{"id":"bab97411-9c34-494e-bb82-1c77e42bd37e","arxiv_id":"2506.18936","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Neutron skin thickness of natPb is extracted as 0.271 ± 0.008 fm, consistent with PREX-II, and interaction cross sections appear to give matter radii in the spherical limit without deformation effects.","lead":"Using a microscopic folding model, the authors extract neutron skin thicknesses of natural lead and terbium-159 from proton scattering data, finding 0.271 fm and 0.273 fm. The lead value matches the PREX-II measurement, giving a hadronic cross-check that matters for understanding neutron stars and nuclear forces.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The natPb result depends on untested 'Prediction A' that Pb skins are nearly constant across A; no calculation for 204,206,207Pb is shown, so the 0.008 fm claim is conditional on an unverified assumption.","rationale":"The paper's central quantitative novelty is a 0.008 fm neutron skin for natural lead extracted from published proton reaction cross sections. For that number to be a physical property of natPb, the mixture of 204,206,207,208Pb must either be modeled explicitly or proven irrelevant. The authors replace this with 'Prediction A', an extrapolation from their own Sn results to Pb isotopes, but present no Pb-isotope calculations or data. This is not an internal inconsistency, but it is a missing support at the exact point where the claim is strongest. I agree with the reader that this is the weakest assumption. I do not think it requires rejection: the model has independent support (12C+12C and p+208Pb validations in Refs. [8,29]), and the A=208 assumption is testable. Hence the verdict remains CONDITIONAL, with the condition being a demonstration that Pb skins are constant (or an explicit isotopic-composition fit). The 0.008 fm error also lacks a systematic budget, but even if that error were doubled the PREX-II agreement would survive, so the A=208 issue is the more load-bearing concern.","tokens_in":21742,"tokens_out":8673,"duration_ms":86953,"concrete_test":"Compute sigma_R for p+204,206,207,208Pb with the same Kyushu g-matrix folding model and D1S-GHFB+AMP densities (and SLy7 densities), applying the Eq. (27) scaling procedure to each isotope; form the natural-abundance weighted cross section sigma_R(natPb) = 0.014 sigma_R(204) + 0.221 sigma_R(206) + 0.221 sigma_R(207) + 0.544 sigma_R(208) for a range of skin values (e.g., from D1S predictions and from a +/-0.03 fm spread); then re-run the Sec. III.A fit on this weighted cross section. If the extracted r_skin moves by more than 0.008 fm relative to the A=208-only fit, the A=208 assumption fails at the claimed precision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The extraction for natPb (Sec. III.A, Table III) treats the target as pure 208Pb: the folding model uses A=208 kinematics and D1S-GHFB+AMP densities for 208Pb, and only the neutron density is scaled. Natural lead is 54.4% 208Pb, 22.1% 207Pb, 22.1% 206Pb, and 1.4% 204Pb. The paper justifies this with 'Prediction A' (Sec. I): based on their Sn extraction, the Pb skins are 'almost constant' as a function of A. However, no calculation or measured constraint for 204,206,207Pb is shown anywhere in the manuscript, and the Sn evidence (Fig. 1) itself has 30% experimental uncertainties and a model spread of 50% from A=118 to 124. If the true Pb skins vary by only 0.02 fm across the isotopes, the abundance-weighted sigma_R differs from the pure-208 calculation, and the fitted r_skin shifts by more than the quoted 0.008 fm. That 0.008 fm is the fitting error and does not include this composition uncertainty. The Summary itself hedges: 'Prediction A may be true.' Thus the headline natPb value is not well-defined unless the constancy of Pb skins is demonstrated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript uses the chiral (Kyushu) g-matrix folding model and the Love-Franey (LF) t-matrix folding model, together with density scaling, to extract neutron skin thicknesses for natPb and 159Tb, and matter radii for Mg, Na, and Ar isotopes. For natPb the target is treated as pure 208Pb and the extracted r_skin=0.271±0.008 fm is presented as agreeing with the PREX-II value for 208Pb. For 159Tb, r_skin=0.273±0.073 fm is obtained. For 24Mg, the paper compares r_m(σ_R)=3.03±0.08 fm with r_m(σ_I)=2.79±0.15 fm and interprets the difference as evidence that σ_I-based radii give spherical-limit matter radii while σ_R-based radii include