{"id":"7fc39eb4-20e1-4ddb-ba96-ef6b47e16f5f","arxiv_id":"1908.03293","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A parameter-free microscopic folding calculation of proton scattering supports neutron dominance in the 2+1 states of 12Be and 16C and shows that the standard Bernstein analysis can underestimate the neutron transition matrix element by about 15%.","lead":"This paper uses a microscopic reaction model to calculate how protons scatter off several light nuclei, including neutron-rich beryllium and carbon isotopes. The results support the idea that neutrons dominate the first excited state of 12Be and 16C, and they warn that older analysis methods may undercount those neutrons.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Sec. IV D sensitivity analysis assumes the AMD radial shape of the neutron transition density is correct; the limited-angle inelastic data do not independently validate the outer tail, so the claimed b_n/b_p reduction and the Bernstein-undershoot conclusion rest on that unvalidated shape.","rationale":"I agree with the reader's weakest-assumption analysis: the radial shape of the AMD neutron transition density is the hinge on which both the Mn/Mp support claim and the Sec. IV D sensitivity correction turn. The paper is otherwise a careful application of an established microscopic folding model, and the authors explicitly disclose the assumption, which is good practice. The 18O comparison with an independently reduced rho_n^tr(r) is genuinely informative about surface-vs-tail sensitivity, and the 12C/16O test cases provide some calibration of the reaction part. However, for 12Be and 16C there is no analogous independent neutron transition density, and the available inelastic data cover very forward angles only. The central claim is therefore not that the data prove the AMD tail, but that the data are consistent with it; the word 'supports' in Sec. IV C is somewhat stronger than the constraint actually provided. This does not overturn the reader's CONDITIONAL verdict: the concern is real but non-fatal, because the paper's own logic identifies the shape assumption and the proposed check is a direct extension of the existing sensitivity analysis. I would not move the verdict to REJECT or UNVERDICTED; a conditional acceptance with a request for the alternative-shape test is proportionate. The one point where I might push slightly beyond the reader is the 16C B(E2) ambiguity, which adds a normalization uncertainty on top of the shape uncertainty, but it is secondary to the shape issue.","tokens_in":18405,"tokens_out":3281,"duration_ms":40743,"concrete_test":"For 12Be and 16C, construct two alternative neutron transition densities with the same Mn/Mp and same proton B(E2) as the default AMD densities, but with the outer-tail amplitude altered (e.g., multiply rho_n^tr(r) by 0.7 and 1.3 for r > 4 fm, compensating at r < 3 fm to keep Mn fixed). Recompute the CC cross sections at E = 55 MeV/u for 12Be and E = 33 MeV/u for 16C, and compare with the data of Refs. [3, 9]. If both alternatives fall within the experimental uncertainties over the measured angular range, the data do not constrain the tail shape. Then repeat the Sec. IV D scaling analysis with these alternative densities to see whether b_n/b_p changes by more than the claimed 0.3 reduction; if it does, the Bernstein-undershoot conclusion is shape-dependent and not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the explicit assumption in Sec. IV D: 'the AMD calculation gives correct r dependence of rho_n^tr and rho_p^tr'. The sensitivity coefficients b_n/b_p are then obtained by varying only the overall normalization of each density in Eq. (5). This separates the shape assumption from the normalization, but it does not test the shape. The central conclusion of Sec. IV C—that the good reproduction of cross sections supports Mn/Mp ~ 2 for 12Be and ~3 for 16C—uses the AMD densities as-is, so both the quoted ratios and the Sec. IV D correction to Bernstein-type analyses inherit the AMD radial shapes. The cross-section comparisons cannot fully certify those shapes. For 12Be the inelastic data cover only theta_lab up to about 4.7 degrees (Fig. 11b), and for 16C only about 3.6 degrees (Fig. 12b), with the text noting that finite beam size, multiple scattering, and detector geometry affect the data. Such a narrow angular window samples mainly the first diffraction maximum, i.e., low momentum transfer, which is not strongly sensitive to the outer-region amplitude of rho_n^tr that drives B(n). In addition, the 16C B(E2) input is uncertain: Refs. [76] and [13] give 2.6(9) and 4.15(73) fm^4, and the paper uses the former. A different low-q normalization could alter the inferred neutron strength. Thus the data can be consistent with the AMD densities without uniquely supporting either the radial tail or the claimed 15% weakening of Mn sensitivity.