Simultaneous microscopic description of charge radii and parity-violating asymmetries in $^{48}$Ca and $^{208}$Pb: resolving the CREX–PREX tension and the model dependence of neutron-skin extraction from parity-violating electron scattering

Precision parity-violating electron scattering (PVES) experiments at Jefferson Lab — CREX on $^{48}$Ca and PREX-II on $^{208}$Pb — measured parity-violating asymmetries $A_{\rm PV}$ whose microscopic interpretation remains unsettled. The first ab initio calculations of $A_{\rm PV}$ for both nuclei, based on an ensemble of 38 chiral-EFT Hamiltonians solved with the in-medium similarity renormalization group and including Coulomb distortion and $\gamma Z$-box plus vacuum-polarization corrections (Noël et al., 2026), deviate from the measurements at 2.0$\sigma$ ($^{48}$Ca, predicted $A_{\rm PV}$ smaller than observed) and 1.1$\sigma$ ($^{208}$Pb, predicted larger), a 1.9$\sigma$ global tension, and no current theoretical calculation reproduces the experimental charge radii and $A_{\rm PV}$ of both nuclei simultaneously. The extraction of neutron skins from $A_{\rm PV}$ measured at a single momentum transfer also retains quantified but non-negligible model dependence even when charge and weak densities are treated consistently, and the $^{208}$Pb charge-density database carries long-standing inconsistencies. The open problem is to establish a consistent microscopic description of the charge and weak structure of $^{48}$Ca and $^{208}$Pb that simultaneously reproduces the measured charge radii and asymmetries within quantified uncertainties, and to resolve the residual model dependence of neutron-skin inference from single-$q$ PVES data.

Background

In a neutron-rich nucleus the neutron density extends beyond the proton density, forming a neutron skin whose thickness $R_{\rm skin}=R_n-R_p$ (the difference of point-neutron and point-proton rms radii) is a primary probe of the isovector sector of the nuclear interaction. Because the proton's weak charge is strongly suppressed relative to the neutron's, parity-violating electron scattering (PVES) — the difference of elastic cross sections for left- and right-handed longitudinally polarized electrons — isolates the neutron distribution: in the plane-wave Born approximation the parity-violating asymmetry $A_{\rm PV}\simeq -(G_F q^2/4\pi\alpha_{\rm el}\sqrt{2})\,Q_{\rm w}F_{\rm w}(q)/(ZF_{\rm ch}(q))$, where $F_{\rm w}(q)$ and $F_{\rm ch}(q)$ are the weak and charge form factors and $q$ the momentum transfer. Significant Coulomb-distortion corrections from the nuclear potential must be included. Since $A_{\rm PV}$ is measured at a single fixed $q$, the weak distribution cannot be unfolded; instead, neutron skins are inferred via a correlation analysis that relates $A_{\rm PV}$ to $R_{\rm skin}$ or to the weak radius $R_{\rm w}$, which introduces nuclear-structure model dependence. The Jefferson Lab experiments PREX-II on $^{208}$Pb ($A_{\rm PV}=550\pm16\pm8$ ppb, implying $R_n-R_p=0.283\pm0.071$ fm) and CREX on $^{48}$Ca ($A_{\rm PV}=2668\pm106\pm40$ ppb, implying $R_n-R_p=0.121\pm0.026\pm0.024$ fm) produced a widely discussed puzzle: a thick skin in lead together with a thin skin in calcium, a pattern that most theoretical models — whether energy density functional (EDF) fits to global nuclear data or ab initio calculations — cannot reproduce. Noël et al. (2026) showed, however, that this skin-level framing is overstated: when theoretically consistent charge and weak densities are used, the measured asymmetries imply substantially smaller skins (see below), and the remaining open discrepancy is the mild tension between the measured $A_{\rm PV}$ values and the constraints from the experimental charge radii. This matters beyond nuclear structure because the neutron skin constrains the density dependence of the nuclear symmetry energy near saturation, conventionally parameterized by the slope $L$, which feeds directly into the equation of state of neutron-star matter. Ab initio nuclear theory derives nuclear structure from two- and three-nucleon forces organized in chiral effective field theory (an EFT of QCD at low energies) and solves the many-body problem with controlled methods; here the in-medium similarity renormalization group (IMSRG), an iterative decoupling transformation of the Hamiltonian, truncated at the two-body level (IMSRG(2)), with the IMSRG(3) extension currently too expensive for $^{208}$Pb. Noël et al. (2026) performed the first such ab initio calculation of $A_{\rm PV}$ for both nuclei, using an ensemble of 38 chiral Hamiltonians to propagate interaction uncertainty, a reanalysis of the $^{208}$Pb charge density from electron-scattering data (whose decades-old database requires substantial inflation of uncertainties, especially near the nuclear center), and radiative corrections from $\gamma Z$ box diagrams and vacuum polarization at the percent level. They found a mild global 1.9$\sigma$ tension with opposite signs in the two nuclei, inferred $R_{\rm skin}(^{208}{\rm Pb})=0.187(25)(18)$ fm from the measured $A_{\rm PV}$ with theoretically consistent charge and weak densities — substantially smaller than the PREX-II central value — and showed that the slope of the $A_{\rm PV}$–$R_{\rm skin}$ correlation differs depending on which variable is treated as independent, so that single-$q$ skin extraction retains non-negligible model dependence with direct implications for the planned MREX experiment at the MESA accelerator in Mainz, which aims to measure $A_{\rm PV}$ in $^{208}$Pb with substantially higher precision.

