Pith. sign in

REVIEW 4 major objections 3 minor 1 cited by

Three covariant functionals with a strong isovector tensor coupling reproduce both the PREX-II and CREX parity-violating electron scattering measurements within 1σ uncertainties.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 21:24 UTC pith:R6CB4RFQ

load-bearing objection Useful existence proof, but the title's IVSO mechanism is contradicted by the paper's own decomposition—the fitted bIV acts through the central mean field, not the spin-orbit potential. the 4 major comments →

arxiv 2511.15385 v2 pith:R6CB4RFQ submitted 2025-11-19 nucl-th nucl-ex

A relativistic mechanism for the enhanced isovector spin-orbit interaction suggested by parity-violating electron scattering experiments

Mengying Qiu , Tong-Gang Yue , Zhen Zhang , Lie-Wen Chen This is my paper
classification nucl-th nucl-ex MSC 81V35 PACS 21.60.-n24.80.+y25.30.Bf
keywords PREX-CREX puzzleisovector spin-orbit interactionisovector tensor couplingcovariant density functional theorypoint-coupling modelparity-violating electron scatteringneutron skin thicknesssymmetry energy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that the PREX-CREX puzzle—the tension between parity-violating electron scattering results on 208Pb (PREX-II) and 48Ca (CREX) that no conventional density functional could resolve—can be removed by treating the isovector tensor coupling in a covariant point-coupling functional as a free parameter rather than fixing it by the Fierz transformation. In the nonrelativistic limit this coupling acts as a strong isovector spin-orbit force, whose strength is roughly six times larger than in the parent functional. Because the two nuclei have different shell fillings, the enhanced force reduces the charge-weak form-factor difference of 48Ca substantially while leaving that of 208Pb essentially unchanged. Three new parametrizations constructed by the authors fit both data sets within 1σ and also retain reasonable binding energies, charge radii, spin-orbit splittings, and a pure neutron matter equation of state consistent with chiral effective field theory.

Core claim

The central discovery is that the isovector tensor coupling ατT—normally locked to about 0.535 fm² by the Fierz rearrangement in the PCF-PK1 functional—can be promoted to a free parameter of 7–9 fm². A systematic nonrelativistic reduction shows that this large ατT enhances the isovector spin-orbit strength bIV by about a factor of six (from roughly 35 to 220 MeV·fm⁵). In 48Ca, whose eight unpaired 1f7/2 neutrons generate a large isovector spin-orbit density, the enhanced bIV lowers ΔF_CW from 0.0405 to about 0.033, matching the CREX value; in 208Pb the contributions of spin-orbit partner orbitals largely cancel, so ΔF_CW remains near the PREX-II value. This provides a consistent relativistic

What carries the argument

The central object is the isovector tensor coupling ατT in the density-dependent point-coupling covariant Lagrangian. The argument runs through a nonrelativistic reduction of the covariant energy density to a Skyrme-like spin-orbit form E_SO = (bIS/2)∇ρ·J + (bIV/2)∇ρ̃·J̃ + (bSV/2)∇ρ·J̃, where bIV = 8B0²ατT − 4B0²ατS. This identity is the mechanism: it converts the relativistic tensor coupling into a strong isovector spin-orbit interaction and explains the isotope-dependent effect on the weak form factor.

Load-bearing premise

The load-bearing premise is that the isovector tensor coupling ατT can be freed from the Fierz transformation and pushed to values of order 7–9 fm² without violating the underlying Lorentz-invariant contact interaction; if this promotion is not theoretically legitimate, the resolution of the puzzle is an artifact of the enlarged parameter space.

What would settle it

The claim would collapse if a consistent Fierz or microscopic derivation shows that ατT cannot plausibly exceed about 1 fm², or if a higher-precision measurement of ΔF_CW in 48Ca at the CREX momentum transfer lands near the PCF-PK1 value 0.041 rather than the ZH values ≈0.033 (current experimental value 0.0277 ± 0.0055 does not distinguish them at 1σ).