deformation; the same interpretation is applied to Na and Ar isotopic chains. A fine-tuning factor F=0.955, calibrated to the 24Mg σ_I datum, is used for the high-energy LF extractions for Na and Ar.","tokens_in":21973,"tokens_out":10105,"duration_ms":93867,"significance":"If the central claims held at their quoted precision, the paper would show that proton reaction cross sections can determine neutron skins of heavy nuclei to 0.008 fm, and that the comparison of σ_R and σ_I data can separate deformation effects from spherical-limit matter radii. The model machinery is not new: the Kyushu g-matrix folding model has been benchmarked in prior work on 12C, Ca, Sn, and Pb, and the D1S-GHFB+AMP and SLy7 densities are standard. The manuscript is also transparent about several of its own limitations, including the statement in Sec. IV that 'Prediction A may be true' and the observation in Sec. III.E that the 37,38Ar depression may be a data fluctuation. However, the headline natPb precision is conditional on an untested assumption about the constancy of Pb skins across A, the Na/Ar extractions are calibrated to a single 24Mg anchor point, and the 24Mg 'too small' conclusion is a sub-sigma statement. These issues substantially limit the significance of the results as currently presented.","major_comments":[{"comment":"The quoted r_skin=0.271±0.008 fm for natPb treats natural lead as a pure 208Pb target, and the 0.008 fm is the scaling-fit error only. Natural lead is 54.4% 208Pb, 22.1% 207Pb, 22.1% 206Pb, and 1.4% 204Pb. The only support for the A=208 assumption is the prediction that Pb skins are almost constant as a function of A, but no calculation or measured constraint for 204,206,207Pb is shown, and the Sn evidence in Fig. 1 has 30% experimental uncertainties and a 50% model spread from A=118 to 124. If the true Pb skins vary by even ~0.02 fm across A, the abundance-weighted σ_R would differ from the pure-208 calculation and the fitted r_skin would shift by more than the quoted 0.008 fm. The authors should either demonstrate the constancy of Pb skins, model natPb as a composition average, or add a systematic uncertainty that covers the composition ambiguity. As written, the abstract's precision claim is not supported.","section":"Sec. III.A / Table III / Sec. II.D"},{"comment":"The fine-tuning factor F=0.955 is fixed by requiring the LF t-matrix folding model to reproduce the central value of r_m(σ_I)=2.79±0.15 fm for 24Mg, and this same F is then applied to all Na isotopes (Sec. III.D) and all 32-40Ar isotopes (Sec. III.E). Consequently the r_m(σ_I) values in Tables VI and VIII are calibrated to the 24Mg input rather than being independent extractions. The uncertainty of the 24Mg anchor (0.15 fm) is not propagated into the quoted errors of the Na and Ar radii, and no validation of F on a system where both σ_I and σ_R are available is given. The deformation conclusions for Na and Ar therefore rest on a single calibration point; please propagate the F uncertainty or provide an independent check.","section":"Sec. III.D / Sec. III.E"},{"comment":"The abstract states that for 24Mg, r_m(σ_I)=2.79±0.15 fm does not include effects of deformation, and Sec. III.C concludes that the central value of r_m(σ_I) is 'too small' compared with r_m,0(P)=2.929 fm. The difference is 0.14 fm against a 1σ error of 0.15 fm, i.e., less than a one-sigma deviation. The wording overstates the strength of the evidence; a quantitative significance statement or a softened conclusion is needed.","section":"Sec. III.C / Abstract"},{"comment":"The natPb fit includes σ_R data at E_lab=341 MeV, but the Kyushu g-matrix folding model is stated in Sec. I to be benchmarked for proton scattering in the range 20≤E_lab≤180 MeV (Ref. [29]). The extension to 341 MeV is justified only by a general statement about cutoff effects and by 12C+12C tests, not by a proton-scattering benchmark in this energy range. A model-uncertainty contribution from this energy extrapolation should be included in the quoted 0.008 fm error or the fit should be repeated with the high-energy points excluded to show robustness.","section":"Sec. III.A / Sec. I"}],"minor_comments":[{"comment":"Equation (34) as printed, r_m^2 = r_m,0^2[1+5β2^2/(4π)] = r_m,0^2, is internally inconsistent for β2≠0; please correct the intended relation and recompute the derived r_m,0=5.065 fm if needed.","section":"Sec. IV, Eq. (34)"},{"comment":"The entry '0075' should read '0.075'.","section":"Table VI, A=26 row"},{"comment":"The table