{"id":"423e2caf-8090-4089-a478-b209e86e2c22","arxiv_id":"1908.00667","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A systematic DWIA reanalysis of all published GSI (p,2p) and (p,pn) data finds reduction factors near 0.9 to 1.0 with a very weak asymmetry dependence and indicates missing higher-order effects in the high-momentum region.","lead":"This paper recalculates proton knockout reactions on carbon, nitrogen, and oxygen isotopes measured at GSI, using the distorted-wave impulse approximation with added relativistic and nonlocality corrections. It finds that the extracted nuclear structure reduction factors depend only weakly on proton-neutron asymmetry, and points to missing higher-order reaction effects at large recoil momenta.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing higher-order effects acknowledged in Sec. IV can generate exactly the weak ΔS slope claimed: the 21N/22O/23O pairs in Table I show low Rs for (p,2p) and high Rs for (p,pn), so the fitted slope may be a reaction-model artifact rather than a property of spectroscopic strength.","rationale":"The paper is a careful DWIA study and the Table I compilation is valuable. My concern is not about numerical errors in the calculation but about the interpretation of the linear fit in Sec. III B. The authors state in Sec. IV that higher-order effects are missing and that these are important at large recoil momentum (Sec. III D, Fig. 5). The GSI cross sections are semi-inclusive and integrate over recoil momentum, so the missing strength directly enters the Rs values. Whether the missing strength biases the ΔS slope depends on how it scales with separation energy. Since weakly bound nucleons have narrower momentum distributions, the high-recoil region contributes a smaller fraction for neutron removal from neutron-rich nuclei than for proton removal from the same nuclei. Table I shows the expected signature: for 21N, Rs(p,2p)=0.70(14) vs Rs(p,pn)=1.25(23); for 22O, 0.87(14) vs 1.08(19); for 23O, 0.99(24) vs 1.08(28). These paired differences at opposite ends of the ΔS axis can produce a negative slope even if the underlying Rs has no ΔS dependence. The paper does not separate the (p,2p) and (p,pn) channels in the fit or quantify the ΔS dependence of the missing higher-order strength. Therefore the headline weak-slope claim is not yet fully supported. The proposed tests—fitting the two channels separately and/or comparing with Faddeev/AGS for a representative pair—would settle the matter.","tokens_in":13730,"tokens_out":10989,"duration_ms":109136,"concrete_test":"Recompute the linear fit of Sec. III B separately for the (p,2p) and (p,pn) subsets using Table I with the same error treatment. If the (p,2p) slope is negative and the (p,pn) slope is consistent with zero, the combined weak-slope result is an artifact of channel mixing. As an independent check, run the Faddeev/AGS calculation of Ref. [16] for 21N(p,2p) and 21N(p,pn) (or 22O and 23O) and replace the DWIA Rs values; if the two Rs move substantially toward each other, the missing higher-order effects bias the DWIA slope.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central claim—a very weak ΔS dependence of Rs—rests on the implicit assumption that the missing higher-order effects, which the authors themselves identify in Sec. IV and Fig. 5, do not vary systematically with ΔS. That assumption is not tested. The mechanism is concrete: the missing strength appears at recoil momenta 150–300 MeV/c (Fig. 5), and the fraction of the semi-inclusive cross section in that region grows with the separation energy of the knocked-out nucleon. Proton removal from neutron-rich nuclei (deeply bound protons) should therefore be underestimated more than neutron removal (weakly bound neutrons). Table I shows exactly this pattern: for 21N, Rs = 0.70(14) in (p,2p) vs 1.25(23) in (p,pn); for 22O, 0.87(14) vs 1.08(19); for 23O, 0.99(24) vs 1.08(28). If this pattern is driven by the missing higher-order mechanism, the fitted slope Rs = 0.947(36) − 2.6(27)×10^−3 ΔS (Sec. III B) is not a property of the spectroscopic strength but an artifact of the reaction model. The paper's own conclusion that