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A high-resolution study of the electromagnetic response of $^{206}$Pb belowthe neutron separation energy is performed using a ($\vec{\gamma}$,$\gamma'$)experiment at the HI$\vec{\gamma}$S facility. Nuclear resonance fluorescencewith 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 dipolestrength below the neutron separation energy are 0.9$\pm$0.2e$^2$fm$^2$ and8.3$\pm$2.0$\mu_{N}^2$, respectively. These measurements are found to be invery good agreement with the predictions from an energy-density functional(EDF) plus quasiparticle phonon model (QPM). Such a detailed theoreticalanalysis allows to separate the pygmy dipole resonance from both the tail ofthe giant dipole resonance and multi-phonon excitations. Combined with earlierphotonuclear experiments above the neutron separation energy, one extracts avalue for the electric dipole polarizability of $^{206}$Pb of$\alpha_{D}\!=\!122\pm10$mb/MeV. When compared to predictions from both theEDF+QPM and accurately calibrated relativistic EDFs, one deduces a range forthe neutron-skin thickness of $R_{\rm skin}^{206}\!=\!0.12$-$0.19$fm and acorresponding range for the slope of the symmetry energy of $L\!=\!48$-$60$MeV.This newly obtained information is also used to estimate theMaxwellian-averaged radiative cross section $^{205}$Pb(n,$\gamma$)$^{206}$Pb at30keV to be $\sigma\!=\!130\!\pm\!25$mb. The astrophysical impact of thismeasurement--on both the s-process in stellar nucleosynthesis and on theequation of state of neutron-rich matter--is discussed.

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