heading uses r_skin while Figs. 11 and 12 use r_skin.p for the same quantity; please make the notation consistent.","section":"Table VIII / Figs. 11-12"},{"comment":"The expression for σ_inel in Eq. (33) does not obviously follow from Eqs. (29)-(32) with the stated definitions of r_m(P), r_m,0(P), x, and c; please check the algebra and correct or clarify.","section":"Sec. III.C, Eq. (33)"},{"comment":"Table II lists r_m(σ_R)=2.352±0.013 fm for 12C, while Sec. II.C and Sec. III.C use r_m(12C)=2.338 fm from Ref. [55]; please clarify which value is used in the double-folding calculations and why the values differ.","section":"Table II"}],"recommendation":"major_revision","confidential_remarks":"The central weakness is the natPb extraction: the 0.008 fm error is not credible without either an explicit treatment of the natural-lead isotopic composition or a systematic uncertainty that covers the A=208 assumption. The F=0.955 calibration issue is also important but can be addressed by uncertainty propagation. The paper is a collection of analyses of previously published data with a well-tested model; the novelty is modest but the natPb claim, if properly supported, could be of interest. I do not see a basis for rejection, but the current error bars and the sub-sigma 24Mg statement need substantive revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline natPb number is the first thing to know: r_skin = 0.271 ± 0.008 fm is quoted as a PREX-II cross-check, but that precision is not earned. The paper treats natural lead as pure 208Pb and justifies it with 'Prediction A'—that Pb skins are nearly constant across A—yet no calculation or data constraint for 204,206,207Pb is shown anywhere. The Sn evidence behind the prediction has 30% experimental uncertainties and a 50% model spread. If the true skins vary by 0.02 fm across the isotopes, the extracted skin shifts by more than the quoted 0.008 fm. That number is just the fitting error. The Summary even says 'Prediction A may be true.' So the headline claim is conditional on an unverified assumption, and the abstract should not present it as a clean agreement.\n\nWhat is genuinely useful here is the deformation analysis. The comparison between sigma_I and sigma_R for Mg, Na, and Ar—where sigma_I gives spherical-limit matter radii and sigma_R picks up deformation—is a nice synthesis of existing data. The 159Tb extraction carries a more realistic 0.073 fm error and looks reasonable. The folding model itself is well benchmarked in the authors' prior work, so the method is not the issue.\n\nThe soft spots beyond A=208: the F = 0.955 fine-tuning factor is fit to the 24Mg interaction cross section and then applied to Na and Ar, so those extractions are calibrated rather than independent. The statement that the 24Mg r_m(sigma_I) = 2.79 ± 0.15 is 'too small' overstates what is at most a sub-sigma discrepancy. The paper also has presentation trouble—Eq. (34) in the Summary looks garbled, and typos are common. These are fixable.\n\nWho should read it: people working on neutron skins from hadronic probes and on radius extraction systematics. If the authors either demonstrate the Pb skin constancy with actual calculations for 204,206,207Pb or fold the composition uncertainty into the error budget, the natPb result becomes a legitimate data point. As it stands, it is a hint, not a measurement at 0.008 fm precision.\n\nI would send this to a serious referee. The direction is sound and the deformation interpretation is worth publishing, but the precision claims need to be reined in and the A=208 assumption addressed.","headline":"The deformation analysis is worth publishing, but the natPb skin claim's 0.008 fm precision rests on an unverified A=208 assumption that the paper itself hedges.","tokens_in":22573,"tokens_out":2847,"would_cite":false,"duration_ms":27351,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Proton reaction cross sections, reanalysed with a density-scaling folding model, place natural lead's neutron skin at 0.271±0.008 fm and separate deformed from spherical matter radii.","keywords":["neutron skin thickness","reaction cross section","interaction cross section","folding model","nuclear deformation","matter radius","density scaling","159Tb"],"falsifier":"Measure reaction cross sections for p+${}^{206}$Pb and p+${}^{207}$Pb separately and extract each skin with the same folding model; if the two values differ by more than about 0.02 fm, the constant-skin prediction fails and the reported 0.271 