Supernova neutrinos as a precise probe of nuclear neutron skin

A precise and model-independent determination of the neutron distribution radius $R_n$ and thus the neutron skin thickness $R_{\mathrm{skin}}$ of atomic nuclei is of fundamental importance in nuclear physics, particle physics, and astrophysics but remains a big challenge in terrestrial labs. We argue that the nearby core-collapse supernova (CCSN) in our Galaxy may render a neutrino flux with unprecedentedly high luminosity, offering the perfect opportunity to determine the $R_n$ and $R_{\mathrm{skin}}$ through the coherent elastic neutrino-nucleus scattering ($\mathrm{CE}\nu \mathrm{NS}$). We evaluate the potential of determining the $R_n$ of lead (Pb) via $\mathrm{CE}\nu \mathrm{NS}$ with the nearby CCSN neutrinos in the RES-NOVA project which is designed to hunt CCSN neutrinos using an array of archaeological Pb based cryogenic detectors. We find that an ultimate precision of $\sim 0.1\%$ for the $R_n$ ($\sim 0.006\mathrm{fm}$ for the $R_{\mathrm{skin}}$) of Pb can be achieved via RES-NOVA in the most optimistic case that the CCSN explosion were to occur at a distance of $\sim 1\mathrm{kpc}$ from the Earth.

Figure 1

The predicted event counts per 1 keV versus nuclear kinetic recoil energy $T$ at the RES-NOVA detector for a SN at 1 kpc ($N_1$, blue solid line) and 5 kpc ($N_5$, red solid line), using the PREX-2 result as the averaged $R_{\mathrm{skin}}$ of Pb. The dashed lines ($\delta N_1$ and $\delta N_5$) show the change amplitude of counts with a 0.06 fm variation of the neutron skin thickness. The relative variation $\delta N/N$ of the counts is given for both SN distances by the black line (right axis).

Figure 2

The expected sensitivity to the variation of neutron skin thickness $\delta R_{\mathrm{skin}}$ for a SN at 1 kpc (blue lines) and 5 kpc (red lines) with 1% (solid lines) and 5% (dashed lines) systematic error.

Figure 3

The expected precision of the averaged neutron radius $R_n$ (in percent) as a function of the systematic uncertainty for a 1 kpc (blue solid line) and 5 kpc (red dashed line) SN. The results from PREX-2 [33] and the future MREX [38] are also included for comparison.