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents microscopic coupled-channel (MCC) calculations of elastic and inelastic proton scattering to the 2_1^+ states of 18O, 10Be, 12Be, and 16C. The proton-nucleus potentials are obtained by single-folding the Melbourne g-matrix NN interaction with matter and transition densities from antisymmetrized molecular dynamics (AMD), with the Brieva-Rook localization for the exchange terms. The method is first tested on 12C and 16O, then applied to the neutron-rich systems. The calculations are compared with independent data at several incident energies, including inverse-kinematics data for the unstable nuclei. The authors report reasonable reproduction of the cross sections, interpret this as support for the AMD neutron transition densities in 12Be and 16C with Mn/Mp ~ 2 and ~ 3, and analyze the sensitivity of the inelastic cross section to Mn and Mp. They conclude that the outer-tail amplitude of the neutron transition density contributes strongly to Mn but weakly to the cross section, so that Bernstein-type phenomenological analyses may underestimate Mn for such exotic systems.","tokens_in":18709,"tokens_out":9910,"duration_ms":113690,"significance":"The paper is a solid application of a well-established, essentially parameter-free folding reaction model to a set of physically interesting neutron-rich nuclei. The use of microscopic AMD transition densities as inputs, without fitting the scattering data, is a genuine strength, and the comparisons with elastic and inelastic data at multiple energies are informative. If the main quantitative conclusion survives scrutiny, the proposed reduction of the effective b_n/b_p sensitivity for 12Be and 16C would be a useful correction to standard analyses of inelastic hadron scattering from exotic nuclei. However, the central new claim is more fragile than the cross-section reproduction: it depends on the assumed radial shape of the AMD transition densities, on the choice of B(E2) normalization for 16C, and on a prior model ambiguity noted by the authors themselves for 12Be.","major_comments":[{"comment":"For 16C, the paper adopts the B(E2) value 2.6(9) fm^4 from Ref. [76] and states that the original AMD densities reproduce the experimental B(E2). However, Table II also lists B(E2)=4.15(73) fm^4 from Ref. [13], which is about two standard deviations larger. Since the proton transition density enters the folding potential and sets the overall normalization of the inelastic cross section, and since the claimed Mn/Mp ~ 3 depends on the relative proton and neutron strengths, the analysis should be repeated with the alternative B(E2) normalization, or at least the resulting changes in the cross sections and in the inferred Mn/Mp should be quantified.","section":"Sec. IV C, Table II, Fig. 12 (16C)"},{"comment":"The central new result, that b_n^{p,p'}/b_p^{p,p'} is reduced by about 15% for 12Be and 16C and that Bernstein-type analyses undershoot Mn, is derived under the explicit assumption that the AMD calculation gives the correct r-dependence of rho_n^tr and rho_p^tr. The inelastic data for 12Be and 16C cover only theta_lab up to about 4.7 and 3.6 degrees, respectively (Figs. 11b and 12b), so they constrain mainly the first diffraction maximum and do not independently validate the outer tail of rho_n^tr that dominates Mn. The robustness of the 15% reduction should be tested, for example by varying the tail amplitude of rho_n^tr while preserving Mn, or by repeating the exercise with an independent structure model. Without such a test, the undershoot conclusion remains plausible but not fully established by the