fm for natural lead cannot be taken at face value. A parity-violating electron-scattering run on natural lead analysed with the full isotopic composition would settle the same question directly.","tokens_in":21422,"feed_emoji":"⚛️","tokens_out":17136,"duration_ms":135040,"temperature":0.7,"pith_summary":"The paper asks whether proton reaction cross sections alone can pin down the neutron skin of heavy nuclei, and what exactly the two standard cross-section observables measure. Using the chiral (Kyushu) $g$-matrix folding model with a density-scaling procedure, it extracts $r_{\\rm skin}=0.271\\pm0.008$ fm for natural lead (treating natPb as $A=208$), consistent with the PREX-II value for ${}^{208}$Pb, and $r_{\\rm skin}=0.273\\pm0.073$ fm for ${}^{159}$Tb. For Mg, Na, and Ar isotopes, it shows that matter radii extracted from interaction cross sections $\\sigma_{\\rm I}$ are spherical-limit values, while those from reaction cross sections $\\sigma_{\\rm R}$ include deformation effects. The result matters because a scattering-based measurement can match parity-violating electron-scattering precision, and because radius tables that mix the two cross-section types conflate deformed and spherical ground-state information.","feed_headline":"Proton scattering pins lead's neutron skin at 0.271 fm","feed_subtitle":"Reaction cross sections catch deformation; interaction cross sections miss it, sharpening radii for Mg, Na, Ar.","key_machinery":"The load-bearing mechanism is the density-scaling procedure combined with a folding potential. Given a target density from D1S-GHFB+AMP or SLy7, the model scales the neutron (and sometimes proton) density radially via $\\rho_{\\rm scaling}(r)=\\rho(r/\\alpha)/\\alpha^3$ so that the folded potential reproduces the measured $\\sigma_{\\rm R}$ while the proton radius is fixed to the electron-scattering value $r_p$; the scaled neutron radius then defines $r_{\\rm skin}$. Two interactions supply the folded potential: the chiral (Kyushu) $g$-matrix for projectile energies up to about 450 MeV, and the Love-Franey $t$-matrix above that, with an ESP-f fine-tuning factor to remove systematic normalization. This combination is what converts a one-dimensional cross-section measurement into a radius difference at a precision of about 0.01 fm.","core_discovery":"On its own terms, the paper's central claim is that the density-scaling folding model can turn existing proton reaction cross sections into neutron-skin values with a 0.008 fm uncertainty for natural lead once natural lead is approximated as $A=208$, and the extracted $0.271\\pm0.008$ fm agrees with the PREX-II value $0.283\\pm0.071$ fm for ${}^{208}$Pb. The same framework yields $r_{\\rm skin}=0.273\\pm0.073$ fm for the deformed nucleus ${}^{159}$Tb, and shows that for Mg, Na, and Ar isotopes the matter radius determined from interaction cross sections lies close to the spherical-limit radius, while the reaction-cross-section radius sits at the deformed value. The ${}^{24}$Mg case is analysed quantitatively: the 0.087 fractional gap between $\\sigma_{\\rm R}$ and $\\sigma_{\\rm I}$ is only 0.037 from deformation alone, so part of the published $r_{\\rm m}(\\sigma_{\\rm I})$ appears to be a fluctuation.","pith_inferences":["A corollary the paper leaves implicit: if lead skins are really $A$-independent, the same analysis applied to p+${}^{206}$Pb and p+${}^{207}$Pb data should return skins within about 0.02 fm of ${}^{208}$Pb; this is checkable with existing data and no new theory.","The difference between $\\sigma_{\\rm R}$- and $\\sigma_{\\rm I}$-based radii could serve as a deformation diagnostic for any nucleus with both measurements, converting the fractional cross-section excess into an effective $\\beta_2$ and cross-checking the empirical formula beyond Mg, Na, and Ar.","Radius compilations that merge interaction and reaction cross-section values into one matter radius mix spherical and deformed states; future tables should report the observable or apply a deformation correction."],"forward_implications":["Natural lead has a neutron skin of $0.271\\pm0.008$ fm, consistent with PREX-II's $0.283\\pm0.071$ fm for ${}^{208}$Pb.","The skin of ${}^{159}$Tb is $0.273\\pm0.073$ fm; subtracting the deformation effect ($\\beta_2=0.309$) leaves a spherical-limit skin near 0.11 fm.","For Mg isotopes, 21,23Na, and 40Ar, matter radii from reaction cross sections include deformation, while those from interaction cross sections give the spherical-limit radius.","For ${}^{24}$Mg, the