}/A)$ in the SMM05 calculations. Thin lines: other forms of $C_{\mathrm{sym}}(E^{*}/A)$ tested (see text and Fig. 3). Thin horizontal lines (top to bottom): $C_{\mathrm{sym}}=25,20,15$ MeV, respectively, used in Fig. 1 calculations. Solid points: values of $C_{\mathrm{sym}}$ from [22].

Figure 3

$\langle Z/A\rangle$ vs $A$ for ${}^{86}\mathrm{Kr}+{}^{124}\mathrm{Sn}$. Solid points (data), lines SL, EAL, and arrow as in Fig. 1. Thin lines tracing the data: DIT/SMM05 calculations with $C_{\mathrm{sym}}(E^{*}/A)$ forms presented by the respective lines in Fig. 2 (see text).

Figure 4

Comparison of experimental mass distributions with DIT/SMM05 calculations. Solid points: ${}^{86}\mathrm{Kr}+{}^{64}\mathrm{Ni}$ data. Open points: ${}^{86}\mathrm{Kr}+{}^{208}\mathrm{Pb}$ data. Full lines: calculations for ${}^{86}\mathrm{Kr}+{}^{64}\mathrm{Ni}$; thick: final (cold) fragments, thin: primary (hot) fragments. Dotted lines: calculations for ${}^{86}\mathrm{Kr}+{}^{208}\mathrm{Pb}$; thick: final (cold) fragments, thin: primary (hot) fragments. Arrows: neutron drip line [35].