{"id":"6aa29917-0c6d-4b6c-a862-b5345e2b9a0b","arxiv_id":"2608.06524","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A Glauber-model study predicts that 26P is the strongest proton-halo candidate among 26P, 27S, and 31Ar, and that no single observable can identify a proton halo.","lead":"This paper predicts what future proton-knockout experiments should measure for three proton-rich nuclei, 26P, 27S, and 31Ar. It concludes that 26P is the strongest proton-halo candidate, while the larger electric charge of 31Ar suppresses its halo despite weaker binding.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The predicted FWHM ranking and the visibility of the narrow 2s1/2 component are not shown to be robust to the fixed Woods-Saxon geometry and Coulomb parameterization; modest changes could invert the 27S vs 31Ar ordering.","rationale":"I agree with the reader's identification of the single-particle Woods-Saxon assumption as the weakest point. The central claim is a specific prediction about which nucleus will show a narrow 2s1/2 momentum component and in what order of strength. That prediction is computed with a fixed geometry and no propagated uncertainties. The paper is honest to qualify conclusions with 'within the present model,' but the abstract's more general statements about multi-observable halo identification imply robustness. My proposed test directly checks whether the ranking and visibility survive reasonable variations of the potential parameters. If the test passes, the central claim is solid; if it fails, the paper's conditional status should be strengthened, e.g., by requiring the robustness study before acceptance. Since the reader already assigned CONDITIONAL, I recommend no change in verdict; the test is the natural condition to impose. The lack of code/data is a separate reproducibility concern, but the physics robustness of the wave-function assumption is the load-bearing issue.","tokens_in":19452,"tokens_out":11237,"duration_ms":104491,"concrete_test":"Recompute the pure 2s1/2 longitudinal FWHM for 27S and 31Ar at 450 MeV/u with the central Woods-Saxon depth readjusted to the adopted S_p for each of r0 = 1.15, 1.20, 1.25, 1.30 A^{1/3} fm and a = 0.55, 0.60, 0.65 fm, and with the Coulomb field generated by a uniformly charged sphere of radius R_C = 1.1–1.3 A^{1/3} fm. If FWHM(31Ar) is not greater than FWHM(27S) over the entire grid, the paper's claim that 27S retains a more pronounced halo than 31Ar is not robust. As a secondary check, convolve the 26P inclusive spectrum with σ_M = 40 MeV/c using C^2S(2s1/2) = 0.36 instead of 0.722; if the narrow component ceases to be a distinct feature, the experimental visibility prediction is fragile.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central predictions—the FWHM values, the 26P > 27S > 31Ar halo ranking, and the claim that a narrow 2s1/2 component survives in the inclusive spectrum—all hinge on the single-particle potential adopted in Sec. II B. The paper fixes r0 = 1.2 A^{1/3} fm, a = 0.6 fm, and V_so = −20 MeV for every nucleus, adjusting only the central depth to reproduce the experimental S_p. This choice fixes the asymptotic normalization of the valence wave function, which directly determines the low-momentum part of the (p,2p) distribution. The paper provides no uncertainty on the resulting FWHM values, and its own Fig. 11 tests sensitivity to S_p but not to the potential geometry. The ordering of 27S (S_p = 0.87 MeV) and 31Ar (S_p = 0.67 MeV) is a delicate cancellation between lower S_p and stronger Coulomb confinement; the calculated difference is only several MeV/c, so a 10–20% change in r0 or a, or a different charge radius in the Coulomb potential, could invert that ordering. Additionally, the inclusive narrow-component visibility depends on the Table I spectroscopic strengths, of which the 1d5/2 values are explicitly 'rough estimates'; a smaller 2s1/2 C^2S would make the narrow s-wave peak harder to resolve after the σ_M = 40 MeV/c convolution. These are concrete, testable model dependencies that the paper does not address.