Giant dipole resonance as a quantitative constraint on the symmetry energy

The possible constraints on the poorly determined symmetry part of the effective nuclear Hamiltonians or effective energy functionals, i.e., the so-called symmetry energy $S(\rho )$, are very much under debate. In the present work, we show that the value of the symmetry energy associated with Skyrme functionals, at densities ρ around 0.1 fm${}^{-3}$, is strongly correlated with the value of the centroid of the Giant Dipole Resonance (GDR) in spherical nuclei. Consequently, the experimental value of the GDR in, e.g., ${}^{208}\mathrm{Pb}$ can be used as a constraint on the symmetry energy, leading to $23.3\hspace{0.17em}\mathrm{MeV}<S(\rho =0.1\hspace{0.17em}{\mathrm{fm}}^{-3})<24.9$ MeV.

Figure 1

Correlation between the quantity $g_{A=208}({\rho }_0)$ and the symmetry energy $S(\rho )$ for the Skyrme forces listed in Table , at $\rho =0.1$ fm${}^{-3}$. The value of the correlation coefficient is $r=0.981$.

Figure 2

Correlation between the energy of the GDR and the quantity $f(0.1)$. The definition of these quantities, and the related discussion, can be found in the text.