Neutron Skin of ${}^{208}\mathrm{Pb}$, Nuclear Symmetry Energy, and the Parity Radius Experiment

A precise determination of the neutron skin $\Delta r_{np}$ of a heavy nucleus sets a basic constraint on the nuclear symmetry energy ($\Delta r_{np}$ is the difference of the neutron and proton rms radii of the nucleus). The parity radius experiment (PREX) may achieve it by electroweak parity-violating electron scattering (PVES) on ${}^{208}\mathrm{Pb}$. We investigate PVES in nuclear mean field approach to allow the accurate extraction of $\Delta r_{np}$ of ${}^{208}\mathrm{Pb}$ from the parity-violating asymmetry $A_{\mathrm{PV}}$ probed in the experiment. We demonstrate a high linear correlation between $A_{\mathrm{PV}}$ and $\Delta r_{np}$ in successful mean field forces as the best means to constrain the neutron skin of ${}^{208}\mathrm{Pb}$ from PREX, without assumptions on the neutron density shape. Continuation of the experiment with higher precision in $A_{\mathrm{PV}}$ is motivated since the present method can support it to constrain the density slope of the nuclear symmetry energy to new accuracy.

Figure 1

Parity-violating asymmetry for ${}^{208}\mathrm{Pb}$ at the kinematics of PREX against the neutron radius of ${}^{208}\mathrm{Pb}$ in nuclear models. The linear fit is ${10}^7{A}_{\mathrm{PV}}=25.83-3.31r_n$. The inner (outer) colored regions depict the loci of the 95% confidence (prediction) bands of the regression (see, e.g., Chap. 3 of 27). An assumed sample measurement $A_{\mathrm{PV}}=0.715\mathrm{ppm}$ of 3% accuracy and its projection on the $r_n$ axis are also drawn.

Figure 2

Same as Fig. 1 against the neutron skin of ${}^{208}\mathrm{Pb}$. The linear fit is ${10}^7{A}_{\mathrm{PV}}=7.88-3.75\Delta r_{np}$. The correlation is found to be quite stable; for example, if we remove the forces excluded by the depicted test constraint, then $r=0.990$. The figure also shows the points calculated with the neutron densities deduced from experiment in Refs. 2, 3, 5.

Figure 3

Neutron skin of ${}^{208}\mathrm{Pb}$ against slope of the symmetry energy. The linear fit is $\Delta r_{np}=0.101+0.00147L$. A sample test constraint from a 3% accuracy in $A_{\mathrm{PV}}$ is drawn.