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Simultaneous reproduction of PREX-II and CREX within 1σ is possible in covariant EDFs while maintaining ground-state properties and the neutron matter equation of state.
  • The strong isovector spin-orbit interaction has a concrete relativistic origin, namely the isovector tensor coupling.
  • The enhanced isovector tensor coupling does not destroy the shell closures of 48Ca or 208Pb; spin-orbit partner orderings remain intact.
  • The neutron skin of 208Pb becomes nearly independent of the symmetry energy slope at saturation density, while the correlation with the slope at 2/3 saturation density survives.
  • Parity-violating electron scattering on 48Ca is a direct probe of the isovector tensor coupling.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A natural next step would be to derive a microscopic bound on ατT from ρ-meson exchange or chiral effective field theory; if such a derivation cannot produce values above ~1 fm², the present functionals should be read as effective, not fundamental.
  • The paper's orbital decomposition suggests that the dominant effect of the strong isovector spin-orbit force on ΔF_CW^48 arises through the central mean field, not through the single-particle spin-orbit potential; this distinction could be tested by measuring ΔF_CW at other momentum transfers or by studying spin-orbit splittings in 48Ca.
  • If future PVES experiments on other N ≈ 28 nuclei confirm the ZH predictions, the isovector tensor coupling would become a new observable-effective parameter, with consequences for neutron-star weak-charge densities and coherent neutrino scattering cross sections.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper proposes a covariant density-dependent point-coupling (DDPC) explanation of the PREX-II/CREX tension. Starting from the PCF-PK1 functional, the authors promote the isovector tensor coupling ατT from its Fierz-derived value to a free parameter, refit a nine-parameter set to a likelihood that includes ΔF_CW(208Pb), ΔF_CW(48Ca), selected ground-state properties, spin-orbit splittings, the symmetry-energy point at 2ρsat/3, and a chiral-EFT neutron-matter constraint, and select three posterior samples (ZH-1/2/3) that reproduce both ΔF_CW values within 1σ. A nonrelativistic reduction is used to identify an enhanced isovector spin-orbit strength bIV, which is claimed to reconcile the two experiments through the different shell structures of 48Ca and 208Pb. However, the paper's own orbital decomposition indicates that the dominant effect of bIV on ΔF_CW(48Ca) is through the central mean field, not the spin-orbit potential, and the two headline observables are fit targets, not predictions.

Significance. If the mechanism claim were robust, this would be a significant step: it would show, within a covariant EDF, that an isovector tensor coupling can generate the strong isovector spin-orbit interaction needed to simultaneously describe PREX-II and CREX without destroying magic numbers or the empirical symmetry-energy constraints. The manuscript is transparent about its fitting protocol and provides particle parameters and extensive supplementary analysis, which is a strength. However, the significance is substantially weakened by two load-bearing issues: (i) the paper's own decomposition attributes the ΔF_CW reduction to central-mean-field modifications, contradicting the title/abstract's claim that a strong isovector spin-orbit interaction is the operative mechanism; and (ii) the agreement with PREX-II and CREX is guaranteed by construction because those observables enter the likelihood and the ZH functionals were selected post hoc from the posterior. The work is therefore best read as an existence proof of a covariant EDF that can accommodate both measurements, not as an explanation or a prediction. With reframing and additional decomposition diagnostics, the core result could stil

major comments (4)
  1. [Main text, 'Resolution' paragraph; SM Sec. S.IV and Fig. S6] The central mechanism claim is contradicted by the paper's own analysis. After deriving the central potential U_q and spin-orbit potential W_q in Eqs. (S33)–(S34), the authors state that the 'dominant effect of bIV arises through modifications of the central mean-field rather than the spin-orbit potential,' and Fig. S6 shows single-orbital contributions to ΔF_CW(48Ca) that are relatively uniform, not the high-l, spin-orbit-partner pattern expected if the SO channel were dominant. Yet the title, abstract, introduction, and summary all attribute the resolution to a 'strong isovector spin-orbit interaction.' This is an internal inconsistency in the causal claim. To support the stated mechanism, the paper must quantify the separate contributions to ΔF_CW from the ∇²ρ̃/∇·J central terms and the spin-orbit terms, e.g., by switching off each term in the effective Hamiltonian. As written, the ev
  2. [SM Sec. S.II, Eq. (S10), and selection criteria] The headline agreement with PREX-II and CREX is guaranteed by construction. ΔF_CW(208Pb) and ΔF_CW(48Ca) appear directly in the log-likelihood (Eq. S10), and the three ZH functionals are selected from the posterior precisely by requiring that they reproduce these values within 1σ (criteria 1–4). Therefore Fig. 1 and Table I demonstrate that parameters exist that fit the data, not that the model resolves the puzzle in a predictive sense. The manuscript should either explicitly frame the result as an existence proof or provide an out-of-sample check, e.g., a cross-validation where the ΔF_CW constraints are excluded in the fit and only the mechanism parameters are transferred, or a demonstration that the fitted ατT is stable when the ΔF_CW data are removed.
  3. [Eq. (1) and Table I (ατT and Fierz relation)] The paper treats ατT as a free parameter while the parent functional PCF-PK1 imposes ατT = (αS + 3ατS + 2αV − 6ατV + 6αT)/18 via the Fierz transformation. The fitted values in Table I are 6.97–9.20 fm², an order of magnitude larger than the PCF-PK1 value of 0.535 fm². Since the nonrelativistic bIV = 8B0²ατT − 4B0²ατS is dominated by this parameter, the entire mechanism rests on the admissibility of decoupling ατT from the Fierz relation. The paper gives no criterion for when such decoupling is legitimate within the underlying Lorentz-invariant contact theory. Without this justification, the large ατT values could simply be an artifact of enlarging the parameter space. I ask the authors to show that the resulting EDF still represents a consistent point-coupling theory (or to identify the physical new degrees of freedom that justify the decoupling).
  4. [SM Sec. S.III and Fig. S1/S2] The claim that the ZH functionals maintain 'reasonable description' of finite nuclei is supported only for a selected set of doubly-magic nuclei, with deviations for 16O and 40Ca exceeding 1% and SO splittings only within 50%. With nine free parameters, the fit quality reported in a few observables is a weak constraint. This is not fatal by itself, but the paper should avoid implying that the ZH functionals are globally competitive EDFs; the analysis is better framed as a proof-of-principle demonstration within a restricted dataset.
minor comments (3)
  1. [SM Eq. (S33)] The central potential contains apparent typos: '1/2(α′_S + α′_S)ρ²' and '1/2(α′_τS + α′_τS)ρ̃²' seem to repeat the same term. Please check the density-derivative terms.
  2. [Fig. 2] The claim 'no spurious core fluctuations' is supported visually by the charge-density comparison, but a quantitative measure (e.g., central-density differences or density-oscillation amplitudes) would strengthen the statement, especially given that the fit protocol did not constrain the density profile directly.
  3. [Introduction and Refs. [48, 50]] The paper leans heavily on the prior nonrelativistic IVSO proposal of the same group (Ref. [48]). The new relativistic contribution should be more clearly separated from that prior work, especially when claiming to 'confirm the decisive role' of IVSO.

