Symmetry energy from electric dipole response of nuclei

The response of nuclei against external electromagnetic field is of fundamental importance. Among the various external fields, the electric dipole (E1) field induces isovector response that is sensitive to the symmetry energy of the nuclear equation of state. The knowledge of the symmetry energy is indispensable for the study of the neutron-star properties including the process of their merger. The density dependence of the symmetry energy has also a strong correlation with the neutron-skin thickness of heavy neutron-rich nuclei. The full E1 response was, however, not determined well.

We have developed an experimental method, employing high-resolution proton inelastic scattering at very forward angles, that is suitable for extracting the full E1 response across the neutron separation energy, covering the PDR and the giant dipole resonance (GDR). The missing mass spectroscopy method enabled us to probe the total strength independently of the decay channels. Multipole decomposition and spin-transfer analyses allowed the extraction of the strength including contributions from unresolved small strengths.

The method has been applied to ²⁰⁸Pb, ¹²⁰Sn, ⁴⁸Ca and other representative stable nuclei. The full E1 strength distributions were extracted for the excitation energies from 5 to ~20 MeV. The static electric-dipole-polarizabilities were precisely determined by applying the inversely-energy-weighted sum-rule of the E1 strength. Constraint bands on the symmetry energy parameters were determined with a help of mean-field model calculations. The method has been expanded for the studies of PDRs, gamma-strength functions, and nuclear level-densities. Coincidence measurements of the gamma decay are progressing.

  I will report on the recent progress on the study of the E1 response of nuclei especially for the works relevant to the symmetry energy.