Pygmy and core polarization dipole modes in \(^{206}\)Pb: connecting nuclear structure to stellar nucleosynthesis

A high-resolution study of the electromagnetic response of \(^{206}\)Pb below the neutron separation energy is performed using a (\(\vec{\gamma}\),\(\gamma'\)) experiment at the HI\(\vec{\gamma}\)S facility. Nuclear resonance fluorescence with 100% linearly polarized photon beams is used to measure spins, parities, branching ratios, and decay widths of excited states in \(^{206}\)Pb from \(4.9\) to \(8.1\)MeV. The extracted $\Sigma$$B\((E1)\)\uparrow\( and \)\Sigma$$B\((M1)\)\uparrow\( values for the total electric and magnetic dipole strength below the neutron separation energy are 0.9\)\pm\(0.2e\)^2\(fm\)^2\( and 8.3\)\pm\(2.0\)\mu_{N}^2\(, respectively. These measurements are found to be in very good agreement with the predictions from an energy-density functional (EDF) plus quasiparticle phonon model (QPM). Such a detailed theoretical analysis allows to separate the pygmy dipole resonance from both the tail of the giant dipole resonance and multi-phonon excitations. Combined with earlier photonuclear experiments above the neutron separation energy, one extracts a value for the electric dipole polarizability of \)^{206}\(Pb of \)\alpha_{D}\!=\!122\pm10\(mb/MeV. When compared to predictions from both the EDF+QPM and accurately calibrated relativistic EDFs, one deduces a range for the neutron-skin thickness of \)R_{\rm skin}^{206}\!=\!0.12\(-\)0.19\(fm and a corresponding range for the slope of the symmetry energy of \)L\!=\!48\(-\)60\(MeV. This newly obtained information is also used to estimate the Maxwellian-averaged radiative cross section \)^{205}\(Pb(n,\)\gamma\()\)^{206}\(Pb at 30keV to be \)\sigma\!=\!130\!\pm\!25$mb. The astrophysical impact of this measurement--on both the s-process in stellar nucleosynthesis and on the equation of state of neutron-rich matter--is discussed.