Circularity Check

1 steps flagged

Headline PREX-CREX observables are fit targets, so the 'resolution' is a demonstration that parameters exist; the paper's own central-field decomposition further undercuts the IVSO-mechanism claim.

specific steps
  1. fitted input called prediction [Main text, 'Resolution of the PREX-CREX puzzle'; SM S.II 'Fitting protocol and dataset', Eq. (S10), Table S2; Fig. 1 caption]
    "The remaining nine parameters, ατS(ρsat), aτS, dτS, ατV(ρsat), aτV, dτV, ατT, αT, and δS, are optimized by fitting to both the PREX-II and CREX data as well as other empirical data."

    The quantities presented as the resolution—ΔF48CW and ΔF208CW matching PREX-II/CREX within 1σ—are direct fit targets: Table S2 lists both ΔFCW values as experimental data with σi fixed to experimental errors, and Eq. (S10) includes them in logL; selection criterion (1) then requires the chosen ZH parametrizations to reproduce them within 1σ. Figure 1 labels the resulting points 'Predicted', but their agreement is enforced by construction, so it demonstrates parameter existence rather than testing the claimed ατT/IVSO mechanism.

full rationale

The central circularity is pattern 2: the headline observables are fitted inputs. The paper is transparent about the fit, and it also makes genuinely derived statements: the nonrelativistic reduction bIV = 8B0²ατT − 4B0²ατS (Eq. S30) is derived, and the EOS, single-particle spectra, and skin predictions are not direct fit targets. These independent pieces keep the score from being higher than 6. The self-citation to Ref. [48] for the IVSO mechanism is not load-bearing because the present reduction is performed in the SM. Separately, the paper's own statement—'the dominant effect of bIV arises through modifications of the central mean-field rather than the spin-orbit potential'—undercuts the abstract/title mechanism claim, but this is a correctness/internal-consistency issue, not a circular-reasoning step. The Fierz-violating free choice of ατT is a modeling assumption, not a circularity.

Axiom & Free-Parameter Ledger

10 free parameters · 5 axioms · 0 invented entities

No new particles, forces, or conserved quantities are postulated. The central new input is a free parameter, ατT, whose values are fit to data rather than predicted; several auxiliary shape parameters are also refitted. The Fierz-relation break is the most consequential ad hoc assumption.

free parameters (10)
  • ατT (isovector tensor coupling) = ZH-1: 6.967 fm²; ZH-2: 9.195 fm²; ZH-3: 7.114 fm²
    Central new degree of freedom; treated as free instead of the Fierz value used in PCF-PK1 (0.535 fm²).
  • αT (isoscalar tensor coupling) = ZH-1: 4.312 fm²; ZH-2: 5.673 fm²; ZH-3: 4.546 fm²
    Fitted isoscalar tensor coupling entering bIS.
  • ατS(ρsat) = ZH-1: -4.701 fm²; ZH-2: -0.8403 fm²; ZH-3: -3.321 fm²
    Isovector-scalar coupling strength at saturation, refitted.
  • aτS = ZH-1: 0.5947; ZH-2: 2.126; ZH-3: 1.802
    Shape parameter for density dependence of ατS.
  • dτS = ZH-1: 0.08152; ZH-2: 0.02165; ZH-3: 0.1386
    Shape parameter for density dependence of ατS.
  • ατV(ρsat) = ZH-1: 5.400 fm²; ZH-2: 1.927 fm²; ZH-3: 4.096 fm²
    Isovector-vector coupling strength at saturation, refitted.
  • aτV = ZH-1: 4.212; ZH-2: 9.430; ZH-3: 6.656
    Shape parameter for density dependence of ατV.
  • dτV = ZH-1: 22.34; ZH-2: 21.24; ZH-3: 15.39
    Shape parameter for density dependence of ατV.
  • δS = ZH-1: -0.7173 fm⁴; ZH-2: -0.7886 fm⁴; ZH-3: -0.7311 fm⁴
    Derivative (finite-range) coupling, refitted.
  • σ_EB, σ_Rc, σ_so (error scales) = not reported
    Nuisance parameters in Eq. S10, treated as free sampling parameters for binding energies, charge radii, and spin-orbit splittings.
axioms (5)
  • domain assumption The covariant point-coupling Lagrangian in Eq. (1), with scalar/vector/isovector/tensor contact terms, adequately represents nucleon-nucleon interactions at nuclear densities.
    Taken from Ref. [55]; all results are computed inside this functional form.
  • ad hoc to paper ατT can be decoupled from the Fierz relation; fitted values ~7-9 fm² are admissible without violating the parent model.
    The paper explicitly breaks the Fierz constraint of PCF-PK1 to explore the effect; this is the main new degree of freedom and is not independently justified.
  • domain assumption The density dependence of αS, ατS, αV, ατV takes the form of Eq. (3) with f_i(1)=1 and f_i''(0)=0.
    This specific functional form is imposed to keep the EDF finite; it is not derived from data or a deeper theory.
  • domain assumption The nonrelativistic reduction to O(B0²), with B0=1/(2m*), is sufficient; the bIV expression in Eq. (S30) follows from this truncation.
    The mechanism conclusion depends on this expansion; higher-order terms are neglected.
  • domain assumption The impulse approximation with nucleon form factors from Table S1 (dipole/Galster, strange quark contributions) correctly gives FC and FW at the measured momentum transfers.
    The ΔFCW values depend on this prescription from Refs. [1,2,21,57], and the paper does not test alternative form-factor treatments.