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes longitudinal momentum distributions, one-proton knockout cross sections, FWHM values, rms radii, and exterior probabilities for proton removal from 26P, 27S, and 31Ar in the Glauber-eikonal (p,2p) model of Ref. [45], using Woods-Saxon single-particle wave functions adjusted to AME2020 separation energies. It also studies Coulomb-barrier systematics, mirror pairs, spectroscopic mixtures from shell-model/VS-IMSRG inputs, detector-resolution convolution, and separation-energy sensitivity. The central claim is that proton-halo identification requires combining momentum-space and coordinate-space observables, and that within this model 26P has the strongest halo signatures, 27S retains pronounced halo features, and 31Ar shows progressive suppression.","tokens_in":19789,"tokens_out":6675,"duration_ms":58853,"significance":"If correct, the paper provides concrete, falsifiable predictions for future R3B (p,2p) measurements: a narrow 2s1/2 component in the longitudinal momentum distribution of 26P (weaker in 27S), with the FWHM ranking driven by separation energy and Coulomb barrier. The calculations are not fitted to the halo conclusion; the ranking follows from external AME2020 separation energies and VS-IMSRG spectroscopic factors plus a standard reaction model. The explicit convolution with experimental resolution and the S_p sensitivity study in Fig. 11 are useful. The main limitation is that the single-particle geometry and the rough 1d5/2 spectroscopic inputs are not varied, which weakens the demonstrated robustness of the ranking and of the inclusive narrow-component visibility.","major_comments":[{"comment":"The central ranking 26P > 27S > 31Ar and the quantitative FWHM values are obtained with a single fixed Woods-Saxon geometry (r0 = 1.2 A^{1/3} fm, a = 0.6 fm, V_so = −20 MeV), with only the central depth adjusted to the separation energy. Because the asymptotic normalization of the valence wave function is set by this geometry, the predicted widths and the ordering are not demonstrated to be robust to the choice of single-particle potential. The 27S (S_p = 0.87 MeV) versus 31Ar (S_p = 0.67 MeV) ordering involves a cancellation between weaker binding and stronger Coulomb confinement; Fig. 11 varies S_p only and does not test r0, a, V_so, or the charge radius used in the Coulomb potential. I request a sensitivity study (e.g., ±10–20% variations of r0 and a, or a comparison with an alternative geometry) with the resulting FWHM values and halo ranking quoted as uncertainty bands.","section":"§II.B and §V.B"},{"comment":"The inclusive momentum distributions and the conclusion that the narrow 2s1/2 component survives configuration mixing rest on the 1d5/2 spectroscopic strengths of Table I, which the text itself labels as 'rough estimates,' and on the assumed E_x = 2 MeV. No uncertainty or alternative mixture is considered. Since a smaller C^2S(2s1/2) relative to the broad 1d5/2 background would make the narrow peak harder to identify after the σ_M = 40–80 MeV/c convolution, the robustness of the inclusive narrow-component claim requires a sensitivity study varying the 2s1/2 spectroscopic factor and the 1d5/2 admixture; otherwise the prediction is underdetermined by the adopted input.","section":"§II.B, Table I, and §IV.A"},{"comment":"The text at the end of the P(r > R_core) discussion states that the sensitivity of this quantity to reasonable variations of R_core is 'discussed below,' but no such discussion appears in Sections IV or V. Since Eq. (4) defines the exterior probability using an adopted R_core = 1.2 A^{1/3} fm, the paper should either provide the promised sensitivity analysis (e.g., varying R_core by ±0.2 fm or using a channel-radius prescription) or revise the text to remove the unfulfilled promise.","section":"§III.C"}],"minor_comments":[{"comment":"Using the term 'independent observables' for r_rms, P(r > R_core), and FWHM is an overstatement because all three are computed from the same single-particle wave function; agreement among them is a model-consistency check rather than an independent empirical test. Please rephrase.","section":"§III.C"},{"comment":"The title contains 'thesdShell' with a missing space; it should read 'the sd Shell' (the same issue appears in the PDF heading).","section":"Title/Abstract"},{"comment":"The data availability statement says the data are not publicly available because depositing them is 'not technically feasible' and/or 'prohibitive'; for calculations of this scale, providing a small companion file with the tabulated FWHM values, adopted C^2S values, and the plotted distribution curves would improve reproducibility and is recommended.","section":"Data Availability"}],"recommendation":"major_revision","confidential_remarks":"The reaction model of Ref. [45] is co-authored by one of the present authors, but it is an established formalism that has been applied by independent groups, so I do not see a circularity problem. The paper is primarily a predictions paper for R3B rather than a methodological advance, which is within the scope of a nuclear-reactions journal. I would also note that the data availability statement may conflict with common journal expectations; the editor may wish to verify whether public deposition of the small numerical tables is required."