higher-order effects are essential for large recoil is an admission that the integrated cross sections, and hence the Rs values, are not reliably described. Without quantifying the ΔS dependence of the missing strength, the headline weak-slope result is not yet established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a partial-wave distorted-wave impulse approximation (DWIA) analysis of all eighteen published R3B/LAND (p,2p) and (p,pn) cross sections on carbon, nitrogen, and oxygen isotopes at 300–450 MeV/u. The authors compute single-particle cross sections using Dirac optical potentials (EDAD2), Woods-Saxon bound states with radii matched to Hartree-Fock and depths fixed by separation energies, Franey-Love t-matrix amplitudes, and shell-model spectroscopic factors. They include nonlocality corrections (Perey and Darwin factors), the Møller factor, and energy-dependent final-state optical potentials, and they estimate uncertainties from alternative inputs. The central result is that the extracted reduction factors Rs = σexp/σth show a very weak dependence on proton-neutron asymmetry ΔS, fitted as Rs = 0.947(36) − 2.6(27)×10⁻³ ΔS with reduced χ²/N = 0.74. The transverse momentum distribution of ¹²C(p,2p)¹¹B is also analyzed and is found to undershoot the data in the 150–300 MeV/c region, which the authors attribute to missing higher-order effects such as multistep scattering or channel coupling.","tokens_in":14084,"tokens_out":4877,"duration_ms":51456,"significance":"If the weak asymmetry dependence of Rs holds, it would strengthen the case that (p,pN) reactions at intermediate energies probe the same spectroscopic strength as transfer and ab initio methods, in contrast to the steeper asymmetry reported from composite-target knockout. The paper is valuable for its systematic quantification of input choices: nonlocality, Møller factor, energy-dependent optical potentials, and NN interaction prescription. The calculations are based on standard, documented ingredients, and no parameter of the reaction model is fitted to the GSI cross sections, which is a clear strength. The comparison with other reaction models and with (e,e′p) results is informative and properly highlights the role of higher-order effects. However, the paper's own admission that important higher-order contributions are missing from the model means that the absolute values of Rs, and potentially their ΔS dependence, are not yet reliably established.","major_comments":[{"comment":"The central claim of a very weak ΔS dependence of Rs rests on the unquantified assumption that the missing higher-order effects, which the authors explicitly identify in Sec. IV and Fig. 5, do not vary systematically with ΔS. The data in Table I show a concrete pattern consistent with such a variation: for 21N, Rs = 0.70(14) in (p,2p) versus 1.25(23) in (p,pn); for 22O, 0.87(14) versus 1.08(19); and for 23O, 0.99(24) versus 1.08(28). Since Fig. 5 shows that the missing strength appears at recoil momenta of 150–300 MeV/c, and since the fraction of the semi-inclusive cross section in that region grows with the separation energy of the knocked-out nucleon, proton removal from neutron-rich nuclei (deeply bound protons) should be underestimated more than neutron removal (weakly bound neutrons). This is exactly the pattern needed to produce a negative fitted slope. The authors do not estimate the magnitude or ΔS dependence of the missing higher-order contributions, so the fitted slope Rs = 0.947(36) − 2.6(27)×10⁻³ ΔS cannot currently be interpreted as a property of spectroscopic strength rather than a reaction-model artifact. I request a quantitative sensitivity estimate, for example by comparing results under restricted quasi-free kinematics, by using a reaction model that includes multistep contributions, or by artificially removing the high-recoil region and refitting the slope.","section":"Sec. III B, Table I, Fig. 5"},{"comment":"The paper states that the close-to-unity reduction factors 'indicate a fundamental problem in current reaction models' and that higher-order effects are missing, yet it also compares the DWIA Rs values with ab initio SCGF and CC results in Fig. 1 