{"id":"e2f0c14d-4115-48ed-a360-a2a2ed032922","arxiv_id":"2411.10690","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Using the Kyushu g-matrix folding model, the authors extract r_skin(208Pb) = 0.309 +/- 0.057 fm from n+208Pb total cross sections and r_skin(48Ca) = 0.163 +/- 0.037 fm from p+48Ca reaction cross sections.","lead":"The paper extracts neutron skin thicknesses for 208Pb, 48Ca, and light C, N, O isotopes from measured reaction and total cross sections using a folding-model analysis. The values agree with the PREX2 and CREX results, and the method singles out 14N and 17O as stable nuclei with relatively thick neutron skins.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 208Pb result depends on a single 14.137 MeV total cross section analyzed with a folding model that omits compound-nucleus contributions, and the paper itself concedes this could explain the residual; the quoted 0.057 fm uncertainty does not include that bias.","rationale":"The reader's weakest_assumption is exactly the compound-nucleus issue in the 208Pb extraction, and the paper's own Section IV contains an explicit admission that compound effects may explain the residual. This is the most load-bearing concern because the headline consistency with PREX2 rests on one measured cross section at a low energy where the folding model is least secure. The concern does not require rejecting the paper: the 48Ca analysis is more broadly based, and the 208Pb value is consistent with earlier determinations from proton and 4He scattering. However, it does mean that the 0.057 fm error is not a complete statement of uncertainty, and the central 208Pb claim should be read as conditional unless the compound-nucleus contribution is quantified. I therefore keep the reader's CONDITIONAL verdict unchanged rather than moving to accept or reject.","tokens_in":19470,"tokens_out":3102,"duration_ms":40134,"concrete_test":"Compute the compound-elastic and compound-inelastic contributions to n+208Pb at 14.137 MeV with a standard statistical model (e.g., TALYS or EMPIRE) using the same neutron/proton densities and a modern optical potential; then subtract the compound part from the measured sigma_T and re-extract r_skin by the same density-scaling procedure. If r_skin shifts by more than 0.057 fm, the quoted central value and uncertainty are not complete. A supporting cross-check is to compare the folding-model sigma_T against evaluated data (e.g., ENDF/B-VIII.0) across 5-20 MeV to see whether the 14.137 MeV point sits on a smooth direct component or on a fluctuation that the model cannot describe.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central 208Pb claim is extracted by scaling the neutron density so that the folding-model total cross section reproduces the single Foster-Glasgow datum at 14.137 MeV. At this energy the measured sigma_T includes compound-elastic and compound-inelastic contributions, while the Kyushu g-matrix folding model provides a one-body optical potential containing only direct (shape-elastic plus absorption) physics. The g-matrix does include Brueckner-Hartree-Fock medium effects, but those are not the same as Hauser-Feshbach compound-nucleus fluctuations, especially for a heavy spherical target with a high level density of 209Pb at about 21.5 MeV excitation. Section IV explicitly states that 'compound nucleus effects appear at low incident energies,' that they 'decrease as Elab increases,' and that 'the small difference between our present value ... and PREX2 may come from compound nucleus effects.' That admission is not converted into a systematic uncertainty. Since the extraction is a one-parameter fit to one datum, any missing component in sigma_T is absorbed by the density-scaling factor and directly shifts r_skin. The quoted +/-0.057 fm propagates only the experimental error of sigma_T, not the model error from the unmodeled compound channel. If the compound-elastic cross section is a few percent of sigma_T at 14.137 MeV, the implied shift in r_skin is comparable to or larger than the quoted precision, so the PREX2-agreement claim is not yet robust at the stated uncertainty.