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a useful, well-scoped theory paper. It takes the Aumann-Bertulani-Ryckebusch Glauber framework, applies it systematically to three sd-shell proton-halo candidates, and produces concrete predictions for R3B: longitudinal momentum widths, removal cross sections, rms radii, exterior probabilities, and a stated ranking. The qualitative ranking is robust because it follows from external inputs—AME2020 separation energies and VS-IMSRG occupancies—not from fitting. That is worth having.\n\nWhat I like: the authors do not oversell a single observable. They test convolution with Gaussian resolution, compare mirror nuclei to isolate Coulomb effects, and show that the narrow 2s1/2 component survives moderate 1d5/2 admixture. The mirror Delta-FWHM is a clean idea. The paper is also honest that \"within the present model\" qualifies every headline statement.\n\nSoft spots, in order of seriousness:\n\n(1) The single-particle wave functions fix r0 = 1.2 A^{1/3} fm, a = 0.6 fm, and V_so = -20 MeV for all three nuclei, adjusting only the central depth to match S_p. That choice fixes the asymptotic normalization, hence the low-momentum shape and the FWHM values. The paper tests sensitivity to S_p (Fig. 11) but not to the potential geometry. The stress-test is right: 27S and 31Ar are separated by only a few MeV/c in FWHM, because 31Ar's lower S_p competes with its larger Coulomb barrier. A modest change in r0 or diffuseness—or a different charge radius in the Coulomb term—could plausibly invert the middle of the ranking. The authors should scan these parameters or quote an uncertainty that includes them.\n\n(2) The inclusive spectra rest on \"rough estimates\" of 1d5/2 spectroscopic strengths and an ad hoc E_x = 2 MeV. That is acknowledged in Table I, but the claim that the narrow s-wave peak is visible after convolution depends on the 2s1/2 strength, and the value for 27S (1.184) is larger than a physical occupancy for that orbital alone and deserves scrutiny.\n\n(3) The correlation among observables is real but partly circular: all observables derive from the same single-particle wave function. Calling them \"independent observables\" in Sec. III.C is too strong.\n\n(4) No data or code are released, and the data-availability note says hosting is not feasible. For a paper whose main output is a set of quantitative predictions, a table of FWHM values with explicit uncertainties would be a minimal remedy.\n\nFor whom: graduate students and experimentalists planning R3B proton-halo runs. It deserves peer review; a referee should push for a geometry sensitivity scan and a proper uncertainty budget.","headline":"Competent, internally consistent predictions for three proton-halo candidates; the 26P > 27S > 31Ar ranking is plausible, but the quantitative FWHM values and the 27S/31Ar separation inherit a fixed Woods-Saxon geometry that is never tested.","tokens_in":20369,"tokens_out":2614,"would_cite":true,"duration_ms":24040,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["25.40.-h","21.10.Gv","21.60.-n"],"model":"deepseek-v4-flash","headline":"The paper predicts that 26P shows the strongest proton-halo signatures of three sd-shell candidates, and that reliable identification requires combining momentum and spatial observables rather than relying on any single width.","keywords":["proton halo","quasifree knockout","(p,2p) reactions","longitudinal momentum distribution","2s1/2 orbital","Coulomb barrier","sd-shell nuclei","Glauber-eikonal model"],"falsifier":"Measure the longitudinal momentum distribution of the residual nucleus in $^{26}$P($p,2p$) at about 450 MeV/u on a hydrogen target with Gaussian momentum resolution of about 40 MeV/c. If the inclusive spectrum shows no component substantially narrower than the $1d_{5/2}$ line shape, while the neutron-removal mirror $^{26}$Na shows the expected narrow peak, the paper's halo ranking for $^{26}$P is falsified.","tokens_in":19225,"feed_emoji":"⚛️","tokens_out":9218,"duration_ms":80633,"temperature":0.7,"pith_summary":"This paper asks whether the proton-rich nuclei $^{26}$P, $^{27}$S, and $^{31}$Ar are proton halos, meaning their outermost proton spends a significant fraction of its time far outside the nuclear core. It argues that