data shown.","section":"Sec. IV D, Eq. (5), Fig. 13"},{"comment":"The statement that the good reproduction of the inelastic cross sections supports the reliability of the adopted AMD neutron transition density, and hence Mn/Mp ~ 2 for 12Be, is weakened by the authors' own citation of Ref. [11]: an earlier MCC calculation using the same AMD densities favored B(n)_lambda=2 = 37 fm^4, whereas the default AMD value used here is 51.1 fm^4. Both calculations appear to describe the data. A quantitative comparison, for example a chi-square analysis or an estimated band of allowed Mn values, is needed before the 12Be data can be said to select the AMD value.","section":"Sec. IV C, paragraph on 12Be neutron transition"},{"comment":"The procedure for extracting the coefficients a_n and a_p is not described in sufficient detail to be reproduced. The text states only that overall factors of rho_n^tr and rho_p^tr are changed and that 'integrated cross sections' are used to reduce the coefficients; it does not specify the angular range or integration used, how the two coefficients are disentangled, or how the complex nature of the reaction amplitudes is handled. Since Eq. (5) is the basis of Fig. 13 and of the final sensitivity claim, these details should be provided.","section":"Sec. IV D, Eq. (5)"}],"minor_comments":[{"comment":"The caption uses 'AMG+GCM' where 'AMD+GCM' is intended; the same typo appears in the text of Sec. III.","section":"Fig. 1 caption and Sec. III"},{"comment":"The scaling factor M_p^{exp}(18Ne)/M_n^{cal} is quoted as 1.72, but the Table II central values give sqrt(50/18.6) = 1.64. Please clarify which value of B(n) was used for the scaling.","section":"Sec. IV B"},{"comment":"The phrase 'reduced from the (p,p') scattering' should read 'deduced from' or 'extracted from'.","section":"Fig. 3 caption"},{"comment":"The text says the scaling factors for 10Be are 'listed in Table II', but the table lists B values rather than the ratios M_p^{exp}/M_p^{cal} and M_n^{exp}/M_n^{cal}; including the explicit scaling factors would improve reproducibility.","section":"Sec. IV C, Table II"},{"comment":"Reference [34] is missing the beginning of the article title, and some author names in the reference list appear corrupted (e.g., 'Forssn' and 'Navrtil' in Ref. [15]).","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper describes a competent application of an established reaction framework, and I do not see a reason to reject it. My main concerns are about the strength of the inference from very limited-angle data for 12Be and 16C, and about the lack of sensitivity tests for the 16C B(E2) ambiguity and for the assumed transition-density shapes. These concerns are addressable with additional calculations and more careful wording, which is why I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version. This is a solid, no-free-parameter coupled-channel study of proton inelastic scattering on 18O, 10Be, 12Be, and 16C using the Melbourne g-matrix and AMD densities. The genuinely new piece is the sensitivity analysis: they compute b_n/b_p for each nucleus and show that for 12Be and 16C, where the neutron transition density has an outer tail, the cross section is about 15% less sensitive to Mn than the standard Bernstein prescription assumes. That is a useful caution for people extracting Mn from (p,p') data.\n\nThe paper earns its keep in the details. They validate the reaction part against 12C and 16O, scale proton transition densities to measured B(E2) values where needed, and compare against elastic and inelastic data at several energies. They also disclose the scaling factors and explicitly state the central assumption in Sec. IV D: the AMD calculation gives the correct r-dependence of the transition densities. That is honest and makes the logic easy to inspect.\n\nThe soft spot is precisely that assumption. For 12Be and 16C, the inelastic data cover only the first few degrees in the lab frame, so they sample the first diffraction maximum and do not independently constrain the outer-region amplitude of rho_n^tr that drives B_n. The agreement with the data is consistent with the AMD densities, but it does not certify the shape that the sensitivity conclusion depends on. Also, the 16C B(E2) input is not unique: they use 2.6(9) fm^4 from one reference, while another gives 4.15(73). Picking the larger value would change the neutron strength and the ratio. A referee should ask them to address that ambiguity. Minor caveats: the central-only g-matrix potential is a simplification, and no code or data are released, so the numbers can't be independently checked.