and concludes consistency of the weak trend. These statements are in tension: if the missing higher-order strength affects the integrated cross sections, then the absolute values of Rs are systematically too high, and the comparison in Fig. 1 is not a clean test of the structure calculations. The authors should explicitly separate conclusions that are robust under the admitted missing effects (e.g., the relative behavior of different input choices) from those that are not (e.g., the absolute magnitude and the slope of Rs versus ΔS).","section":"Sec. III C and Sec. IV"}],"minor_comments":[{"comment":"The adopted 10% uncertainty for the single-particle wave functions is stated without a detailed derivation; the text says it is based on Refs. [25,36] and a comparison with (e,e′p) analyses, but a short explanation of how this number was obtained would improve transparency.","section":"Sec. III A"},{"comment":"The σth column is given without uncertainties, while the text quotes total relative uncertainties of 15–25% for Rs. It would be clearer to show the theoretical uncertainty on σth or to state explicitly that the quoted uncertainties on Rs already include it.","section":"Table I"},{"comment":"The sentence 'some higher-order effects, which is essential for an accurate cross-section description at large recoil momentum, is missing' has a subject–verb agreement error: 'effects' is plural, so 'are missing' (or rephrase as 'an effect ... is missing').","section":"Abstract and Sec. IV"},{"comment":"The caption mentions the blue dotted line as the nonlocality-corrected result scaled by 0.655, but the body text says the scaling factor is 0.66. The numbers should be made consistent.","section":"Fig. 5"}],"recommendation":"major_revision","confidential_remarks":"The paper is a careful and useful uncertainty analysis of the DWIA framework, and the authors' honesty about the missing higher-order effects is commendable. However, the headline result—the weak ΔS dependence of Rs—is not yet established because the admitted missing strength could plausibly produce exactly the observed pattern in Table I. This is fixable with a sensitivity analysis or a more qualified conclusion, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Phuc, Yoshida, and Ogata have done the first partial-wave DWIA calculation for all 18 published GSI (p,pN) cases, with Perey, Darwin, and Møller corrections. The calculation is clean: no parameter is fitted to the knockout data, every input comes from the literature (EDAD2 optical potentials, Woods-Saxon bound states with Hartree-Fock radii, Franey-Love t-matrix, shell-model SFs), and the uncertainty budget is transparent. The TMD comparison for 12C(p,2p) is genuinely useful because it exposes the high-momentum deficit directly. The weak ΔS slope they find is consistent with earlier eikonal, TC, and FAGS analyses, so at face value this is a useful methodological reference.\n\nThe stress test lands, though. The authors themselves admit in Sec. IV that the factorized amplitude in Eq. (1) omits higher-order processes, and Fig. 5 shows the missing strength is concentrated at recoil momenta 150–300 MeV/c. For a deeper bound nucleon, a larger fraction of the integrated cross section sits in that region, so the integrated σ_th is increasingly underestimated. That makes Rs = σ_exp/σ_th artificially high for deeply bound removal. The pattern in Table I—21N(p,2p) at 0.70 versus 21N(p,pn) at 1.25, and similar for 22O and 23O—is exactly what you would see if the high-ΔS proton-removal points were inflated. Correcting for that inflation moves the 0.70 even lower, which steepens the negative ΔS slope rather than weakening it. The paper does not quantify the ΔS dependence of the missing strength, so the weak slope is not yet established as a property of the spectroscopic strength. It could be a common artifact of all the factorized reaction models, not just this one.\n\nThe other issues are minor. No code is released, but the inputs are standard and reproducible in principle. The comparison with ab initio CC and SCGF is suggestive, but those are structure calculations and do not address the reaction mechanism.