Complete Electric Dipole Response and the Neutron Skin in ${}^{208}\mathrm{Pb}$

A benchmark experiment on ${}^{208}\mathrm{Pb}$ shows that polarized proton inelastic scattering at very forward angles including 0° is a powerful tool for high-resolution studies of electric dipole ($E1$) and spin magnetic dipole ($M1$) modes in nuclei over a broad excitation energy range to test up-to-date nuclear models. The extracted $E1$ polarizability leads to a neutron skin thickness $r_{\mathrm{skin}}={0.156}_{-0.021}^{+0.025}\mathrm{fm}$ in ${}^{208}\mathrm{Pb}$ derived within a mean-field model [Phys. Rev. C 81, 051303 (2010)], thereby constraining the symmetry energy and its density dependence relevant to the description of neutron stars.

Figure 1

(a) Spectrum of the ${}^{208}\mathrm{Pb}$ $(\overrightarrow{p},{\overrightarrow{p}}^{\prime })$ reaction at $E_p=295\mathrm{MeV}$ with the spectrometer placed at 0°. (b) Total spin transfer $\Sigma$.

Figure 2

Decomposition of non-spin-flip ($\Delta S=0$) and spin-flip ($\Delta S=1$) cross section parts based on the MDA and PT, respectively, in the excitation energy region $5–9\mathrm{MeV}$. The hatched areas indicate the experimental uncertainties. Excellent agreement between the two completely independent methods is observed.

Figure 3

(a) $B(E1)$ strengths in ${}^{208}\mathrm{Pb}$ in the region $E_x\simeq 4.8–8.2\mathrm{MeV}$ as deduced from the present work in comparison with $(\gamma ,{\gamma }^{\prime })$ and $(n,\gamma )$ experiments [26, 29, 30, 31]. (b) Photoabsorption cross sections in the GDR region from the present work compared to $(\gamma ,xn)$ [32] and total photoabsorption [33] measurements.

Figure 4

Experimental $B(E1)$ strength distribution in (a) ${}^{208}\mathrm{Pb}$ in comparison to (b) QPM and (c) RTBA calculations described in the text. Note the different scales below and above 8.2 MeV.

Figure 5

Extraction of the neutron skin in ${}^{208}\mathrm{Pb}$ based on the correlation between $r_{\mathrm{skin}}$ and the dipole polarizability ${\alpha }_D$ established in Ref. 8.