Fully self-consistent study of charge-exchange resonances and the impact on the symmetry energy parameters

We have examined within a fully self-consistent theoretical framework the energy difference between the anti-analog giant dipole resonance (AGDR) and the isobaric analog state (IAS), $E_{\mathrm{AGDR}}-E_{\mathrm{IAS}}$, as an indicator of the neutron skin and of the density behavior of the symmetry energy. We have improved two specific points in our HF+RPA calculations: (1) the exchange term of the two-body Coulomb interaction is treated exactly without Slater approximation; and (2) the two-parameters spin-orbit interaction is treated in a consistent way within the energy density functional theory. The estimated values for the neutron skin in ${}^{208}\mathrm{Pb}$ and the slope parameter of symmetry energy are compared with previous analysis available in the literature.

Figure 1

The energy of the IAS as a function of neutron skin in ${}^{208}\mathrm{Pb}$ calculated with SAMi-J interactions with the exact Coulomb exchange (empty circles) and the Slater approximation (full circles). We also display (stars) the results obtained with the covariant DD-ME Lagrangians [44].

Figure 2

The energy difference $E_{\mathrm{AGDR}}-E_{\mathrm{IAS}}$ of AGDR and IAS as a function of the neutron-skin thickness, obtained by using the SAMi-J family of Skyrme functionals. The calculated values are presented as solid circles. Two different experimental data [32, 33] are also shown as solid (magenta) and dashed (blue) lines, respectively. The arrows indicate the neutron skin constrained by these experimental data. We also display results obtained with the covariant DD-ME Lagrangians of Ref. [32].

Figure 3

(a) and (b) show the correlations between the neutron-skin thickness and either the symmetry energy $J$ at saturation density or the corresponding slope parameter $L$, respectively. The constraints provided by the experimental data already shown in Fig. 2.