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reanalyzes published cross-section data to extract neutron skin thicknesses using the Kyushu g-matrix folding model for low energies and the Love-Franey t-matrix folding model for intermediate energies. It reports r_skin(208Pb)=0.309±0.057 fm from the single n+208Pb total cross section measured by Foster and Glasgow at 14.137 MeV, r_skin(48Ca)=0.163±0.037 fm from p+48Ca reaction cross sections at 23–48 MeV, and skin values for C, N, and O isotopes from interaction cross sections. The results are compared with PREX2 and CREX values, and 14N and 17O are identified as stable nuclei with relatively large skin thicknesses.","tokens_in":19778,"tokens_out":4080,"duration_ms":41654,"significance":"If the extractions are robust, the paper would provide independent hadronic-scattering checks of the PREX2 and CREX neutron-skin values and would demonstrate the predictive reach of the Kyushu folding model across a wide energy range. The manuscript has genuine strengths: it tests the folding model against p+208Pb and 12C+12C data, compares D1M and D1S Gogny densities for 48Ca, and presents systematic tables of radii and skins for C, N, and O isotopes. However, the quoted uncertainties are almost exclusively experimental; model dependence from the fine-tuning factors and from the choice of densities is acknowledged in Sec. IV but not propagated into the final errors. Because several extractions are one-parameter fits calibrated on the same data, the current significance is limited pending a quantitative treatment of these systematic uncertainties.","major_comments":[{"comment":"The 208Pb extraction is a one-parameter fit to a single total cross section at 14.137 MeV (Fig. 2). The quoted ±0.057 fm propagates only the experimental uncertainty of σ_T, not the model uncertainty. The paper itself states in Sec. IV that compound-nucleus effects appear at low incident energies and that the small difference from PREX2 may come from those effects, yet no systematic uncertainty is assigned. Since any missing contribution to σ_T is absorbed by the neutron-density scaling of Eq. (9), the central value and the PREX2 agreement are not robust at the stated precision. Please model the compound-nucleus contribution or add a quantitative systematic error and weaken the claim accordingly.","section":"III A and IV"},{"comment":"The p+48Ca extraction uses f = 0.968537 obtained by averaging σ_R(exp)/σ_R(ref) over the very data points that are then fitted after scaling the densities. This makes the extracted r_skin partly determined by the fitted f and does not provide an independent check. The quoted ±0.037 fm excludes the model dependence of f and of the density choice (D1M vs D1S). Please quantify the sensitivity of r_skin to f and to the density functional and include those contributions in the final uncertainty.","section":"III C 3"},{"comment":"The global factor F = 0.93766 is fitted to 12C+12C data and then applied to C, N, and O isotopes on a 12C target at 710–1020 MeV/u. Section IV notes that a 0.35% change in F shifts r_m by 0.33%, but the tables in Sec. III D quote only the experimental cross-section errors. This omitted F-uncertainty propagates directly into the r_skin values for N, O, and C, including the headline 14N and 17O results. Please propagate the F uncertainty into every reported skin value or state explicitly, with a quantitative argument, why it is negligible.","section":"III D and IV"},{"comment":"The p+14N analysis follows the same ESP-f procedure: f = 0.86196 is the average of σ_R(exp)/σ_R(th) over the same data, and the densities are then scaled to reproduce those data. The resulting r_skin(14N)=0.267±0.056 fm therefore inherits the same circularity and unquantified model dependence. Please clarify what independent information this extraction provides, or remove the strong comparison with PREX2.","section":"III E 1"}],"minor_comments":[{"comment":"The section heading 'MEHOD' should be 'METHOD'.","section":"II"},{"comment":"There are duplicated words such as 'the the σ_T' and 'nuclei having nuclei having'; the manuscript needs careful proofreading.","section":"Abstract and text"},{"comment":"In the opening line of Sec. III D, 'shown blow' should be 'shown below'.","section":"III D"},{"comment":"In Sec. III C, 'nuleon' should be 'nucleon'.","section":"III C"},{"comment":"The relation 'Ar2_m = Zr^2_p + N r^2_n' is typeset ambiguously; write A⟨r^2⟩_m = Z⟨r^2⟩_p + N⟨r^2⟩_n to avoid confusion with A times r^2_m.","section":"II A"},{"comment":"The caption of Fig. 17 mentions shell corrections and deformation, but the figure is not referenced in the main text at the point of discussion; please clarify the role of this figure and its connection to the C, N, O skin results.","section":"III D 1"}],"recommendation":"major_revision","confidential_remarks":"The paper is largely a reanalysis of published data using the authors' own folding-model framework, and the referee report focuses on missing model uncertainties rather than on the experimental data, which appear to be reproduced faithfully. The main concern is that the central 208Pb and 48Ca claims are extracted with fine-tuning procedures that are either not independent of the data being fitted or omit acknowledged systematic effects; these issues are fixable but require substantial additional analysis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick read: the genuinely new pieces are the extraction of r_skin(208Pb) from the Foster-Glasgow n+208Pb total cross section at 14.137 MeV, and the p+48Ca extraction with D1M-GHFB+AMP densities, which updates their earlier D1S result. The 48Ca value, 0.163 ± 0.037 fm, is consistent with CREX, and the D1M densities are arguably an improvement over D1S. The light-isotope survey finds 14N with a large skin (0.267 ± 0.056 fm), interesting for a Z=N stable nucleus. The folding-model machinery is standard and well tested in their prior work.