pith-pipeline@v1.3.0-alltime-deepseek · 25272 in / 14356 out tokens · 142497 ms · 2026-08-03T21:24:23.581154+00:00 · methodology

0 comments
read the original abstract

Recent high-precision parity-violating electron scattering (PVES) measurements on $^{208}$Pb (PREX-II) and $^{48}$Ca (CREX) reveal a tension in their simultaneous description within modern nuclear energy density functionals (EDFs). Analyses of these data suggest that an enhanced isovector spin-orbit interaction may help account for both measurements, but its relativistic origin in covariant density functional theory remains to be clarified. We show that, within the framework of a covariant density-dependent point-coupling EDF, an enhanced isovector tensor coupling can naturally induce such a strong isovector spin-orbit interaction. This mechanism provides a promising route toward a simultaneous description of the PREX-II and CREX results while preserving a reasonable description of finite nuclei and nuclear matter. PVES on $^{48}$Ca thus provides a sensitive probe of the covariant isovector tensor interaction.

Figures

Figures reproduced from arXiv: 2511.15385 by Lie-Wen Chen, Mengying Qiu, Tong-Gang Yue, Zhen Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Predicted charge-weak form-factor differences ∆ [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The charge (solid lines) and weak (dashed lines) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Radial dependence of the isoscalar and isovector [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Emulator-Assisted Nuclear DFT Inference and Its Consequences for the Structure of Neutron Stars

    nucl-th 2026-04 unverdicted novelty 6.0

    Emulator-assisted Bayesian inference of an extended Skyrme EDF, jointly constrained by nuclear observables, ab initio calculations, and NICER data, produces posteriors yielding consistent neutron star crust and core p...

Reference graph

Works this paper leans on

121 extracted references · 1 canonical work pages · cited by 1 Pith paper

  1. [1]

    w/o IST (w/o IVT)

    We further access the performance of the three new EDFs in describing the equation of state of pure neutron matter, EPNM(ρ), and the ground states properties of representa- tive (semi-)doubly magic nuclei. The predicted EPNM(ρ) agrees well with results from chiral effective field theory, and the calculated binding energies and charge radii of most (semi-)do...

  2. [2]

    B. A. Brown, Neutron radii in nuclei and the neutron equation of state, Phys. Rev. Lett. 85, 5296 (2000)

    2000

  3. [3]

    Typel and B

    S. Typel and B. A. Brown, Neutron radii and the neutron equation of state in relativistic models, Phys. Rev. C 64, 027302 (2001)

    2001

  4. [4]

    Akimov et al

    D. Akimov et al. (COHERENT), Observation of Co- herent Elastic Neutrino-Nucleus Scattering, Science 357, 1123 (2017)

    2017

  5. [5]

    Cadeddu, C

    M. Cadeddu, C. Giunti, Y. F. Li, and Y. Y. Zhang, Aver- age CsI neutron density distribution from COHERENT data, Phys. Rev. Lett. 120, 072501 (2018)

    2018

  6. [6]

    Huang, C.-L

    X.-R. Huang, C.-L. Sun, L.-W. Chen, and J. Gao, Bayesian inference of supernova neutrino spectra with multiple detectors, JCAP 09, 040

  7. [7]

    Piekarewicz, Weak-charge radius of Ar40: From CREX constraints to CE νNS sensitivity, Phys

    J. Piekarewicz, Weak-charge radius of Ar40: From CREX constraints to CE νNS sensitivity, Phys. Rev. C 112, 054312 (2025)

    2025

  8. [8]

