Supernova neutrinos as a precise probe of nuclear neutron skin

Abstract

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 ($\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$). We evaluate the potential of determining the ${R}_{n}$ of lead (Pb) via $\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$ 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 $\ensuremath{\sim}0.1%$ for the ${R}_{n}$ ($\ensuremath{\sim}0.006\text{ }\text{ }\mathrm{fm}$ 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 $\ensuremath{\sim}1\text{ }\text{ }\mathrm{kpc}$ from the Earth.