2026/07/24 by Soonchul Choi, Tae-Sun Park, Panagiota Papakonstantinou
#nucl-th
Recent experimental advances could soon allow the accurate extraction of not only the root-mean-square radius but also the fourth radial moment of the nuclear electric charge density distribution. The fourth radial moment of the nuclear density distribution, R4≡√[4]<r4>, provides a sensitive probe of the nuclear surface thickness, as it is more susceptible to the large-r distributions than the root-mean-square radius (R2). In this work, we examine the utility of R4 for constraining the nuclear equation of state (EoS) at subsaturation densities, specifically for the proton distribution and within the framework of Skyrme energy density functionals. Using a statistical analysis based on predictions from one hundred Skyrme functional models, we demonstrate strong correlations between the energy per particle curvature K(ρ) at ρ= 0.08 fm-3 and R4 (or the ratio R4/2=R4/R2) in representative nuclei such as 48Ca and 208Pb. We establish that R4/2, being sensitive to the density tail, serves as an efficient proxy for sub-saturation K(ρ) within the tested Skyrme functional space. Knowledge of R4/2 within 0.5% precision or better, for example in 48Ca or 208Pb, could constrain the curvature of the energy per particle of symmetric matter at 0.08 fm-3 within 20 MeV or less.