    Zheng, Z

    H. Zheng, Z. Zhang, and L.-W. Chen, Form Factor Ef- fects in the Direct Detection of Isospin-Violating Dark Matter, JCAP 08 (011), 011

  9. [9]

    R. J. Furnstahl, Neutron radii in mean field models, Nucl. Phys. A 706, 85 (2002)

    2002

  10. [10]

    Yoshida and H

    S. Yoshida and H. Sagawa, Neutron skin thickness and equation of state in asymmetric nuclear matter, Phys. Rev. C 69, 024318 (2004)

    2004

  11. [11]

    L.-W. Chen, C. M. Ko, and B.-A. Li, Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei, Phys. Rev. C 72, 064309 (2005)

    2005

  12. [12]

    Centelles, X

    M. Centelles, X. Roca-Maza, X. Vinas, and M. Warda, Nuclear symmetry energy probed by neutron skin thick- ness of nuclei, Phys. Rev. Lett. 102, 122502 (2009)

    2009

  13. [13]

    L.-W. Chen, C. M. Ko, B.-A. Li, and J. Xu, Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei, Phys. Rev. C 82, 024321 (2010)

    2010

  14. [14]

    P. G. Reinhard and W. Nazarewicz, Information content of a new observable: The case of the nuclear neutron skin, Phys. Rev. C 81, 051303 (2010)

    2010

  15. [15]

    Roca-Maza, M

    X. Roca-Maza, M. Centelles, X. Vinas, and M. Warda, Neutron skin of 208P b, nuclear symmetry energy, and the parity radius experiment, Phys. Rev. Lett. 106, 252501 (2011)

    2011

  16. [16]

    B. K. Agrawal, J. N. De, and S. K. Samaddar, Deter- mining the density content of symmetry energy and neu- tron skin: an empirical approach, Phys. Rev. Lett. 109, 262501 (2012)

    2012

  17. [17]

    Zhang and L.-W

    Z. Zhang and L.-W. Chen, Constraining the symmetry energy at subsaturation densities using isotope binding energy difference and neutron skin thickness, Phys. Lett. B 726, 234 (2013)

    2013

  18. [18]

    Mondal, B

    C. Mondal, B. K. Agrawal, M. Centelles, G. Col` o, X. Roca-Maza, N. Paar, X. Vi˜ nas, S. K. Singh, and S. K. Patra, Model dependence of the neutron-skin thickness on the symmetry energy, Phys. Rev. C 93, 064303 (2016)

    2016

  19. [19]

    A. R. Raduta and F. Gulminelli, Nuclear skin and the curvature of the symmetry energy, Phys. Rev. C 97, 064309 (2018)

    2018

  20. [20]

    Thiel, C

    M. Thiel, C. Sfienti, J. Piekarewicz, C. J. Horowitz, and M. Vanderhaeghen, Neutron skins of atomic nuclei: per aspera ad astra, J. Phys. G 46, 093003 (2019)

    2019

  21. [21]

    W. G. Newton and G. Crocombe, Nuclear symmetry en- ergy from neutron skins and pure neutron matter in a Bayesian framework, Phys. Rev. C 103, 064323 (2021)

    2021

  22. [22]

    Reinhard, X

    P.-G. Reinhard, X. Roca-Maza, and W. Nazarewicz, In- formation Content of the Parity-Violating Asymmetry in Pb208, Phys. Rev. Lett. 127, 232501 (2021)

    2021

  23. [23]

    W. G. Lynch and M. B. Tsang, Decoding the density dependence of the nuclear symmetry energy, Phys. Lett. B 830, 137098 (2022)

    2022

  24. [24]

    A. W. Steiner, M. Prakash, J. M. Lattimer, and P. J. El- lis, Isospin asymmetry in nuclei and neutron stars, Phys. Rep. 411, 325 (2005)

    2005

  25. [25]

    Baran, M

    V. Baran, M. Colonna, V. Greco, and M. Di Toro, Re- action dynamics with exotic nuclei, Phys. Rep. 410, 335 (2005)

    2005

  26. [26]

    J. M. Lattimer and M. Prakash, Neutron Star Observa- tions: Prognosis for Equation of State Constraints, Phys. Rept. 442, 109 (2007)

    2007

  27. [27]

    B. A. Li, L. W. Chen, and C. M. Ko, Recent progress and new challenges in isospin physics with heavy-ion re- actions, Phys. Rep. 464, 113 (2008)

    2008

  28. [28]

    C. J. Horowitz, E. F. Brown, Y. Kim, W. G. Lynch, R. Michaels, A. Ono, J. Piekarewicz, M. B. Tsang, and H. H. Wolter, A way forward in the study of the symme- 6 try energy: experiment, theory, and observation, J. Phys. G 41, 093001 (2014)

    2014

  29. [29]

    Gandolfi, A

    S. Gandolfi, A. Gezerlis, and J. Carlson, Neutron Matter from Low to High Density, Ann. Rev. Nucl. Part. Sci. 65, 303 (2015)

    2015

  30. [30]

