Neutron density distribution and neutron skin thickness of ${}^{208}\mathrm{Pb}$

We present and discuss numerical predictions for the neutron density distribution of ${}^{208}\mathrm{Pb}$ using various nonrelativistic and relativistic mean-field models for the nuclear structure. Our results are compared with the very recent pion photoproduction data from Mainz. The parity-violating asymmetry parameter for elastic electron scattering at the kinematics of the PREX experiment at JLab and the neutron skin thickness are compared with the available data. We consider also the dependence between the neutron skin and the parameters of the expansion of the symmetry energy.

Figure 1

Theoretical weak charge density in comparison with the experimental error band as determined in Ref. [55] for ${}^{208}\mathrm{Pb}$ with the kinematics of the PREX experiment.

Figure 2

Parity-violating asymmetry at the kinematics of the PREX experiments vs the neutron rms radius for ${}^{208}\mathrm{Pb}$. The dashed orange line is a linear fit of the correlation between the neutron rms radius and $A_{pv}$. The red square shows the experimental data from PREX [9] with statistical and systematic errors.

Figure 3

Parity-violating asymmetry at the kinematics of the PREX experiments versus the neutron skin for ${}^{208}\mathrm{Pb}$. The red square shows the experimental data from PREX [9] with statistical and systematic errors. The dashed orange line is a linear fit of the correlation between the neutron skin and $A_{pv}$. The vertical solid green lines show the constraints on $R_{\mathrm{skin}}$ from Mainz $(\gamma ,{\pi }^0)$ measurements [12]. The vertical purple dashed lines show the constraints on $R_{\mathrm{skin}}$ from Osaka polarized proton elastic scattering measurements [5].

Figure 4

Neutron skin for ${}^{208}\mathrm{Pb}$ versus the slope of the symmetry energy $L$ (the orange dashed line represents the best fit correlation). The purple dotted lines are the $1\sigma$ contours extracted from PREX [9]. The red solid lines show the constraints from Mainz $(\gamma ,{\pi }^0)$ measurements [12] and the green dotted lines show the constraints on $R_{\mathrm{skin}}$ from Osaka polarized proton elastic scattering measurements [5].

Figure 5

Neutron skin for ${}^{208}\mathrm{Pb}$ versus the curvature of the symmetry energy $K_{\mathrm{sym}}$ (the orange dashed line represents the best fit correlation). The purple dotted lines are the $1\sigma$ contours extracted from PREX [9]. The red solid lines show the constraints from Mainz $(\gamma ,{\pi }^0)$ measurements [12] and the green dotted lines show the constraints on $R_{\mathrm{skin}}$ from Osaka polarized proton elastic scattering measurements [5].