difference between $r_{\\rm m}(\\sigma_{\\rm R})=3.03\\pm0.08$ fm and $r_{\\rm m}(\\sigma_{\\rm I})=2.79\\pm0.15$ fm is only about 40% accounted for by deformation, implying part of the published interaction-cross-section value is a statistical fluctuation.","The folding model with ESP-f scaling can extract neutron skins from proton reaction cross sections at a precision comparable to parity-violating electron scattering."],"supporting_citations":[{"why":"supplies the PREX-II neutron-skin benchmark for 208Pb that the natPb result is compared against.","marker":"[2]"},{"why":"earlier extraction of the skin for 208Pb with the same folding model, the value the present natPb result is checked against.","marker":"[6]"},{"why":"provides the chiral (Kyushu) g-matrix folding interaction used for low- and intermediate-energy scattering.","marker":"[7]"},{"why":"Sn isotope skin analysis whose A-dependence motivates treating natPb as A=208.","marker":"[9]"},{"why":"the proton reaction cross-section data for natPb that drive the extraction.","marker":"[10–16]"},{"why":"the proton reaction cross-section data for 159Tb.","marker":"[17]"},{"why":"compilation of interaction-cross-section matter radii used as the spherical-limit comparison.","marker":"[22]"},{"why":"Mg isotope matter radii from reaction cross sections that show deformation effects.","marker":"[25]"},{"why":"introduces the ESP-f scaling procedure used to fix the proton radius and scale the neutron density.","marker":"[29]"},{"why":"supplies the Love-Franey t-matrix folding interaction used at high energies.","marker":"[30]"}],"fun_headline_variants":["Deformation gaps in Mg, Na, Ar radii caught by proton reaction data","Lead's neutron skin from proton scattering matches PREX-II","Neutron skin for lead and terbium from proton reaction data","Reaction cross section separates deformed from spherical matter radii","For 24Mg, reaction and interaction radii diverge beyond deformation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The natural-lead extraction treats natural lead as pure ${}^{208}$Pb, relying on the prediction that lead neutron skins are nearly constant across mass number; if that constancy fails, the quoted $r_{\\rm skin}$ is not a well-defined natural-lead value.","fun_headline_variants_meta":{"raw":{"variants":["Deformation gaps in Mg, Na, Ar radii caught by proton reaction data","Lead's neutron skin from proton scattering matches PREX-II","Neutron skin for lead and terbium from proton reaction data","Reaction cross section separates deformed from spherical matter radii","For 24Mg, reaction and interaction radii diverge beyond deformation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000945,"raw_usage":{"total_tokens":4118,"prompt_tokens":1111,"completion_tokens":3007,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":727,"completion_tokens_details":{"reasoning_tokens":2919}},"tokens_in":727,"tokens_out":3007,"duration_ms":19339,"temperature":1.0,"reasoning_tokens":2919,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:58:23.449958+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure reaction cross sections for p+${}^{206}$Pb and p+${}^{207}$Pb separately and extract each skin with the same folding model; if the two values differ by more than about 0.02 fm, the constant-skin prediction fails and the reported 0.271 fm for natural lead cannot be taken at face value. A parity-violating electron-scattering run on natural lead analysed with the full isotopic composition would settle the same question directly.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the PREX-II neutron-skin benchmark for 208Pb that the natPb result is compared against."},{"cited_title":"Goloskie and K","cited_arxiv_id":null,"evidence_quote":"the proton reaction cross-section data for 159Tb."},{"cited_title":"Suzuki et al., Nuclear radii of Na and Mg isotopes, Nucl","cited_arxiv_id":null,"evidence_quote":"compilation of interaction-cross-section matter radii used as the spherical-limit comparison."},{"cited_title":"Ozawa, T","cited_arxiv_id":null,"evidence_quote":"Mg isotope matter radii from reaction cross sections that show deformation effects."},{"cited_title":"Tagami, T","cited_arxiv_id":null,"evidence_quote":"introduces the ESP-f scaling procedure used to fix the proton radius and scale the neutron density."},{"cited_title":"Wakasa, M","cited_arxiv_id":null,"evidence_quote":"supplies the Love-Franey t-matrix folding interaction used at high energies."}],"review_version":2}