    ¨Ozel and P

    F. ¨Ozel and P. Freire, Masses, Radii, and the Equation of State of Neutron Stars, Ann. Rev. Astron. Astrophys. 54, 401 (2016)

    2016

  31. [31]

    Baldo and G

    M. Baldo and G. F. Burgio, The nuclear symmetry en- ergy, Prog. Part. Nucl. Phys. 91, 203 (2016)

    2016

  32. [32]

    Roca-Maza and N

    X. Roca-Maza and N. Paar, Nuclear equation of state from ground and collective excited state properties of nu- clei, Prog. Part. Nucl. Phys. 101, 96 (2018)

    2018

  33. [33]

    Drischler, J

    C. Drischler, J. W. Holt, and C. Wellenhofer, Chiral Ef- fective Field Theory and the High-Density Nuclear Equa- tion of State, Ann. Rev. Nucl. Part. Sci. 71, 403 (2021)

    2021

  34. [34]

    Li, B.-J

    B.-A. Li, B.-J. Cai, W.-J. Xie, and N.-B. Zhang, Progress in Constraining Nuclear Symmetry Energy Using Neu- tron Star Observables Since GW170817, Universe 7, 182 (2021)

    2021

  35. [35]

    J. M. Mammei, C. J. Horowitz, J. Piekarewicz, B. Reed, and C. Sfienti, Neutron Skins: Weak Elastic Scatter- ing and Neutron Stars, Annu. Rev. Nucl. Part. Sci. 10.1146/annurev-nucl-102122-024207 (2023)

    work page doi:10.1146/annurev-nucl-102122-024207 2023

  36. [36]

    Adhikari et al

    D. Adhikari et al. (PREX), Accurate Determination of the Neutron Skin Thickness of 208Pb through Parity- Violation in Electron Scattering, Phys. Rev. Lett. 126, 172502 (2021)

    2021

  37. [37]

    Adhikari et al

    D. Adhikari et al. (CREX), Precision Determination of the Neutral Weak Form Factor of Ca48, Phys. Rev. Lett. 129, 042501 (2022)

    2022

  38. [38]

    B. T. Reed, F. J. Fattoyev, C. J. Horowitz, and J. Piekarewicz, Implications of PREX-2 on the Equation of State of Neutron-Rich Matter, Phys. Rev. Lett. 126, 172503 (2021)

    2021

  39. [39]

    Reinhard, X

    P.-G. Reinhard, X. Roca-Maza, and W. Nazarewicz, Combined Theoretical Analysis of the Parity-Violating Asymmetry for Ca48 and Pb208, Phys. Rev. Lett. 129, 232501 (2022)

    2022

  40. [40]

    Zhang and L.-W

    Z. Zhang and L.-W. Chen, Bayesian inference of the sym- metry energy and the neutron skin in Ca48 and Pb208 from CREX and PREX-2, Phys. Rev. C 108, 024317 (2023)

    2023

  41. [41]

    Y¨ uksel and N

    E. Y¨ uksel and N. Paar, Implications of parity-violating electron scattering experiments on 48Ca (CREX) and 208Pb (PREX-II) for nuclear energy density functionals, Phys. Lett. B 836, 137622 (2023)

    2023

  42. [42]

    Miyatsu, M.-K

    T. Miyatsu, M.-K. Cheoun, K. Kim, and K. Saito, Can the PREX-2 and CREX results be understood by rel- ativistic mean-field models with the astrophysical con- straints?, Phys. Lett. B 843, 138013 (2023)

    2023

  43. [43]

    Kumar, S

    M. Kumar, S. Kumar, V. Thakur, R. Kumar, B. K. Agrawal, and S. K. Dhiman, CREX- and PREX-II- motivated relativistic interactions and their implications for the bulk properties of nuclear matter and neutron stars, Phys. Rev. C 107, 055801 (2023)

    2023

  44. [44]

    Mondal and F

    C. Mondal and F. Gulminelli, Nucleonic metamodeling in light of multimessenger, PREX-II, and CREX data, Phys. Rev. C 107, 015801 (2023)

    2023

  45. [45]

    S. Yang, R. Li, and C. Xu, α clustering in nuclei and its impact on the nuclear symmetry energy, Phys. Rev. C 108, L021303 (2023)

    2023

  46. [46]

    B. T. Reed, F. J. Fattoyev, C. J. Horowitz, and J. Piekarewicz, Density dependence of the symmetry en- ergy in the post–PREX-CREX era, Phys. Rev. C 109, 035803 (2024)

    2024

  47. [47]

    Salinas and J

    M. Salinas and J. Piekarewicz, Impact of tensor coupling s with scalar mixing on covariant energy density function- als, Phys. Rev. C 109, 045807 (2024)

    2024

  48. [48]

    Roca-Maza and D

    X. Roca-Maza and D. H. Jakubassa-Amundsen, QED Corrections to the Parity-Violating Asymmetry in High- Energy Electron-Nucleus Collisions, Phys. Rev. Lett. 134, 192501 (2025)

    2025

  49. [50]

