Probing the symmetry energy from the nuclear isoscaling

Using different parametrizations of the nuclear mass formula, we study the sensitivity of the isoscaling parameters to the mass formula employed in grand-canonical calculations. Previous works on isoscaling have suggested that the symmetry energy implied in such calculations is anomalously smaller than that suggested by fits to nuclear masses. We show that surface corrections to the symmetry energy naturally broadens the isotopic distribution thus allowing for values of the symmetry energy which more closely match those obtained from nuclear masses.

Figure 1

Difference between the calculated binding energies and the empirical values of Ref. 34 as a function of the mass number for the three mass formulas used in this work.

Figure 2

Isoscaling parameter α obtained using different binding energies in the grand-canonical calculations as a function of the temperature.

Figure 3

Upper panel: isoscaling parameter α obtained using LDM1 as a function of $C_{\mathrm{sym}}$. In case (a) all the LDM1 parameters are kept fixed, except for $C_{\mathrm{sym}}$, whereas, in case (b), for each value of $C_{\mathrm{sym}}$, the other LDM1 parameters are refitted to the empirical binding energies. Lower panels: $\Delta B$ for different values of $C_{\mathrm{sym}}$. The left panels correspond to case (a) and the right ones to case (b).

Figure 4

Isotopic distribution of fragments produced in the decay of the ${}^{112}\mathrm{Sn}$ nucleus at $T=6$ MeV.