Optimizing the relativistic energy density functional with nuclear ground state and collective excitation properties

We introduce a new relativistic energy density functional constrained by the ground state properties of atomic nuclei along with the isoscalar giant monopole resonance energy and dipole polarizability in ${}^{208}\mathrm{Pb}$. A unified framework of the relativistic Hartree-Bogoliubov model and random phase approximation based on the relativistic density-dependent point coupling interaction is established in order to determine the DD-PCX parametrization by ${\chi }^2$ minimization. This procedure is supplemented with the covariance analysis in order to estimate statistical uncertainties in the model parameters and observables. The effective interaction DD-PCX accurately describes the nuclear ground state properties including the neutron-skin thickness, as well as the isoscalar giant monopole resonance excitation energies and dipole polarizabilities. The implementation of the experimental data on nuclear excitations allows constraining the symmetry energy close to the saturation density, and the incompressibility of nuclear matter by using genuine observables on finite nuclei in the ${\chi }^2$ minimization protocol, rather than using pseudo-observables on the nuclear matter, or by relying on the ground state properties only, as it has been customary in the previous studies.

Figure 1

Top: the difference between the experimental [39] and calculated binding energies for Ca, Ni, Sn, and Pb isotopes. Bottom: the calculated charge radii in comparison with the experimental values [41]. The calculations are performed using the DD-PCX, DD-PC1 [7], and DD-ME2 [8] interactions. Available data for the PC-PK1 interaction from Refs. [9, 40] are also shown.

Figure 2

The dipole polarizabilities for ${}^{48}\mathrm{Ca},{}^{68}\mathrm{Ni}$, and ${}^{208}\mathrm{Pb}$ (left) and tin isotopic chain (right). The calculations are performed using RHB+(Q)RPA with DD-PCX, DD-PC1, and DD-ME2 interactions. The experimental data are taken from Refs. [17, 19, 20, 21, 22].

Figure 3

The neutron skin thickness for ${}^{208}\mathrm{Pb}$ predicted by different experiments and nuclear energy density functionals. The experimental data are taken from $\left(\gamma ,{\pi }^0\right)$ [48], PREX [16], $\left(p,p^{\prime }\right)$ [19], $\left(p,p\right)$ [49], $\overline{p}$ [50], LAND(PDR) [51]. The calculations with the nonrelativistic interactions: SV-min [4], SLy5-min [31], $\mathrm{Sk}\chi m^{*}$ [47], and relativistic interactions: FSUGold [46], DDME-min [31], DD-ME2 [8], DD-PC1 [7], PC-PK1 [9].