{"id":"90222fd9-b4fc-4020-818a-88c34ded794f","arxiv_id":"2607.05647","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"Proton (sub)shell closures enhance neutron odd-even staggering asymmetry across N=82; new 138Sb mass and HFB calculations support this for even-Z but leave odd-Z harder to explain.","lead":"New mass measurements of 137,138Sb and HFB calculations show that proton shell closures at Z=50 and Z=64 strengthen the asymmetry of neutron odd-even staggering across N=82. The work maps how shell structure and pairing compete in neutron-rich nuclei near 132Sn, with odd-Z systems remaining harder to model.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the reader's already-flagged non-self-consistent deformation.","rationale":"The strongest claim is supported by (i) the extended experimental systematics of Δ^(3)(N=81) vs Δ^(3)(N=83) that peak at Z=50 and Z=64, (ii) parameter-free spherical HFB that already reproduces the qualitative pattern, and (iii) deformed HFB that improves the absolute scale of Δ^(3)(N=83) through mid-shell. The new 137,138Sb masses cleanly extend the odd-Z data and are not over-claimed. The non-self-consistent deformation is the genuine soft spot, but it is already identified by the reader and does not reverse the even-Z conclusion. No further internal inconsistency or hidden assumption rises to load-bearing status; the CONDITIONAL verdict with high confidence is therefore left unchanged.","tokens_in":17261,"tokens_out":504,"duration_ms":4538,"concrete_test":"Re-run the deformed HFB of Fig. 1(e) with self-consistent β2 minimization (or at least Z-dependent FRDM values) for the N=81 and N=83 isotones up to Z=60; if the curvature and absolute scale of Δ^(3)(N=83) remain within ~0.1 MeV of the present curves, the even-Z claim is robust to the deformation prescription.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest_assumption correctly isolates the softest point in the even-Z argument: deformed HFB uses prescribed, Z-independent FRDM averages for β2 rather than a variational minimum, and the paper itself states that this makes Δ^(3) from E_corr unreliable for Z>60. That limitation is already explicit in the supplemental material and does not undermine the qualitative success through mid-shell (Z≲60) or the spherical-HFB trends that already capture the Z=50 maximum. The odd-Z half of the story is acknowledged as phenomenological only. No additional load-bearing inconsistency appears in the central claim that proton (sub)shell structure enhances the neutron OES asymmetry across N=82.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper interprets existing mass data near 132Sn to show that proton (sub)shell structure at Z=50 and Z=64 enhances the asymmetry between neutron odd-even staggering Δ^(3)(N=81) and Δ^(3)(N=83). Original spherical and deformed HFB calculations for even-Z nuclei attribute this to neutron pairing correlations that grow with Z and smear the N=82 closure away from proton shell closures. New TITAN MR-TOF mass measurements of 137Sb (improved precision) and 138Sb (first determination) extend the analysis to odd-Z nuclei, where the shell-pairing interplay is harder to capture phenomenologically or with HFB, motivating further work.","tokens_in":17451,"tokens_out":978,"duration_ms":13931,"significance":"The result, if robust, clarifies how proton shell structure modulates neutron pairing far from stability, a competition of direct relevance to nuclear structure and r-process modeling. Strengths include independent experimental masses (with calibrant checks and AME consistency for 137Sb), HFB that reproduces Sn OES and even-Z isotonic trends through Z≈60 without ad-hoc fitting to the asymmetry itself, and an explicit link between single-particle gaps (including the Z=64 subshell) and the observed OES pattern. The new 138Sb mass and the even-Z HFB success constitute concrete, falsifiable advances.","major_comments":[{"comment":"Supplemental Material (deformed HFB paragraph and Fig. 1(e) discussion): The quantitative agreement for Δ^(3)(N=83) up to Z≈60 relies on prescribed, Z-independent quadrupole deformations β2 taken as FRDM averages rather than variational minima. While the paper notes that this treatment renders E_corr-based Δ^(3) unreliable for Z>60, the main-text claim of successful deformed-HFB description