\n\nNone of this is disqualifying. The authors themselves say higher-quality data are needed. The 18O case actually shows the framework can be sensitive to the radial shape of rho_n^tr when the data go to larger angles, which is evidence that the method works where the data are informative. The paper deserves peer review, and with moderate revision—mostly on the B(E2) ambiguity and a more prominent caveat about the shape assumption—it would be a useful reference for anyone doing hadronic inelastic scattering on neutron-rich nuclei.","headline":"A careful no-free-parameter folding study that supports neutron-dominated 2+ excitations in 12Be and 16C and warns that Bernstein-type analyses can underestimate Mn when the neutron transition density has an outer tail; the warning is plausible but rests on AMD radial shapes that the limited-angle data do not independently validate.","tokens_in":19335,"tokens_out":3293,"would_cite":true,"duration_ms":35656,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["25.40.Ep","21.60.Gx","24.10.Eq","27.20.+n"],"model":"deepseek-v4-flash","headline":"Inelastic proton scattering off $^{12}$Be and $^{16}$C, computed with a parameter-free microscopic folding model, supports neutron-dominated $2^+_1$ excitations with $M_n/M_p\\approx 2$ and $\\approx 3$, and implies that standard analyses…","keywords":["inelastic proton scattering","neutron-rich nuclei","transition density","coupled-channel calculation","antisymmetrized molecular dynamics","Melbourne g-matrix","neutron transition matrix element","Bernstein prescription"],"falsifier":"Compute the $2^+_1$ transition densities of $^{12}$Be and $^{16}$C with an ab initio method using chiral $NN+3N$ interactions; if the resulting neutron transition density lacks the pronounced outer-region amplitude relative to the proton part, or if folding those densities with the Melbourne interaction fails to reproduce the measured inelastic cross sections, the claim that $M_n/M_p\\approx 2$ and $\\approx 3$ and that Bernstein analyses undershoot $M_n$ would be undermined. Alternatively, a new measurement of the inelastic proton cross section for $^{16}$C at $E\\approx 50$ MeV/u extending past $\\theta_{\\mathrm{cm}}\\approx 30^{\\circ}$ could discriminate between the AMD and collective-model densities because their predicted peak heights differ.","tokens_in":18121,"feed_emoji":"⚛️","tokens_out":11335,"duration_ms":103001,"temperature":0.7,"pith_summary":"This paper asks how much of the first $2^+$ excitation in the neutron-rich nuclei $^{18}$O, $^{10}$Be, $^{12}$Be, and $^{16}$C is carried by neutrons rather than protons, and whether proton inelastic scattering can see it. The authors compute elastic and inelastic proton scattering with a coupled-channel model that folds the Melbourne $g$-matrix nucleon-nucleon interaction with matter and transition densities from antisymmetrized molecular dynamics, leaving no free reaction parameters. The computed cross sections reproduce measured elastic and inelastic data, and the agreement supports neutron-dominated $2^+_1$ excitations in $^{12}$Be and $^{16}$C, with neutron-to-proton transition matrix element ratios $M_n/M_p\\approx 2$ and $\\approx 3$. They then show that the neutron transition densities in these nuclei have a large-amplitude outer tail that inflates $M_n$ but contributes little to the scattering cross section, so the standard Bernstein-style analysis, which assumes proton and neutron transition densities have the same radial shape, would underestimate the neutron matrix element. If right, the result changes how neutron collectivity should be extracted from hadron scattering data on neutron-rich unstable nuclei.","feed_headline":"Proton scattering exposes neutron-dominant excitations in 12Be and 16C","feed_subtitle":"Microscopic fits give Mn/Mp ≈ 2 for 12Be, ≈ 3 for 16C; standard analysis would miss it.","key_machinery":"The load-bearing object