\n\nNow the soft spots, in proportion. The 208Pb result is the weakest link. It is a one-parameter fit to a single total-cross-section datum at 14.137 MeV. At that energy, compound-nucleus (Hauser-Feshbach) contributions to sigma_T are not negligible, and the Kyushu g-matrix folding model does not include them. The authors themselves concede in Section IV that 'the small difference between our present value and PREX2 may come from compound nucleus effects.' That admission is not converted into a systematic uncertainty. The quoted ±0.057 fm propagates only the experimental error of sigma_T. If compound-elastic is a few percent of sigma_T, the implied shift in r_skin is comparable to the quoted precision. So the PREX2 agreement is not yet robust at the stated uncertainty.\n\nSecond, the fine-tuning factors are fitted to the same data used for the physics extraction. For p+48Ca, f is the average of sigma_R(exp)/sigma_R(ref) over the same points, and the densities are then scaled to reproduce those data. The extracted r_skin is partly determined by the fitted f. Section IV's sensitivity test (0.35% change in F shifts r_m by 0.33%) shows model dependence exists, but it is not propagated into the quoted errors. For the light isotopes, the global F=0.93766 comes from 12C+12C and is applied to C, N, O; that is reasonable, but again the model dependence is not folded in.\n\nThird, the 4He+208Pb section excludes the 29.3 MeV/u data point post hoc. The authors justify it by the Coulomb barrier, but the exclusion is made after seeing the result. That is a minor red flag.\n\nThe central claims are plausible and consistent with PREX2/CREX, and the method is standard. But the 208Pb value should not be used as a precision constraint until the compound-nucleus systematic is quantified. The paper deserves a serious referee, because the 48Ca and light-isotope analyses add useful data points, and the systematic issues are fixable in revision.\n\nRecommendation: send to peer review, but the referee report should request a quantitative estimate of compound-nucleus contributions and model-dependent uncertainties before publication.","headline":"A careful folding-model reanalysis that gets PREX2- and CREX-consistent skins, but the 208Pb number rests on one datum with unquantified compound-nucleus effects.","tokens_in":20403,"tokens_out":2930,"would_cite":false,"duration_ms":25935,"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":"A single 14.137 MeV neutron total-cross-section measurement places the 208Pb neutron skin at 0.309 ± 0.057 fm, in agreement with PREX2.","keywords":["neutron skin thickness","208Pb","48Ca","folding model","total neutron cross section","reaction cross section","nuclear radii","halo nucleus"],"falsifier":"Measure total neutron cross sections of $^{208}$Pb at several energies between 8 and 20 MeV and analyze them with the same folding model after subtracting compound-nucleus contributions computed with a statistical reaction code; the extraction would be falsified if including those contributions at 14.137 MeV shifts the fitted skin by more than $0.057$ fm, or if the fitted value drifts systematically with energy.","tokens_in":19172,"feed_emoji":"⚛️","tokens_out":14533,"duration_ms":120811,"temperature":0.7,"pith_summary":"The paper claims that scattering cross sections can determine neutron skin thickness and can reproduce the values obtained from parity-violating electron scattering. From the measured total neutron cross section of $n$+$^{208}$Pb scattering at 14.137 MeV, it extracts $r_{\\rm skin}(^{208}{\\rm Pb}) = 0.309 \\pm 0.057$ fm, consistent with the $0.283 \\pm 0.071$ fm reported by the parity-violating electron-scattering experiment PREX2. From measured proton reaction cross sections on $^{48}$Ca at 23–48 MeV, it extracts $r_{\\rm skin}(^{48}{\\rm Ca}) = 0.163 \\pm 0.037$ fm, consistent with the $0.121 \\pm 0.050$ fm reported by the parity-violating experiment CREX. It then scans the C, N, O isotope chains and identifies $^{14}$N ($0.267 \\pm 0.056$ fm) and $^{17}$O ($0.197 \\pm 0.067$ fm) as light stable nuclei with sizable skins. These numbers matter because neutron skins measure how strongly neutron and proton distributions separate, a benchmark for nuclear density functionals and for the behavior of neutron-rich matter.","feed_headline":"Neutron scattering sets 208Pb skin at 0.309 fm, matching PREX2","feed_subtitle":"Proton-scattering data pin 48Ca skin at 0.163 fm, in line with CREX, and flag 14N and 17O as thick-skinned nuclei.","key_machinery":"The load-bearing mechanism is density scaling inside a folding-model optical potential. At low and intermediate energies the paper computes the projectile-target potential by folding a chiral $g$-matrix interaction, which incorporates nuclear-medium effects, with the projectile and target densities; at higher energies it uses a $t$-matrix-based folding model renormalized by a fine-tuning factor $F=0.93766$ calibrated on $^{12}$C+$^{12}$C scattering. The extraction works by scaling the neutron density (and, where needed, the proton density) through $\\alpha = \\sqrt{\\langle r^2\\rangle_{\\rm scaled}/\\langle r^2\\rangle}$ until the calculated cross section reproduces the measured one, always holding $r_p$ fixed at its electron-scattering or charge-changing value. The skin value is then the difference between the scaled neutron radius and the fixed proton radius. For $^{48}$Ca the densities used are the D1M-GHFB+AMP self-consistent mean-field densities with angular momentum projection, which the paper shows reproduce the binding energy and matter radius better than the D1S variant.","core_discovery":"The central discovery is that one high-precision total cross section at a single energy can pin down a neutron skin. Using the chiral $g$-matrix folding model, the paper scales the neutron density of $^{208}$Pb so that the calculated total cross section reproduces the measured 14.137 MeV value, under the constraint that the proton radius stays at the experimental charge-radius value; this yields $r_{\\rm skin}(^{208}{\\rm Pb})=0.309\\pm0.057$ fm, overlapping PREX2. For $^{48}$Ca, proton reaction cross sections between 23 and 48 MeV, analyzed with the D1M-GHFB+AMP densities and a fine-tuning factor, give $r_{\\rm skin}(^{48}{\\rm Ca})=0.163\\pm0.037$ fm, overlapping CREX; the D1M densities are shown to reproduce the binding energy and matter radius better than the D1S densities. On the isotope chains, the same machinery finds $r_{\\rm skin}(^{14}{\\rm N})=0.267\\pm0.056$ fm and $r_{\\rm skin}(^{17}{\\rm O})=0.197\\pm0.067$ fm, and marks $^{22}$N as halo-like by two quantitative criteria. The paper concludes that each extracted value agrees with the corresponding parity-violation experiment, so cross-section measurements offer an independent route to neutron skins.","pith_inferences":["If the single-energy extraction is robust, archived total and reaction cross sections across many nuclei could be re-analyzed with the same density-scaling procedure, producing a much wider neutron-skin survey than PREX2 and CREX alone provide; this is an application the paper does not itself make.","The unmodeled compound-nucleus contribution at 14.137 MeV, which the paper acknowledges may explain the small offset from PREX2, is a concrete place to test the method: including a statistical-model correction could either harden the $0.309$ fm value or reveal a bias larger than the quoted error.","The large skin found for the self-conjugate nucleus $^{14}$N is, in the paper's view, a Coulomb effect; a testable extension is to compare the $^{14}$N skin extracted with the same method against density functionals computed with the Coulomb force artificially switched off, to see whether the $0.267$ fm value collapses as expected."],"forward_implications":["A single measured total cross section at 14.137 MeV determines the $^{208}$Pb neutron skin with uncertainty comparable to PREX2, without needing an electron beam.","Low-energy proton reaction cross sections on $^{48}$Ca give a skin consistent with CREX, so proton scattering can serve as an independent check on parity-violation results.","Among C, N, O isotopes, $^{14}$N and $^{17}$O stand out as light stable nuclei with thick skins, making them accessible targets for studying skin effects without radioactive beams.","Minima of $r_m/A^{1/3}$ locate the $N=8$ major shell in N and C isotopes and the $N=14$ subshell in O, N, C, indicating soft cores in light neutron-rich chains.","$^{22}$N satisfies the paper's two halo criteria and is classified as halo-like, with $H_1=0.148$ and $H_2=0.241$."],"supporting_citations":[{"why":"Supplies the n+208Pb total cross section at 14.137 MeV from which the 208Pb skin is extracted.","marker":"[11]"},{"why":"Gives