\n\nRecommendation: send it to review. The referee should ask for an estimate of how much the missing higher-order effects shift the ΔS slope—for example, by comparing with the RIKEN quasifree data of Ref. [14] or adding a simple model for the high-momentum tail. If the shift is large, the headline needs to be downgraded. Even as is, the paper is a careful, honest piece of work that deserves referee time.","headline":"Solid partial-wave DWIA reanalysis of GSI (p,pN) data; the weak ΔS slope is the weakest link because the acknowledged missing higher-order effects may flatten it.","tokens_in":14655,"tokens_out":9134,"would_cite":true,"duration_ms":90068,"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":"The paper reanalyzes all 18 published inverse-kinematics (p,pN) knockout cases with the distorted-wave impulse approximation and finds that the extracted reduction factor has nearly no proton-neutron asymmetry dependence, while the…","keywords":["distorted-wave impulse approximation","proton knockout","inverse kinematics","spectroscopic factors","reduction factor","nonlocality","Møller factor","momentum distributions"],"falsifier":"Run a full three-body Faddeev/AGS calculation for $^{12}$C(p,2p)$^{11}$B that includes multistep scattering together with the nonlocality, Møller-factor, and energy-dependent optical-potential corrections used here: if the 150–300 MeV/c undershoot of the transverse momentum distribution disappears, the DWIA factorization is the culprit; if it persists, the discrepancy comes from input physics rather than the factorization. A simpler check is a same-channel measurement at quasifree kinematics, where DWIA should already agree.","tokens_in":13519,"feed_emoji":"⚛️","tokens_out":11399,"duration_ms":105976,"temperature":0.7,"pith_summary":"This paper asks whether the distorted-wave impulse approximation (DWIA), the standard tool for extracting single-particle strength from proton knockout reactions, gives reliable answers for the new inverse-kinematics data on rare isotopes. It reanalyzes all published (p,2p) and (p,pn) cases for carbon, nitrogen, and oxygen isotopes in the 300–450 MeV/u range, using a partial-wave DWIA that includes nonlocality corrections, the relativistic Møller factor, and energy-dependent optical potentials. The central finding is that the extracted reduction factor $R_s = \\sigma_{\\rm exp}/\\sigma_{\\rm th}$ shows at most a very weak dependence on proton-neutron asymmetry, in agreement with ab initio structure calculations and with other reaction models. A second result is that the calculated transverse momentum distribution for $^{12}$C($p$,2$p$)$^{11}$B falls below the data at recoil momenta between 150 and 300 MeV/c, which the authors take as evidence that higher-order reaction effects are missing from current models. If these conclusions hold, the method is reliable for extracting relative single-particle quenching in quasi-free kinematics, but integrated semi-inclusive cross sections need a treatment that goes beyond the standard factorization.","feed_headline":"Proton knockout: quenching factor barely moves with neutron excess","feed_subtitle":"A full DWIA reanalysis of 18 isotope knockout cases finds Rs ≈ 0.95 with a tiny slope—and exposes missing higher-order effects.","key_machinery":"The load-bearing object is the factorized DWIA transition amplitude $\\langle \\chi_1^{(-)}\\chi_2^{(-)} | t_{pN} | \\chi_0^{(+)}\\phi_{nljm}\\rangle$; the factorization separates the three-body scattering wave function into two two-body distorted waves, which is the premise that makes the calculation tractable. Around that amplitude the paper stacks four correction terms: the Perey factor for the nonlocality of the bound single-particle wave function, the Darwin factor for relativistic corrections to the Dirac scattering waves, the Møller factor $\\eta$ that converts the $pN$ cross section between the two-nucleon frame and the three-body frame, and energy-dependent Dirac optical potentials for the distorted waves. The ratio $R_s = \\sigma_{\\rm exp}/\\sigma_{\\rm th}$ extracted from these ingredients is the quantity whose asymmetry dependence the paper claims is weak.","core_discovery":"On