is the system- and energy-dependent sensitivity ratio $b_n^{(p,p')}/b_p^{(p,p')}$, extracted from the linearized relation $\\sigma(p,p') = \\left| a_n M_n + a_p M_p \\right|^2$. The paper obtains the coefficients $a_n$ and $a_p$ by repeating the coupled-channel calculation with the neutron (or proton) transition density scaled by a common factor, then reads off the ratio that controls how strongly the measured cross section constrains the neutron transition matrix element. The argument also depends on the radial shapes of the AMD transition densities: in $^{12}$Be and $^{16}$C, $\\rho_n^{\\mathrm{tr}}(r)$ is not proportional to $\\rho_p^{\\mathrm{tr}}(r)$ but has additional amplitude around $r\\approx 3$ fm and beyond, which contributes to $M_n$ while contributing only weakly to the cross section.","core_discovery":"The central discovery is that the measured inelastic proton scattering cross sections to the $2^+_1$ states of $^{12}$Be and $^{16}$C are reproduced by a microscopic coupled-channel calculation that folds the Melbourne $g$-matrix interaction with AMD transition densities, and the agreement supports neutron-to-proton transition matrix element ratios $M_n/M_p\\approx 2$ and $\\approx 3$ in these nuclei. By artificially scaling the neutron or proton transition density and recomputing the cross sections, the paper derives the sensitivity ratio $b_n^{(p,p')}/b_p^{(p,p')}$ and finds it is about 0.3 smaller than the standard value for $^{12}$Be and $^{16}$C, i.e., the cross section is about 15% less sensitive to $M_n$ than assumed in the Bernstein prescription. Because the AMD neutron transition densities in these nuclei have a large-amplitude outer tail that contributes strongly to $M_n$ but only weakly to the scattering cross section, the authors conclude that a Bernstein-style analysis using collective-model transition densities with $\\rho_n^{\\mathrm{tr}}(r)\\propto \\rho_p^{\\mathrm{tr}}(r)$ would undershoot the neutron matrix element for such exotic systems.","pith_inferences":["The same decoupling between a large outer neutron transition tail and a modest cross-section contribution should occur in other neutron-rich nuclei where valence neutrons occupy radially extended orbits while protons are shell-closed, such as $^{14}$Be or $^{20}$C; testing those cases would show whether the effect is generic.","The calculated energy dependence of $b_n/b_p$ (decreasing with energy) could be exploited: if one extracts $M_n$ from data at two beam energies using the Bernstein prescription and the values disagree, that disagreement would be a direct signature of the radial-shape effect reported here.","The paper's sensitivity analysis uses cross sections integrated over the measured angular range; examining specific momentum-transfer windows may show even stronger deviations, so reanalyzing existing data bin-by-bin could sharpen the test without new experiments."],"forward_implications":["For $^{12}$Be and $^{16}$C, the data are consistent with neutron-dominated $2^+_1$ transitions, $M_n/M_p\\approx 2$ and $\\approx 3$, reinforcing the picture that the $N=8$ magic number is broken and $sd$-shell neutrons drive the excitation.","Bernstein-prescription analyses of inelastic proton data on such neutron-rich nuclei would systematically underestimate $M_n$; e.g., the earlier extraction $B^{(n)}_{\\lambda=2}=17$ fm$^4$ for $^{12}$Be lies far below the microscopic value $51.1$ fm$^4$.","The parameter-free microscopic folding model can serve as a cross-check for inverse-kinematics reaction analyses of unstable nuclei, avoiding part of the optical-potential uncertainty.","Higher-quality differential cross-section data, especially beyond the first peak, can distinguish the AMD transition density from collective-model forms and directly test the predicted reduction in sensitivity to $M_n$."],"supporting_citations":[{"why":"Supplies the Melbourne $g$-matrix effective nucleon-nucleon interaction that is folded with the target densities to build the proton-nucleus potentials.","marker":"[33]"},{"why":"Provides the simplified single-folding model with Brieva-Rook localization that the paper extends to inelastic coupled-channel calculations.","marker":"[35]"},{"why":"Gives the AMD wave functions and transition densities of $^{12}$Be, $^{16}$C, and $^{10}$Be used as the structure inputs.","marker":"[4]"},{"why":"Earlier microscopic coupled-channel analysis of proton scattering on $^{12}$Be with the same AMD densities, providing a baseline $M_n$ value with which the present result is compared.","marker":"[11]"},{"why":"Defines the Bernstein prescription $\\sigma\\propto|b_n M_n + b_p M_p|^2$ whose assumption of proportional neutron and proton transition densities is shown to fail for the exotic cases.","marker":"[1]"},{"why":"Supplies inelastic proton scattering data for $^{10}$Be and $^{12}$Be measured in inverse kinematics used to test the calculations.","marker":"[3]"},{"why":"Supplies $^{16}$C inelastic scattering data and $B(E2)$ results used in the comparison and in the earlier Bernstein analysis.","marker":"[9]"},{"why":"Provides the experimental neutron transition density for $^{18}$O derived from $(p,p')$, used to test the sensitivity of the cross sections to the radial shape of the neutron transition density.","marker":"[19]"}],"fun_headline_variants":["Proton scattering shows Mn/Mp ≈ 2 in 12Be, ≈ 3 in 16C","Neutron-dominant 2+ states in 12Be, 16C from proton data","Exotic neutron tails drive excitations in 12Be, 16C","Proton scattering exposes neutron excess in 12Be, 16C"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the AMD calculation gives the correct radial shape of the neutron and proton transition densities, especially the outer-region amplitude of the neutron transition density in $^{12}$Be and $^{16}$C; if that radial shape is wrong, the conclusion that Bernstein analyses undershoot $M_n$ does not follow even if the cross sections are reproduced.","fun_headline_variants_meta":{"raw":{"variants":["Proton scattering shows Mn/Mp ≈ 2 in 12Be, ≈ 3 in 16C","Neutron-dominant 2+ states in 12Be, 16C from proton data","Exotic neutron tails drive excitations in 12Be, 16C","Proton scattering exposes neutron excess in 12Be, 16C"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000249,"raw_usage":{"total_tokens":1588,"prompt_tokens":1018,"completion_tokens":570,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":634,"completion_tokens_details":{"reasoning_tokens":476}},"tokens_in":634,"tokens_out":570,"duration_ms":6073,"temperature":1.0,"reasoning_tokens":476,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:18:26.491585+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the $2^+_1$ transition densities of $^{12}$Be and $^{16}$C with an ab initio method using chiral $NN+3N$ interactions; if the resulting neutron transition density lacks the pronounced outer-region amplitude relative to the proton part, or if folding those densities with the Melbourne interaction fails to reproduce the measured inelastic cross sections, the claim that $M_n/M_p\\approx 2$ and $\\approx 3$ and that Bernstein analyses undershoot $M_n$ would be undermined. Alternatively, a new measurement of the inelastic proton cross section for $^{16}$C at $E\\approx 50$ MeV/u extending past $\\theta_{\\mathrm{cm}}\\approx 30^{\\circ}$ could discriminate between the AMD and collective-model densities because their predicted peak heights differ.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Melbourne $g$-matrix effective nucleon-nucleon interaction that is folded with the target densities to build the proton-nucleus potentials."},{"cited_title":"Minomo, K","cited_arxiv_id":null,"evidence_quote":"Provides the simplified single-folding model with Brieva-Rook localization that the paper extends to inelastic coupled-channel calculations."},{"cited_title":"Takashina and Y","cited_arxiv_id":null,"evidence_quote":"Earlier microscopic coupled-channel analysis of proton scattering on $^{12}$Be with the same AMD densities, providing a baseline $M_n$ value with which the present result is compared."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies $^{16}$C inelastic scattering data and $B(E2)$ results used in the comparison and in the earlier Bernstein analysis."},{"cited_title":"Kelly et al","cited_arxiv_id":null,"evidence_quote":"Provides the experimental neutron transition density for $^{18}$O derived from $(p,p')$, used to test the sensitivity of the cross sections to the radial shape of the neutron transition density."}],"review_version":1}