    T. Zhao, Z. Lin, B. Kumar, A. W. Steiner, and M. Prakash, Characterizing the nuclear models informed by PREX and CREX: a view from Bayesian inference, arXiv:2406.05267 [nucl-th] (2024)

    Pith/arXiv arXiv 2024

  50. [51]

    Kunjipurayil, J

    A. Kunjipurayil, J. Piekarewicz, and M. Salinas, Role of the isovector spin-orbit potential in mitigating the CREX-PREX dilemma, Phys. Rev. C 112, 014310 (2025)

    2025

  51. [52]

    R. J. Furnstahl, J. J. Rusnak, and B. D. Serot, The Nuclear spin orbit force in chiral effective field theories, Nucl. Phys. A 632, 607 (1998)

    1998

  52. [53]

    W. Z. Jiang, Y. L. Zhao, Z. Y. Zhu, and S. F. Shen, Role of rhoNN tensor coupling and 2s (1/2) occupation in light exotic nuclei, Phys. Rev. C 72, 024313 (2005)

    2005

  53. [54]

    Sulaksono, T

    A. Sulaksono, T. J. Burvenich, P. O. Hess, and J. A. Maruhn, Nonrelativistic limit of point-coupling model, Int. J. Mod. Phys. E 20, 139 (2011)

    2011

  54. [55]

    Niksic, D

    T. Niksic, D. Vretenar, and P. Ring, Relativistic Nuclear Energy Density Functionals: Adjusting parameters to binding energies, Phys. Rev. C 78, 034318 (2008)

    2008

  55. [56]

    Q. Zhao, Z. Ren, P. Zhao, and J. Meng, Covariant density functional theory with localized exchange terms, Phys. Rev. C 106, 034315 (2022)

    2022

  56. [57]

    Typel and H

    S. Typel and H. H. Wolter, Relativistic mean field calcu- lations with density dependent meson nucleon coupling, Nucl. Phys. A 656, 331 (1999)

    1999

  57. [58]

    C. J. Horowitz and J. Piekarewicz, Impact of spin-orbit currents on the electroweak skin of neutron-rich nuclei, Phys. Rev. C 86, 045503 (2012)

    2012

  58. [59]

    Klupfel, P

    P. Klupfel, P. G. Reinhard, T. J. Burvenich, and J. A. Maruhn, Variations on a theme by Skyrme: A systematic study of adjustments of model parameters, Phys. Rev. C 79, 034310 (2009)

    2009

  59. [61]

    Qiu, B.-J

    M. Qiu, B.-J. Cai, L.-W. Chen, C.-X. Yuan, and Z. Zhang, Bayesian model averaging for nuclear symme- try energy from effective proton-neutron chemical poten- tial difference of neutron-rich nuclei, Phys. Lett. B 849, 138435 (2024)

    2024

  60. [62]

    Machleidt and F

    R. Machleidt and F. Sammarruca, Recent advances in chiral EFT based nuclear forces and their applications, Prog. Part. Nucl. Phys. 137, 104117 (2024)

    2024

  61. [63]

    Yue, L.-W

    T.-G. Yue, L.-W. Chen, Z. Zhang, and Y. Zhou, Con- straints on the symmetry energy from PREX-II in the multimessenger era, Phys. Rev. Res. 4, L022054 (2022)

    2022

  62. [64]

    Kumar, S

    M. Kumar, S. Kumar, Queena, R. Kumar, and S. K. Dhi- man, Trends of nuclear matter and neutron-star observ- ables post CREX-PREX-II results within the relativistic 7 mean field model, Phys. Rev. C 110, 055802 (2024)

    2024

  63. [65]

    Resolving the PREX-CREX puzzle in covariant dens ity functional theory

    H. De Vries, C. De Jager, and C. De Vries, Nuclear charge-density-distribution parameters from elastic elec- tron scattering, Atomic Data and Nuclear Data Tables 36, 495 (1987) . Supplemental Material for “Resolving the PREX-CREX puzzle in covariant dens ity functional theory” Mengying Qiu, 1 Tong-Gang Yue,2 Zhen Zhang, 1, 3, ∗ and Lie-Wen Chen 2, † 1Sino...

    1987

  64. [66]

    05 0. 10 0. 15 ρn [fm− 3]

  65. [67]

    0 EPNM(ρ) [MeV] Machleidt & Sammarruca χ EFT PCF-PK1 ZH-1 ZH-2 ZH-3 FIG. S5. The pure neutron matter equations of state as functions of neutron density ρn are shown for ZH-1 (red solid), ZH-2 (purple dashed), and ZH-3 (blue dash-dotted lines). For comp arison, PCF-PK1 is plotted as a green dotted line, and the combined χEFT prediction from various many-bo...