the paper's own terms, the discovery is that a full partial-wave DWIA calculation, with the Perey factor for the bound-state wave function, the Darwin factor for the Dirac scattering waves, the Møller factor, and energy-dependent optical potentials, reproduces the trend of all 18 published (p,pN) cross sections well enough to extract reduction factors clustered near 0.9–1.0. A linear fit gives $R_s = 0.947(36) - 2.6(27)\\times 10^{-3}\\,\\Delta S$ with reduced $\\chi^2/N = 0.74$, where $\\Delta S$ is the proton-neutron separation-energy asymmetry. The near-flat slope is consistent with coupled-cluster and self-consistent Green's function reduced spectroscopic factors and with transfer-to-continuum and earlier DWIA analyses, and it stands in contrast to the steep asymmetry reported for nucleon-removal reactions. The same calculation underestimates the high-recoil part (150–300 MeV/c) of the $^{12}$C($p$,2$p$)$^{11}$B transverse momentum distribution, which the authors interpret as a genuine missing piece—likely multistep scattering or channel coupling—rather than a defect of the data or of the optical-potential choice.","pith_inferences":["The authors' own diagnosis implies a concrete prediction: if higher-order processes are the cause, the discrepancy between DWIA and data should grow monotonically with recoil momentum, vanish at the quasifree point, and be largely independent of the target isotope once the single-particle wave function is fixed.","Because the Møller factor is a known function of beam energy, a scan of the same knockout channel across 300–450 MeV/u could isolate its contribution and sharpen the extracted $R_s$ without changing nuclear-structure inputs.","The near-unity $R_s$ values, combined with the missing high-momentum strength, suggest that semi-inclusive inverse-kinematics knockout may systematically overestimate spectroscopic factors unless the acceptance is restricted; this could reconcile the (p,pN) results with the smaller $(e,e'p)$ quenching factors.","Extending the same correction set to a nonlocal dispersive optical model, which the authors note is underway, would test whether the Perey/Darwin treatment captures all nonlocality or whether part of the high-momentum discrepancy is a wave-function effect rather than a reaction effect."],"forward_implications":["Reduction factors extracted from intermediate-energy (p,pN) data should not be read as evidence for a strong proton-neutron asymmetry dependence of spectroscopic quenching; the fitted slope is consistent with zero within uncertainties.","Absolute values of $R_s$ from this DWIA lie above the $(e,e'p)$ benchmark for $^{12}$C and $^{16}$O, so if electron knockout is the reference, the integrated data contain extra strength that the present model cannot generate.","Neglecting the nonlocality corrections and the Møller factor shifts $R_s$ by up to roughly 18–26%, and these effects partly cancel the missing higher-order strength; future model comparisons must include them.","Momentum distributions, not just integrated cross sections, are needed to expose missing reaction mechanisms; the 150–300 MeV/c undershoot is the diagnostic signature.","Measurements with kinematics tightly restricted to the quasifree condition give smaller $R_s$ values, so restricting acceptance reduces the influence of the higher-order effects the paper identifies."],"supporting_citations":[{"why":"Supplies the DWIA formalism, the factorization of the three-body wave function used in Eq. (1), and the normal-kinematics benchmark the paper extends.","marker":"[4]"},{"why":"Provides the partial-wave inverse-kinematics DWIA formulation and relativistic kinematics on which this calculation is built.","marker":"[9]"},{"why":"The exclusive $^{12}$C(p,2p)$^{11}$B data whose transverse momentum distribution is analyzed in Sec. III D.","marker":"[32]"},{"why":"Supplies semi-inclusive oxygen (p,2p) data and the eikonal-DWIA and self-consistent Green's function comparison points.","marker":"[33]"},{"why":"Provides a set of (p,2p) and (p,pn) data and the Faddeev/AGS analysis points compared here.","marker":"[34]"},{"why":"Supplies additional (p,pN) data and the shell-model