Problem Statement

Can nuclear theory provide a consistent microscopic description of the electroweak structure of $^{48}$Ca and $^{208}$Pb — a calculation, or a well-defined class of calculations, that simultaneously reproduces the measured parity-violating asymmetries ($A_{\rm PV}=2668\pm106\pm40$ ppb for CREX on $^{48}$Ca; $A_{\rm PV}=550\pm16\pm8$ ppb for PREX-II on $^{208}$Pb) and the experimental charge radii of both nuclei? Reproduction means agreement within combined theoretical and experimental uncertainties, with the uncertainties quantified and residual deviations reported as per-nucleus and combined significances in the same convention as Noël et al. (2026) — currently 2.0$\sigma$ (CREX), 1.1$\sigma$ (PREX-II) and 1.9$\sigma$ global — and with the charge-radius inputs used for calibration stated explicitly, whether the Angeli–Marinova (2013) compilation values or a reanalysis of the electron-scattering data with consistently inflated uncertainties and muonic-atom constraints as in Noël et al. (2026) ($R_{\rm ch}(^{208}{\rm Pb})=5.5077(36)$ fm), since the treatment of the inconsistent $^{208}$Pb charge-density database is itself part of the problem. This first question is resolved affirmatively by exhibiting such a calculation or class of calculations meeting the reproduction criterion, and it is resolved negatively — a resolution of equal standing — by demonstrating, with uncertainties quantified in the same convention, that no such calculation exists. Independently of which branch of this question is established, a complete solution must also resolve the residual model dependence in inferring the neutron skin $R_{\rm skin}$ and weak radii from $A_{\rm PV}$ measured at a single momentum transfer that persists even with the theoretically consistent charge and weak densities already constructed by Noël et al. (2026): the sensitivity of the inferred skins to the analysis choices documented there (theoretical versus experimental charge density; inferring $R_{\rm w}$ versus $R_{\rm skin}$ directly) and the slope asymmetry of the $A_{\rm PV}$–$R_{\rm skin}$ correlation must be shown to lie within the stated uncertainties or otherwise eliminated, for the existing CREX/PREX-II data; the implications for future single-$q$ measurements such as the planned MREX experiment at MESA are context for this requirement rather than a separate deliverable.

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