Excitation energy dependence of the symmetry energy of finite nuclei

A finite-range density and momentum-dependent effective interaction is used to calculate the density and temperature dependence of the symmetry energy coefficient $C_{\mathrm{sym}}(\rho ,T)$ of infinite nuclear matter. This symmetry energy is then used in the local density approximation to evaluate the excitation energy dependence of the symmetry energy coefficient of finite nuclei in a microcanonical formulation that accounts for thermal and expansion effects. The results are in good harmony with the recently reported experimental data from energetic nucleus-nucleus collisions.

Figure 1

Symmetry energy coefficient of infinite nuclear matter as a function of density for different variants of the SBM interaction (see text) at $T=0.0$ MeV (top panel). In the bottom panel the temperature dependence of $C_{\mathrm{sym}}$ at several fixed densities is shown for $n=1/6$.

Figure 2

The equilibrium temperature (top panel), equilibrium central density (middle panel) and the symmetry energy coefficient (bottom panel) as a function of excitation energy for the $A=150$ isobars (Cs and Sm). The experimental data for $T$ are from Ref. [33], those for $\rho /{\rho }_0$ are from Refs. [30] (circles) and [31, 32] (squares), and those for $C_{\mathrm{sym}}$ are from Refs. [10] (inverted triangles and circles) and [29] (squares).

Figure 3

Same as in Fig. 2 for the systems ${}^{40}\mathrm{S}$ and ${}^{150}\mathrm{Sm}$ to show the mass dependence.