Constraints on neutron skin thickness in ${}^{208}\mathrm{Pb}$ and density-dependent symmetry energy

Accurate knowledge about the neutron skin thickness $\Delta R_{np}$ in ${}^{208}\mathrm{Pb}$ has far-reaching implications for different communities of nuclear physics and astrophysics. Yet, the novel lead radius experiment (PREX) did not yield any stringent constraint on $\Delta R_{np}$ recently. We employ a more practicable strategy to probe the neutron skin thickness of ${}^{208}\mathrm{Pb}$ based on a high linear correlation between the $\Delta R_{np}$ and $J-a_{\text{sym}}$, where $J$ and $a_{\text{sym}}$ are the symmetry energy (coefficient) of nuclear matter at saturation density and of ${}^{208}\mathrm{Pb}$. An accurate $J-a_{\text{sym}}$ thus places a strong constraint on the $\Delta R_{np}$. Compared with the parity-violating asymmetry $A_{\text{PV}}$ in the PREX, the reliably experimental information on the $J-a_{\text{sym}}$ is much more easily available thanks to the wealth of measured data on nuclear masses and decay energies. The density dependence of the symmetry energy is also well constrained with the $J-a_{\text{sym}}$. Finally, with a “tomoscan” method, we find that one just needs to measure the nucleon densities in ${}^{208}\mathrm{Pb}$ starting from $R_m=7.61\pm 0.04$ fm to obtain the $\Delta R_{np}$ in hadron scattering experiments, regardless of its interior profile being hampered by strong absorption.

Figure 1

Neutron skin thickness $\Delta R_{np}$ in ${}^{208}\mathrm{Pb}$ against the $J-a_{\text{sym}}$ with different nuclear energy-density functionals.

Figure 2

Correlation of the slope parameter $L$ at densities $\rho =0.16 {\mathrm{fm}}^{-3}$ and $\rho =0.11 {\mathrm{fm}}^{-3}$ with $J-a_{\text{sym}}$.

Figure 3

Density-dependent symmetry energy at high densities.

Figure 4

(a) Radial distribution function $f\left(r\right)$ of the neutron skin thickness in ${}^{208}\mathrm{Pb}$. The contributions from the two parts in the red shaded regions cancel each other out. The area under the curve of $f\left(r\right)$ starting from $R_m$ (blue filled region) is equal to the neutron skin thickness $\Delta R_{np}$. (b) Calculated $R_m$ values with different energy density functionals. The colored solid symbols are from the interactions generating the reference density ${\rho }_A\simeq 0.55{\rho }_0,a_{\text{sym}}\simeq 22.4$ MeV, and $J\simeq 32.4$ MeV. (c) Error accumulation of the $\Delta R_{np}$ measurement in hadron scattering experiments as a function of distance $r$, where the nucleonic density distributions are from Tables III and IV in Ref. [26].