Neutron Skin of ${}^{208}\mathrm{Pb}$ from Coherent Pion Photoproduction

Information on the size and shape of the neutron skin on ${}^{208}\mathrm{Pb}$ is extracted from coherent pion photoproduction cross sections measured using the Crystal Ball detector together with the Glasgow tagger at the MAMI electron beam facility. On exploitation of an interpolated fit of a theoretical model to the measured cross sections, the half-height radius and diffuseness of the neutron distribution are found to be $c_n=6.70\pm 0.03(\text{stat}\mathrm{.})\mathrm{fm}$ and $a_n=0.55\pm 0.01(\text{stat}{\mathrm{.})}_{-0.03}^{+0.02}(\text{sys}\mathrm{.})\mathrm{fm}$, respectively, corresponding to a neutron skin thickness $\mathrm{\Delta }{r}_{np}=0.15\pm 0.03(\text{stat}{\mathrm{.})}_{-0.03}^{+0.01}(\text{sys}\mathrm{.})\mathrm{fm}$. The results give the first successful extraction of a neutron skin thickness with an electromagnetic probe and indicate that the skin of ${}^{208}\mathrm{Pb}$ has a halo character. The measurement provides valuable new constraints on both the structure of nuclei and the equation of state for neutron-rich matter.

Figure 1

The fits to the spectrum of $\mathrm{\Delta }{E}_{\pi }^{\text{diff}\mathrm{.}}$ for $E_{\gamma }=200\mathrm{MeV}$ for a momentum transfer near the first diffraction maximum (left) and the first diffraction minimum (right).

Figure 2

Differential cross sections for the reaction ${}^{208}\mathrm{Pb}(\gamma ,{\pi }^0){}^{208}\mathrm{Pb}$ (black circles) for the $E_{\gamma }$ regions indicated. The $y$ axis employs a square-root scale to improve the clarity. The red solid line shows the interpolated fit of the theoretical model to the data. The $q$ range of the fit is indicated by the horizontal bar. The dashed blue line shows the model predictions without including the pion-nucleus interaction.

Figure 3

The best fit for diffuseness (upper) and half-height radius (lower) for the neutron distribution for each $E_{\gamma }$ bin. The horizontal lines show the average over $E_{\gamma }$, and the shaded band shows the estimated systematic error (see text)

Figure 4

The quantity ($a_n-a_p$) plotted versus ($c_n-c_p$) for ${}^{208}\mathrm{Pb}$. The red inverted triangle shows the present result with statistical and systematic errors shown by solid and dashed lines, respectively. The symbols show the predictions from the various nuclear structure calculations, obtained from Ref. [47].