should more explicitly flag this external input as a caveat, because the mid-shell success is not fully self-contained.","section":"Supplemental Material, deformed HFB; main text Fig. 1(e)"},{"comment":"OES including odd-Z nuclei section and Summary: The statement that both spherical and deformed HFB are inconsistent with experimental odd-Z Δ^(3)(N) is central to the motivation for future work, yet no quantitative comparison (curves, residuals, or table) is provided. Adding the corresponding HFB results (even if only in the Supplemental Material) would make the acknowledged limitation concrete and allow readers to judge its severity.","section":"OES including odd-Z nuclei; Summary"}],"minor_comments":[{"comment":"Fig. 1(c)–(e) and related text: The vertical dashed lines marking Z=50 and Z=64 are helpful, but the near-degeneracy argument for the absence of a Z=58 subshell (≲0.7 MeV) would be clearer if the single-particle spectrum of Supplemental Fig. 2 were referenced more explicitly in the main text.","section":"Fig. 1 and Phenomenological interpretation"},{"comment":"Table I and Experiment section: The mass-resolving power R≈390 000 and the hyper-EMG fitting procedure are stated, but a brief note on how the 14 counts for 138Sb still yield a reliable centroid (and the assigned 68 keV uncertainty) would aid non-specialist readers.","section":"Experiment; Table I"},{"comment":"Eq. (1) and surrounding text: The three-point formula is standard, yet a short remark that higher-order formulas were checked and give consistent trends would preempt questions about finite-difference artifacts near shell closures.","section":"Phenomenological interpretation"},{"comment":"References: Recent mass work on nearby chains (e.g., the 2025 Sn and Ce results already cited) is well covered; adding a pointer to the latest AME updates or FRDM deformation tables used for β2 would improve reproducibility.","section":"References / Supplemental Material"}],"recommendation":"minor_revision","confidential_remarks":"The even-Z HFB success and the new Sb masses are solid and suitable for a high-impact Letter. The non-self-consistent deformation is already flagged by the authors and does not invalidate the qualitative picture; the odd-Z shortfall is likewise acknowledged. Minor revisions addressing the two major points above should suffice. Scope and novelty fit the journal well."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The paper’s real additions are the first mass of 138Sb, a 2.5\times tighter 137Sb, and a clear phenomenological extension of the Hakala OES asymmetry out to Z=68 that flags dual maxima at the Z=50 and Z=64 proton (sub)shells. That pattern was not in the earlier shell-model or DFT papers that stopped near Te/Xe. Their original HFB (spherical then deformed, with optional pn pairing) tracks the even-Z Δ^(3)(N=81,83) data through Z≈60 without fitting the asymmetry itself; Sn OES is only a validation check. That is honest work.\n\nThe soft spot is exactly the one already flagged: deformed HFB uses Z-independent FRDM averages for β2 rather than a variational minimum, and the authors themselves say the E_corr-derived Δ^(3) becomes unreliable above Z≈60. Spherical HFB already captures the Z=50 maximum and the overall rise, so the central even-Z claim still stands, but the quantitative success near mid-shell rests on that external choice. Odd-Z is weaker: both spherical and deformed HFB fail, so the Sb/I recovery with added neutrons is left as phenomenology. They state the limitation and call for better odd-system theory; that is fair.\n\nMasses look solid (MR-TOF, calibrant checks, AME agreement). Citations are appropriate. Free parameters (Woods-Saxon, pairing strength, prescribed β2) are standard for this class of calculation and not tuned to the asymmetry being explained. No circularity.