Ab initio predictions link the neutron skin of $^{208}$Pb to nuclear forces

The study investigates how the neutron skin thickness of heavy nuclei, particularly 208Pb, encodes information about the isovector sector of nuclear forces and connects to the neutron-matter equation of state relevant for neutron stars. Mean-field energy density functional approaches predict a wide range for the neutron skin in 208Pb due to poorly constrained isovector terms, and systematic uncertainty estimation is challenging in those frameworks. In contrast, ab initio methods with quantified uncertainties have successfully treated neutron matter and medium-mass nuclei such as 48Ca, but 208Pb has remained inaccessible due to computational limitations. Recent advances in quantum many-body algorithms, uncertainty quantification, and fast emulators now enable ab initio predictions up to 208Pb. The purpose is to develop a unified framework linking nucleon–nucleon scattering and few-body data to medium- and heavy-mass nuclei (up to 208Pb) and nuclear matter near saturation, to predict the 208Pb neutron skin with quantified uncertainties and to explore its correlations with nuclear matter parameters and experimental observables.

• Mean-field calculations yield a broad range of predicted neutron skin thicknesses in 208Pb because isovector components of energy density functionals are weakly constrained by binding energies and charge radii; adding electric dipole polarizability information can help but introduces model dependence that is difficult to quantify.
• Ab initio computations have achieved precise results for the neutron-matter equation of state and for the neutron skin in 48Ca, offering a path to systematic uncertainty estimation.
• Heavy nuclei have been increasingly accessible due to algorithmic breakthroughs, with prior ab initio applications to tin isotopes. However, a consistent ab initio treatment of 208Pb had not been realized.
• The parity-violating electron scattering experiment PREX provided a recent extraction of the 208Pb neutron skin, while other probes (elastic proton scattering, antiprotonic atoms, coherent pion photoproduction) and multimessenger astrophysical constraints also inform the neutron skin and symmetry energy but entail varying degrees of model dependence.
• Theoretical groundwork in chiral effective field theory (EFT), including treatments with Δ isobars and quantified truncation errors, underpins modern nuclear force construction and uncertainty quantification.

• Nuclear interactions: Based on chiral EFT including Δ isobar degrees of freedom. At next-to-next-to-leading order (NNLO) in Weinberg power counting, long-range pion exchanges are fixed; four πN low-energy constants (LECs) are set from pion–nucleon scattering. Thirteen additional nuclear LECs (two- and three-nucleon short-range) are constrained.
• History matching and emulation: Employed iterative history matching to explore the 17-dimensional LEC space, using eigenvector continuation emulators for fast, accurate predictions. History-matching observables include nucleon–nucleon phase shifts (up to 200 MeV), deuteron energy, radius, quadrupole moment, and the energies/radii of 3H, 3He, and 16O. Five waves of parameter space reduction were performed using an implausibility measure that incorporates experimental, emulator, method, and model (EFT truncation) errors. Starting from millions of candidate samples, 34 non-implausible interaction parameterizations remained.
• Ab initio solvers and model spaces: For finite nuclei (Ca isotopes and 208Pb), used coupled cluster (CC), in-medium similarity renormalization group (IMSRG), and many-body perturbation theory (MBPT). Model spaces up to 15 major harmonic oscillator shells (e_max=14, ℏω=10 MeV). Three-nucleon forces truncated at E_3max=28 and included via normal-ordered two-body approximation; a dedicated storage scheme retained only linear combinations entering the normal-ordered two-body terms. Convergence was analyzed and extrapolated; ground-state energies were shifted by −75 ± 60 MeV due to basis extrapolations, with a small +0.005 ± 0.010 fm shift in neutron skin.
• Many-body details: IMSRG at IMSRG(2) with Magnus formulation; operators for radii, form factors, and E1 operator consistently transformed. Dipole polarizability α_D from EOM-IMSRG(2,2) and Lanczos continued fraction. MBPT to third order for energies, second order for radii. CC calculations at CCSD for 208Pb with triples estimated as 10% of CCSD correlation energy; for 40Ca, used A-CCSD(T), and EOM-CCSD for the 2+ state (with −1 MeV triples estimate).
• Emulators for 16O: Sub-space projected CC with CCSDT-3 training vectors at 68 LEC design points enabled rapid evaluations during history matching, verified by cross-validation (<0.2% error).
• Calibration and posterior sampling: The 34 non-implausible interactions were weighted via a Gaussian likelihood (sampling/importance resampling) using calibration data from 48Ca (E/A, R_p, E_2+), with independent EFT and method errors. Sensitivity checks with non-diagonal covariance and Student-t likelihoods yielded ~1% changes in credibility regions.
• EFT truncation errors: Modeled via an expansion with natural-sized coefficients and expansion parameter Q≈0.41–0.42. For energies in finite nuclei, model errors anchored to nuclear matter analysis; for radii and α_D, used order-by-order differences across isotopic chains to set model error scales.
• Nuclear matter calculations and error model: Nuclear matter equation of state (EOS) computed with CCD(T) on a momentum-space lattice, including residual 3N effects in triples, using 66 neutrons (PNM) and 132 nucleons (SNM) with periodic boundary conditions. A Bayesian machine-learning error model based on multi-task Gaussian processes quantified density-dependent EFT truncation and CC method errors and their correlations across PNM and SNM. Learned hyperparameters set correlation lengths and variances; finite-size and cluster-operator truncation errors were incorporated with conservative credible intervals.
• Posterior predictive distributions (PPDs): Generated by resampling the 34 weighted interactions and adding sampled method and model errors. Predictions cover finite-nucleus observables (energies, R_p, R_n, α_D, form factors) and EOS properties (ρ0, E/A, K, S, L). Correlations with R_skin(208Pb) were analyzed.