spectroscopic factors used in the $\\sigma_{\\rm th}$ sums.","marker":"[35]"},{"why":"Gives the transfer-to-continuum analysis and shell-model inputs used for comparison and for the single-particle configurations.","marker":"[36]"},{"why":"Coupled-cluster ab initio reduced spectroscopic factors used to judge the asymmetry trend.","marker":"[23]"},{"why":"Self-consistent Green's function ab initio reduced spectroscopic factors used for the same comparison.","marker":"[24]"},{"why":"Supplies the EDAD2 Dirac phenomenological optical potentials used for all distorted waves.","marker":"[45]"}],"fun_headline_variants":["DWIA reanalysis: R_s ≈ 0.95, slope barely moves with asymmetry","Proton knockout: reduction factor near unity, tiny asymmetry slope","Missing higher-order effects exposed in DWIA proton knockout","18 (p,pN) cases: reduction factors near 0.95, flat trend","DWIA on (p,pN): Rs ~0.95, high-momentum tail unexplained"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The extraction starts from a factorized transition amplitude in which the three-body scattering wave function is written as a product of two two-body distorted waves; if multistep scattering or channel coupling contributes significantly, every computed cross section and reduction factor shifts.","fun_headline_variants_meta":{"raw":{"variants":["DWIA reanalysis: R_s ≈ 0.95, slope barely moves with asymmetry","Proton knockout: reduction factor near unity, tiny asymmetry slope","Missing higher-order effects exposed in DWIA proton knockout","18 (p,pN) cases: reduction factors near 0.95, flat trend","DWIA on (p,pN): Rs ~0.95, high-momentum tail unexplained"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000613,"raw_usage":{"total_tokens":2951,"prompt_tokens":1145,"completion_tokens":1806,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":761,"completion_tokens_details":{"reasoning_tokens":1702}},"tokens_in":761,"tokens_out":1806,"duration_ms":11090,"temperature":1.0,"reasoning_tokens":1702,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:40:03.762566+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a full three-body Faddeev/AGS calculation for $^{12}$C(p,2p)$^{11}$B that includes multistep scattering together with the nonlocality, Møller-factor, and energy-dependent optical-potential corrections used here: if the 150–300 MeV/c undershoot of the transverse momentum distribution disappears, the DWIA factorization is the culprit; if it persists, the discrepancy comes from input physics rather than the factorization. A simpler check is a same-channel measurement at quasifree kinematics, where DWIA should already agree.","supporting_citations":[{"cited_title":"Y oshida, M","cited_arxiv_id":null,"evidence_quote":"Provides the partial-wave inverse-kinematics DWIA formulation and relativistic kinematics on which this calculation is built."},{"cited_title":"Panin, J","cited_arxiv_id":null,"evidence_quote":"The exclusive $^{12}$C(p,2p)$^{11}$B data whose transverse momentum distribution is analyzed in Sec. III D."},{"cited_title":"The reduction factor Rs = σexp/σ th is given in the last column","cited_arxiv_id":null,"evidence_quote":"Supplies semi-inclusive oxygen (p,2p) data and the eikonal-DWIA and self-consistent Green's function comparison points."},{"cited_title":"Flavigny, A","cited_arxiv_id":null,"evidence_quote":"Supplies additional (p,pN) data and the shell-model spectroscopic factors used in the $\\sigma_{\\rm th}$ sums."},{"cited_title":"Gómez-Ramos and A","cited_arxiv_id":null,"evidence_quote":"Gives the transfer-to-continuum analysis and shell-model inputs used for comparison and for the single-particle configurations."},{"cited_title":"Jensen, G","cited_arxiv_id":null,"evidence_quote":"Coupled-cluster ab initio reduced spectroscopic factors used to judge the asymmetry trend."},{"cited_title":"democratic","cited_arxiv_id":null,"evidence_quote":"Self-consistent Green's function ab initio reduced spectroscopic factors used for the same comparison."},{"cited_title":"Møller, Kgl","cited_arxiv_id":null,"evidence_quote":"Supplies the EDAD2 Dirac phenomenological optical potentials used for all distorted waves."}],"review_version":1}