the PREX2 value that the 208Pb extraction is compared against.","marker":"[2]"},{"why":"Supplies the p+48Ca reaction cross sections in 23–48 MeV from which the 48Ca skin is determined.","marker":"[17]"},{"why":"Gives the CREX value that the 48Ca extraction is compared against.","marker":"[3]"},{"why":"Defines the chiral g-matrix folding model used for the low-energy cross sections.","marker":"[7]"},{"why":"Establishes the folding model's reliability and introduces the ESP-f scaling procedure on proton scattering.","marker":"[9]"},{"why":"Provides the previous 208Pb skin extraction from p+208Pb reaction cross sections, used as a consistency reference.","marker":"[6]"},{"why":"Supplies the 48Ca+12C interaction cross sections at 280 MeV per nucleon used as a reference check.","marker":"[19]"},{"why":"Gives the previous reanalysis of p+48Ca and 48Ca+12C scattering that motivates using D1M over D1S densities for 48Ca.","marker":"[22]"}],"fun_headline_variants":["One cross section pins 208Pb skin at 0.309 fm, matches PREX2","Proton reaction cross sections fix 48Ca skin at 0.163 fm, near CREX","Cross sections match parity experiments for 208Pb and 48Ca skins","Scattering data flag thick skins in 14N and 17O"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The $^{208}$Pb extraction assumes that everything contributing to the measured total cross section at 14.137 MeV, including compound-nucleus formation, is either negligible or correctly described by the folding model; the paper itself notes that compound-nucleus effects appear at low energies and could account for the small difference from PREX2, yet they are not included in the model or in the quoted $0.057$ fm error.","fun_headline_variants_meta":{"raw":{"variants":["One cross section pins 208Pb skin at 0.309 fm, matches PREX2","Proton reaction cross sections fix 48Ca skin at 0.163 fm, near CREX","Cross sections match parity experiments for 208Pb and 48Ca skins","Scattering data flag thick skins in 14N and 17O"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000964,"raw_usage":{"total_tokens":4375,"prompt_tokens":1485,"completion_tokens":2890,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":1101,"completion_tokens_details":{"reasoning_tokens":2800}},"tokens_in":1101,"tokens_out":2890,"duration_ms":19777,"temperature":1.0,"reasoning_tokens":2800,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T19:25:21.853444+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure total neutron cross sections of $^{208}$Pb at several energies between 8 and 20 MeV and analyze them with the same folding model after subtracting compound-nucleus contributions computed with a statistical reaction code; the extraction would be falsified if including those contributions at 14.137 MeV shifts the fitted skin by more than $0.057$ fm, or if the fitted value drifts systematically with energy.","supporting_citations":[{"cited_title":"[56], Li, Luo and Wang compiled the charge radii Rch of 236 nuclei measured by laser spectroscopy experi- ment, and calculated the uncertainties","cited_arxiv_id":null,"evidence_quote":"Supplies the n+208Pb total cross section at 14.137 MeV from which the 208Pb skin is extracted."},{"cited_title":"Scaling the D1M-GHFB+AMP pro- ton and neutron densities for 48Ca , we can obtain r48 skin(skin) = 0.180 ± 0.058 fm","cited_arxiv_id":null,"evidence_quote":"Gives the PREX2 value that the 208Pb extraction is compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the CREX value that the 48Ca extraction is compared against."},{"cited_title":"Figure 13 shows our rn of Ref","cited_arxiv_id":null,"evidence_quote":"Defines the chiral g-matrix folding model used for the low-energy cross sections."},{"cited_title":"Figure 16 shows our values on σR and the data [51]","cited_arxiv_id":null,"evidence_quote":"Establishes the folding model's reliability and introduces the ESP-f scaling procedure on proton scattering."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the previous 208Pb skin extraction from p+208Pb reaction cross sections, used as a consistency reference."},{"cited_title":"Effects of chiral three-nucleon forces on $^{4}$He-nucleus scattering in a wide range of incident energies","cited_arxiv_id":"1712.07033","evidence_quote":"Supplies the 48Ca+12C interaction cross sections at 280 MeV per nucleon used as a reference check."},{"cited_title":"Neutron skin thickness of $^{208}$Pb, $^{116,120,124}$Sn, and $^{40}$Ca determined from reaction cross sections of $^{4}$He scattering","cited_arxiv_id":"2107.06441","evidence_quote":"Gives the previous reanalysis of p+48Ca and 48Ca+12C scattering that motivates using D1M over D1S densities for 48Ca."}],"review_version":1}