no single observable can settle this: a narrow longitudinal momentum distribution, a large root-mean-square radius, and a high probability of finding the proton outside the core must all point the same way. Using a Glauber-eikonal reaction model for quasifree $(p,2p)$ knockout at 450 MeV per nucleon, with Woods-Saxon wave functions tuned to measured proton separation energies, the paper predicts that $^{26}$P shows the strongest proton-halo signatures, $^{27}$S retains pronounced halo-like features, and $^{31}$Ar is more suppressed by its larger Coulomb barrier. If correct, the paper gives specific, testable predictions for upcoming $(p,2p)$ experiments and shows why proton halos should not be treated as neutron halos with the sign of the charge flipped.","feed_headline":"26P predicted strongest proton-halo signature","feed_subtitle":"Knockout theory says a narrow 2s1/2 momentum peak separates 26P, 27S, 31Ar.","key_machinery":"The machinery is the link between the asymptotic tail of a weakly bound proton wave function and the width of the longitudinal momentum distribution after knockout. The valence proton is placed in a $2s_{1/2}$ Woods-Saxon orbital—an $s$-wave orbital with no centrifugal barrier—whose central depth is adjusted to reproduce the experimental separation energy while the geometry ($r_0 = 1.2 A^{1/3}$ fm, $a = 0.6$ fm, $V_{so} = -20$ MeV) is fixed; the Glauber-eikonal reaction model of Ref. [45] converts that wave function into the residue momentum distribution. The complementary spatial diagnostics are the rms radius $r_{\\mathrm{rms}} = [\\int_0^\\infty r^2 |u(r)|^2 dr]^{1/2}$ and the exterior probability $P(r > R_{\\mathrm{core}}) = \\int_{R_{\\mathrm{core}}}^\\infty |u(r)|^2 dr$, with $R_{\\mathrm{core}} = 1.2 A^{1/3}$ fm, which together with the FWHM form the internally consistent halo signature.","core_discovery":"The central claim is that within the adopted single-particle-plus-reaction model, $^{26}$P exhibits the strongest proton-halo signatures, $^{27}$S retains pronounced halo-like features, and $^{31}$Ar is more confined, and that this ranking cannot be established from any single observable. The narrow longitudinal-momentum component produced by the weakly bound $2s_{1/2}$ orbital is the primary reaction signature, but it becomes interpretable only when combined with the single-particle rms radius and the exterior probability $P(r > R_{\\mathrm{core}})$. The paper further shows that Coulomb confinement systematically broadens proton momentum distributions relative to neutrons with the same separation energy, so weak binding alone is insufficient to characterize a proton halo. The practical conclusion is that future $(p,2p)$ measurements should seek a narrow $2s_{1/2}$ peak in the inclusive momentum distribution and that a consistent set of momentum-space and coordinate-space indicators, not any single width, is the reliable halo criterion.","pith_inferences":["Beyond the paper, the combined criterion suggests a quantitative working definition of a proton halo—for example, a minimum exterior probability or a maximum FWHM for a given separation energy—that could be applied to other proton-rich candidates.","If a high-resolution $(p,2p)$ measurement of $^{26}$P fails to show the predicted narrow peak, the single-particle assumption that the many-body overlap has the same long-distance tail as the Woods-Saxon wave function would be the first element to revisit, rather than the reaction model.","The framework is naturally extendable to heavier proton-rich nuclei, where the Coulomb barrier grows further; the authors mention this direction but do not quantify it.","Exclusive measurements gating on the $1d_{5/2}$ excited-state residue would separate the two components and provide a sharper test of the FWHM and spectroscopic strengths assumed here."],"forward_implications":["A $(p,2p)$ measurement on $^{26}$P at 450 MeV/u with momentum resolution near 40 MeV/c should reveal a narrow $2s_{1/2}$ component in the inclusive longitudinal momentum distribution, with a weaker but visible version for $^{27}$S.","Adding realistic $1d_{5/2}$ spectroscopic strength broadens but does not erase the narrow peak, so configuration mixing does not destroy the halo signature.","For equal separation energies, a larger core charge broadens the momentum distribution and reduces the exterior probability, so the ordering $^{26}$P, $^{27}$S, $^{31}$Ar reflects binding energy and Coulomb barrier jointly.","Mirror-pair calculations predict systematically broader proton-removal than neutron-removal