  66. [68]

    Impact of spin-orbit curre nts on the electroweak skin of neutron-rich nuclei,

    C. J. Horowitz and J. Piekarewicz, “Impact of spin-orbit curre nts on the electroweak skin of neutron-rich nuclei,” Phys. Rev. C 86, 045503 (2012) , arXiv:1208.2249 [nucl-th]

    Pith/arXiv arXiv 2012

  67. [69]

    Informati on Content of the Parity-Violating Asymmetry in Pb208,

    P.-G. Reinhard, X. Roca-Maza, and W. Nazarewicz, “Informati on Content of the Parity-Violating Asymmetry in Pb208,” Phys. Rev. Lett. 127, 232501 (2021) , arXiv:2105.15050 [nucl-th]

    Pith/arXiv arXiv 2021

  68. [70]

    A small proton charge radius from an electron–proton scattering ex periment,

    W. Xiong et al. , “A small proton charge radius from an electron–proton scattering ex periment,” Nature 575, 147–150 (2019)

    2019

  69. [71]

    Review of Particle Physics,

    M. Tanabashi et al. (Particle Data Group), “Review of Particle Physics,” Phys. Rev. D 98, 030001 (2018)

    2018

  70. [72]

    Nucleon strange electromagnetic form factors,

    C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath , K. Hadjiyiannakou, K. Jansen, and G. Koutsou, “Nucleon strange electromagnetic form factors,” Phys. Rev. D 101, 031501 (2020) , arXiv:1909.10744 [hep-lat]

    Pith/arXiv arXiv 2020

  71. [73]

    Variations on a theme by Skyrme: A systematic study of adjustments of model parameters,

    P. Klupfel, P. G. Reinhard, T. J. Burvenich, and J. A. Maruhn, “ Variations on a theme by Skyrme: A systematic study of adjustments of model parameters,” Phys. Rev. C 79, 034310 (2009) , arXiv:0804.3385 [nucl-th]

    Pith/arXiv arXiv 2009

  72. [74]

    Parameterizatio n of the Woods-Saxon Potential for Shell-Model Calculations ,

    N. Schwierz, I. Wiedenhover, and A. Volya, “Parameterizatio n of the Woods-Saxon Potential for Shell-Model Calculations ,” (2007), arXiv:0709.3525 [nucl-th]

    Pith/arXiv arXiv 2007

  73. [75]

    On the difference between proton and neutron spin orbit splittings in nuclei,

    V. I. Isakov, K. I. Erokhina, H. Mach, M. Sanchez-Vega, and B. Fogelberg, “On the difference between proton and neutron spin orbit splittings in nuclei,” Eur. Phys. J. A 14, 29–36 (2002) , arXiv:nucl-th/0202044

    Pith/arXiv arXiv 2002

  74. [76]

    B ayesian model averaging for nuclear symmetry energy from effective proton-neutron chemical potential difference of ne utron-rich nuclei,

    M. Qiu, B.-J. Cai, L.-W. Chen, C.-X. Yuan, and Z. Zhang, “B ayesian model averaging for nuclear symmetry energy from effective proton-neutron chemical potential difference of ne utron-rich nuclei,” Phys. Lett. B 849, 138435 (2024) , arXiv:2312.07031 [nucl-th]

    Pith/arXiv arXiv 2024

  75. [77]

    Recent advances in chiral EFT based nuclear forces and their applications,

    R. Machleidt and F. Sammarruca, “Recent advances in chiral EFT based nuclear forces and their applications,” Prog. Part. Nucl. Phys. 137, 104117 (2024) , arXiv:2402.14032 [nucl-th]

    Pith/arXiv arXiv 2024

  76. [78]

    Precision Determination of the Neutral Weak Form Factor of Ca48,

    D. Adhikari et al. (CREX), “Precision Determination of the Neutral Weak Form Factor of Ca48,” Phys. Rev. Lett. 129, 042501 (2022) , arXiv:2205.11593 [nucl-ex]

    Pith/arXiv arXiv 2022

  77. [79]

    Accurate Determination of the Neutron Skin Thickness o f 208Pb through Parity-Violation in Electron Scattering,

    D. Adhikari et al. (PREX), “Accurate Determination of the Neutron Skin Thickness o f 208Pb through Parity-Violation in Electron Scattering,” Phys. Rev. Lett. 126, 172502 (2021) , arXiv:2102.10767 [nucl-ex]

    Pith/arXiv arXiv 2021

  78. [80]

    The AME 2020 atomic mass evaluation (II). Tables, graphs and references,

    M. Wang, W. J. Huang, F. G. Kondev, G. Audi, and S. Naimi, “ The AME 2020 atomic mass evaluation (II). Tables, graphs and references,” Chin. Phys. C 45, 030003 (2021)

    2020

  79. [81]

    Table of experimental nucle ar ground state charge radii: An update,

    I. Angeli and K. P. Marinova, “Table of experimental nucle ar ground state charge radii: An update,” Atom. Data Nucl. Data Tabl. 99, 69–95 (2013)

    2013

  80. [82]

    Charge-radius change and nuclear moments in the heavy tin is otopes from laser spectroscopy: Charge 11 radius of **132Sn,

    F. Le Blanc et al. , “Charge-radius change and nuclear moments in the heavy tin is otopes from laser spectroscopy: Charge 11 radius of **132Sn,” Phys. Rev. C 72, 034305 (2005)

    2005

Showing first 80 references.