Universal relation between dipole polarizability of finite nuclei and neutron-star compactness

TL;DR

The work addresses the stiffness-uncertainty of the nuclear equation of state by establishing an EOS-insensitive universal relation between finite-nucleus dipole polarizability $\alpha_D$ and neutron-star compactness, mediated by the dimensionless quantity $\zeta = \beta_{1.4}\,\tilde{L}^{-1}$ with $\tilde{L}=L/L_0$. Using a broad set of energy-density functionals (relativistic DD--PC, DD--ME, NL and non-relativistic Skyrme), the authors show an exponential $\zeta$–$\alpha_D$ correlation that remains robust across EOSs, and they parametrize it as $\zeta(\alpha_D,A,\delta)=c_1(A)e^{-c_2(A)\alpha_D}+c_3(\delta)$ with $A$- and $\delta$-dependent coefficients. The CNSP-4 and CNSP-10 experimental dipole data provide two bounds on $\zeta$, which translate into bounds on the neutron-star radius $R_{1.4}$ and the symmetry-energy slope $L$, including an explicit $R_{1.4}$–$L$ relation and the product $R_{1.4}L$ as a consistency criterion. The framework also yields predictions for $\alpha_D$ in nuclei not yet measured (e.g., $^{52}$Ca, $^{90}$Zr, $^{132}$Sn$)$ that agree with microscopic EDF calculations, illustrating its predictive power. Overall, the study links terrestrial nuclear measurements to neutron-star physics in a model-independent way and provides a practical tool to constrain the density dependence of the symmetry energy and neutron-star structure.

Abstract

The nuclear equation of state, which determines the structure and properties of neutron stars, remains subject to substantial theoretical uncertainties, leading to model dependence in predicted observables. Universal relations have emerged as a powerful tool to mitigate this dependence by linking neutron star observables in a framework-independent manner. In this work, we introduce a new universal relation that \emph{bridges} finite nuclei and neutron stars through the dimensionless quantity $ζ= β_{1.4}\tilde{L}^{-1}$, which couples the compactness of a $1.4~M_{\odot}$ neutron star to the slope of the nuclear symmetry energy at saturation. The relation is examined under a broad set of relativistic energy density functionals with point-coupling and meson-exchange interactions, as well as non-relativistic Skyrme functionals. We demonstrate that $ζ$ exhibits a strong exponential correlation with the electric dipole polarizability $α_D$ in finite nuclei across all considered equations of state. By exploiting experimental $α_D$ data for selected neutron-rich nuclei, we constrain $ζ$ and translate these constraints into equation-of-state-independent bounds on the neutron star radius $R_{1.4}$ and the symmetry-energy slope $L$, providing insights into the properties of neutron star matter.

Figures (4)

• Figure 1: (a) The energy density as a function of pressure for the full set of EOSs. (b) The corresponding gravitational mass as a function of radius for the full set of EOSs. The shaded contour labeled HESS indicates constraints inferred from the HESS J1731--347 supernova remnant Doroshenko-2022. Additional observational constraints are shown for: (i) PSR J0740+6620 Fonseca_2021Dittmann_2024, (ii) PSR J0437--4715 Choudhury_2024, (iii) PSR J0030+0451 Riley_2019Raaijmakers_2019, and (iv) PSR J1231--1411 Salmi_2024. Horizontal shaded bands denote mass measurements of the massive pulsars PSR J1614--2230 Arzoumanian-2018, PSR J0348+0432 Antoniadis-2013, and PSR J0952--0607 Romani-2022, providing lower bounds on the maximum neutron star mass. Constraints from the binary neutron star merger GW170817 Abbott-2019 are also indicated.
• Figure 2: The dimensionless quantity $\zeta \equiv \beta_{1.4}\,\tilde{L}^{-1}$ as a function of the electric dipole polarizability $\alpha_D$ for the full set of EOSs. Vertical shaded regions indicate experimental values of $\alpha_D$ for: (a) $^{48}$Ca Birkhan2017, (b) $^{68}$Ni PhysRevLett.111.242503, (c) $^{120}$Sn Rokamaza2015PhysRevC.92.031305, (d) $^{208}$Pb Rokamaza2015PhysRevLett.107.062502, and (e--j) $^{112-124}$Sn Bassauer2020. The solid curve represents the universal relation \ref{['eq:un_rel']}, with the shaded band indicating its associated uncertainty.
• Figure 3: The radius of a canonical $1.4~M_{\odot}$ neutron star, $R_{1.4}$, as a function of the slope of the symmetry energy $L$ for the full set of EOSs. Curved shaded regions indicate constraints inferred from the CNSP-4 and CNSP-10 sets of nuclei. The solid curve shows the systematic trend described by Eq. \ref{['eq:radius_L']}, with the associated uncertainty represented by the shaded band. Vertical arrows denote neutron-star radius constraints from Refs. Capano-2020doi:10.1126/science.abb4317, while the horizontal shaded region indicates the radius of PSR J0437--4715 Choudhury_2024.
• Figure 4: The dimensionless quantity $\zeta \equiv \beta_{1.4}\tilde{L}$ as a function of the electric dipole polarizability $\alpha_D$ for the full set of EOSs, shown for (a) $^{52}$Ca, (b) $^{90}$Zr, and (c) $^{132}$Sn. The solid curve represents the universal relation \ref{['eq:un_rel']}, with the associated uncertainty indicated by the shaded band. Horizontal shaded regions indicate constraints inferred from the CNSP-4 and CNSP-10 sets of nuclei, while vertical shaded regions indicate the corresponding bounds on the dipole polarizability.