distributions, quantified by a positive $\\Delta\\mathrm{FWHM}_{\\mathrm{mirror}}$, isolating the Coulomb effect.","No single observable—width, radius, or exterior probability—identifies a proton halo reliably; the paper's criterion requires them to agree."],"supporting_citations":[{"why":"Supplies the Glauber-eikonal quasifree (p,2p) reaction model used to compute all momentum distributions and cross sections.","marker":"[45]"},{"why":"Provides the in-medium nucleon-nucleon cross sections and Pauli-blocking corrections used inside the reaction model.","marker":"[46]"},{"why":"Ab initio mirror-energy-difference calculations that supply the 2s1/2 spectroscopic strengths and motivate the halo candidates.","marker":"[28]"},{"why":"Companion ab initio study of isospin-symmetry breaking used for the same spectroscopic input and candidate selection.","marker":"[29]"},{"why":"Precision mass measurements that identified 26P, 27S, and 31Ar as proton-halo candidates through mirror energy differences.","marker":"[27]"},{"why":"AME2020 atomic mass evaluation from which the adopted proton separation energies S_p are taken.","marker":"[67]"},{"why":"The proposed R3B early-science program at FAIR that motivates the 450 MeV/u (p,2p) predictions.","marker":"[30]"}],"fun_headline_variants":["26P leads proton-halo signatures; 27S, 31Ar follow","Proton halo clues: combine momentum, radii, and Coulomb effects","26P strongest proton-halo candidate from knockout theory","Proton halo identification needs more than momentum widths","26P top proton halo, 27S pronounced, 31Ar confined"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the true many-body wave function of the removed proton has the same long-distance tail as the single-particle Woods-Saxon wave function, whose geometry is fixed and whose depth is adjusted only to match the measured separation energy; if that tail is different, the predicted momentum widths and the halo ranking shift.","fun_headline_variants_meta":{"raw":{"variants":["26P leads proton-halo signatures; 27S, 31Ar follow","Proton halo clues: combine momentum, radii, and Coulomb effects","26P strongest proton-halo candidate from knockout theory","Proton halo identification needs more than momentum widths","26P top proton halo, 27S pronounced, 31Ar confined"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000297,"raw_usage":{"total_tokens":1743,"prompt_tokens":990,"completion_tokens":753,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":606,"completion_tokens_details":{"reasoning_tokens":664}},"tokens_in":606,"tokens_out":753,"duration_ms":6357,"temperature":1.0,"reasoning_tokens":664,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T04:17:01.633529+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the longitudinal momentum distribution of the residual nucleus in $^{26}$P($p,2p$) at about 450 MeV/u on a hydrogen target with Gaussian momentum resolution of about 40 MeV/c. If the inclusive spectrum shows no component substantially narrower than the $1d_{5/2}$ line shape, while the neutron-removal mirror $^{26}$Na shows the expected narrow peak, the paper's halo ranking for $^{26}$P is falsified.","supporting_citations":[{"cited_title":"Direct Reactions and Spectroscopy with Hydro- gen Targets at the Radioactive Isotope Beam Factory (RIBF),","cited_arxiv_id":null,"evidence_quote":"Supplies the Glauber-eikonal quasifree (p,2p) reaction model used to compute all momentum distributions and cross sections."},{"cited_title":"Nuclear structure of drip-line nuclei eluci- dated through precision mass measurements of 23Si, 26P, 27,28S, and 31Ar,","cited_arxiv_id":null,"evidence_quote":"Ab initio mirror-energy-difference calculations that supply the 2s1/2 spectroscopic strengths and motivate the halo candidates."},{"cited_title":"Ab initio calculations of mirror energy differences insd-shell nu- clei,","cited_arxiv_id":null,"evidence_quote":"Companion ab initio study of isospin-symmetry breaking used for the same spectroscopic input and candidate selection."},{"cited_title":"Nonperturbative shell-model in- teractions from the in-medium similarity renormaliza- tion group,","cited_arxiv_id":null,"evidence_quote":"AME2020 atomic mass evaluation from which the adopted proton separation energies S_p are taken."},{"cited_title":"Investigation of isospin-symmetry break- ing in mirror energy differences and nuclear masses with ab initiocalculations,","cited_arxiv_id":null,"evidence_quote":"The proposed R3B early-science program at FAIR that motivates the 450 MeV/u (p,2p) predictions."}],"review_version":1}