Radii of neutron drops probed via the neutron skin thickness of nuclei

Multineutron systems are crucial to understanding the physics of neutron-rich nuclei and neutron stars. Neutron drops, neutrons confined in an external field, are investigated systematically in both nonrelativistic and relativistic density functional theories and with ab initio calculations. We demonstrate a new strong linear correlation, which is universal in the realm of mean-field models, between the rms radii of neutron drops and the neutron skin thickness of ${}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}$, i.e., the difference between the neutron and proton rms radii of a nucleus. Due to its high quality, this correlation can be used to deduce the radii of neutron drops from the measured neutron skin thickness in a model-independent way, and the radii obtained for neutron drops can provide a useful constraint for realistic three-neutron forces. We also present a new correlation between the slope $L$ of the symmetry energy and the radii of neutron drops, and provide the first validation of such a correlation by using density-functional models and ab initio calculations. These newly established correlations, together with more precise measurements of the neutron skin thicknesses of ${}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}$ and/or accurate determinations of $L$, will have an enduring impact on the understanding of multineutron interactions, neutron-rich nuclei, neutron stars, etc.

Figure 1

Total energies (scaled by $\hslash \omega N^{4/3}$) of $N\text{-neutron}$ systems in a HO trap ($\hslash \omega =10$ MeV) predicted with various relativistic density functionals (solid symbols). The shaded area indicates the ab initio QMC results from Refs. [14, 15] for the $\mathit{NN}$ interaction $\mathrm{AV}{8}^{\prime }$ (center dashed line) as well as the $\mathrm{AV}{8}^{\prime }$ plus $3N$ interactions of UIX (upper solid line) and IL7 (lower solid line).

Figure 2

(a) Neutron skin thickness $\mathrm{\Delta }{r}_{np}$ of ${}^{208}\mathrm{Pb}$ against the rms radius $R$ of 20 neutrons trapped in a HO potential with $\hslash \omega =$ 10 MeV for various nuclear density functionals. The inner (outer) colored regions depict the 95% confidence (prediction) intervals of the linear regression, and Pearson's correlation coefficient $r$ is also displayed ( $r$ is a value between +1 and 1 inclusive, where +1 is total positive correlation, 0 is no correlation, and 1 is total negative correlation; see, e.g., Ref. [56]). The data of $\mathrm{\Delta }{r}_{np}$ in different measurements with antiprotonic atoms [31] (circle), pion photoproduction [28] (square), and electric dipole polarizability [57] (diamond) are also given together with their projections on the radius of the neutron drop. (b) Same plot, but for the neutron skin thickness $\mathrm{\Delta }{r}_{np}$ of ${}^{48}\mathrm{Ca}$. The estimate of $\mathrm{\Delta }{r}_{np}$ is from a prediction of electric dipole polarizability [58].

Figure 3

The rms radii for three neutron drops determined from their linear correlations with the neutron skin thicknesses of ${}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}$. For comparison, the ab initio results obtained using phenomenological forces and local chiral forces of Ref. [63] are also shown.

Figure 4

Values of the slope $L$ of the symmetry energy against rms radii of 20 neutrons in a HO with $\hslash \omega =10$ MeV, obtained with density functional theories (open circles) and ab initio methods (solid circles).