\n\nThis is for people who work on mass systematics, pairing functionals, or r-process inputs near 132Sn. It deserves a serious referee. I would engage with the even-Z systematics and the new Sb points; the odd-Z half is a useful flag rather than a finished story.","headline":"Solid new Sb masses plus a clean even-Z reading of OES asymmetry at Z=50 and Z=64; HFB works through mid-shell but deformation is prescribed and odd-Z remains open.","tokens_in":18215,"tokens_out":481,"would_cite":true,"duration_ms":4627,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Proton shell closures make neutron pairing gaps asymmetric across N=82.","keywords":["nuclear shell structure","pairing correlations","odd-even staggering","132Sn","Hartree-Fock-Bogolyubov","mass measurements","neutron-rich nuclei"],"falsifier":"A self-consistent deformed HFB calculation (or an independent shell-model calculation with the same single-particle spectrum) that fails to recover the experimental rise of Δ(3)(N=83) from Z=50 to the mid-shell, or new mass measurements of more neutron-rich Sn, Sb or I isotopes that erase the reported recovery of staggering for odd-Z nuclei at N=85,86.","tokens_in":18164,"feed_emoji":"⚛️","tokens_out":645,"duration_ms":5699,"temperature":0.7,"pith_summary":"Near the doubly magic nucleus 132Sn, the energy cost of adding or removing an unpaired neutron does not change smoothly across the N=82 shell. Existing mass data show that this odd-even staggering is strongly asymmetric at Z=50 and again at the Z=64 proton subshell, and nearly symmetric in proton mid-shell nuclei. Original Hartree-Fock-Bogolyubov calculations reproduce the even-Z pattern by letting neutron pairing grow with proton number; the stronger pairing washes out the N=82 discontinuity away from proton shell closures. New TITAN mass measurements of 137,138Sb extend the map into odd-Z nuclei, where the same competition appears but is harder to capture with the same mean-field tools. The work therefore isolates a concrete, measurable signature of how proton shell structure modulates neutron pairing far from stability.","feed_headline":"Proton shells make neutron pairing gaps asymmetric","feed_subtitle":"Mass data and HFB show the N=82 staggering is largest at Z=50 and Z=64.","key_machinery":"The three-point odd-even staggering indicator Δ(3)(N) extracted from binding energies (or from the HFB pairing correlation energy Ecorr), which isolates the pairing contribution to the gap across the N=82 shell and thereby maps how proton shell structure modulates neutron pairing.","core_discovery":"Proton shell structure enhances the asymmetry of neutron odd-even staggering across N=82: the difference between the three-point indicators Δ(3)(N=81) and Δ(3)(N=83) is largest at the proton (sub)shell closures Z=50 and Z=64, and HFB calculations attribute this to neutron pairing correlations that grow with Z and smear the N=82 closure away from those closures.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Proton shells drive asymmetric neutron pairing near 132Sn","Neutron odd-even gaps peak in asymmetry at Z=50 and 64","Proton structure enhances N=82 neutron pairing unevenness","Mass data and HFB show proton shells skew neutron staggering","Shell closures make neutron pairing gaps asymmetric around Sn"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The deformed HFB calculations rely on fixed, Z-independent quadrupole deformations taken from an external mass model rather than being determined self-consistently for each nucleus.","fun_headline_variants_meta":{"raw":{"variants":["Proton shells drive asymmetric neutron pairing near 132Sn","Neutron odd-even gaps peak in asymmetry at Z=50 and 64","Proton structure enhances N=82 neutron pairing unevenness","Mass data and HFB show proton shells skew neutron staggering","Shell closures make neutron pairing gaps asymmetric around Sn"]},"model":"grok-4.5","effort":"low","cost_usd":0.003894,"raw_usage":{"total_tokens":1191,"prompt_tokens":765,"num_sources_used":0,"completion_tokens":65,"cost_in_usd_ticks":38940000,"prompt_tokens_details":{"text_tokens":765,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":361,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":765,"tokens_out":65,"duration_ms":3591,"temperature":1.0,"reasoning_tokens":361,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-11T04:22:57.386083+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A self-consistent deformed HFB calculation (or an independent shell-model calculation with the same single-particle spectrum) that fails to recover the experimental rise of Δ(3)(N=83) from Z=50 to the mid-shell, or new mass measurements of more neutron-rich Sn, Sb or I isotopes that erase the reported recovery of staggering for odd-Z nuclei at N=85,86.","supporting_citations":[],"review_version":1}