• Ab initio predictions reproduce bulk properties of 208Pb within quantified uncertainties and validate against measured electric dipole polarizabilities in 48Ca and 208Pb.
• Neutron skin of 208Pb: R_skin(208Pb) = 0.14–0.20 fm (68% credible interval), with median 0.171 fm and 90% CR [0.120, 0.221]. Prediction shows mild tension (~1.5σ) with PREX but agrees with extractions from elastic proton scattering, antiprotonic atoms, coherent pion photoproduction, and constraints from gravitational waves.
• Nuclear matter at saturation (posterior medians; 68% CR): E/A = −16.9 MeV [−17.9, −15.4]; ρ0 = 0.167 fm−3 [0.150, 0.181]; S = 31.1 MeV [29.1, 33.2]; L = 52.7 MeV [38.3, 68.5]; K = 287 MeV [242, 331]. These are consistent with empirical bounds and reveal correlations between R_skin(208Pb) and EOS parameters, especially L.
• Strong correlation found between the weak form factor F_w and electric form factor F_e at the PREX momentum transfer; small variance across non-implausible samples for F_w−F_e in 48Ca and 208Pb.
• The predicted thin neutron skin arises from isovector physics constrained by NN scattering. Both R_skin(208Pb) and L correlate with np scattering in the 3S1 channel around 50 MeV; attempts to increase L beyond the predicted range by tuning contacts degrade scattering phase shifts beyond expected higher-order corrections.
• The framework establishes consistent links from NN scattering and few-body data to medium- and heavy-nucleus properties and the EOS, enabling quantitative predictions with uncertainties across the nuclear chart.

The study demonstrates that chiral EFT-based ab initio methods, constrained by NN scattering and few-body observables and augmented with emulator-enabled global parameter exploration and rigorous uncertainty quantification, can predict properties of a heavy nucleus (208Pb) and the neutron skin with credible intervals. The predicted R_skin(208Pb) is thin and tightly constrained, in line with multiple hadronic and electromagnetic probes but showing mild tension with PREX. The tightness of the prediction stems from scattering data constraining the isovector sector, which in turn constrains neutron matter and skins. Correlations are quantified between R_skin(208Pb) and EOS quantities such as L, matching trends known from mean-field models but now within an ab initio framework. Attempts to shift L and R_skin upward by retuning LECs while preserving saturation properties compromise NN phase-shift quality, highlighting the consistency requirements imposed by scattering data. Further experimental precision on neutron skins and parity-violating form factors will critically test the ab initio description and its error models. The approach validates that information from scattering systematically propagates to many-body nuclei and nuclear matter, providing a coherent picture across scales.

This work presents the first quantitative ab initio predictions for 208Pb with full uncertainty quantification, linking NN scattering and few-body data through chiral EFT to heavy nuclei and the nuclear-matter EOS. Using iterative history matching with fast emulators and multiple many-body solvers (CC, IMSRG, MBPT), the authors identified 34 non-implausible interaction parameterizations and produced posterior predictive distributions for finite nuclei and nuclear matter. They predict a thin 208Pb neutron skin (0.14–0.20 fm), consistent with several probes but mildly in tension with PREX, and obtain EOS properties at saturation consistent with empirical constraints. The framework reveals robust correlations between R_skin and L and demonstrates that scattering data significantly constrain isovector physics. Future work should extend to higher EFT orders, explore regulator independence by increasing cutoffs, and confront predictions with more precise electroweak measurements, thereby enhancing precision and testing the robustness of the ab initio program across the nuclear landscape.

• EFT truncation: Interactions are at NNLO with quantified but finite truncation errors; higher-order contributions are not yet included.
• Many-body approximations: CC limited to CCSD for 208Pb with estimated triples; IMSRG(2) and MBPT truncations introduce method errors. Normal-ordered two-body approximation used for 3N forces in finite nuclei.
• Model-space truncations and extrapolations: Finite e_max and E_3max required extrapolations; residual shifts and uncertainties remain.
• Emulator and calibration scope: Final parameter ensemble consists of 34 samples; although weighted, finite sampling may underresolve complex posterior features. Calibration leveraged 48Ca bulk and E2+ only; additional calibration data could refine posteriors.
• Form factors: EFT and method errors for weak and electric form factors at PREX/CREX kinematics were not fully quantified (variance across samples reported, but no full error model provided).
• Tension with PREX: Mild discrepancy suggests either experimental-systematic issues or missing physics/higher-order effects in the theoretical framework, to be resolved by future work.