{"id":"52ad567b-5f9b-48e6-939e-e63ee2edb273","arxiv_id":"2505.10247","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A survey of 42 Skyrme functionals finds that beta-decay Q-values are reproduced best for symmetry energy 32.8 +/- 0.7 MeV and effective mass above 0.75 at saturation density.","lead":"This paper checks 42 Skyrme energy density functionals against measured beta-decay Q-values for even-even nuclei. It concludes that functionals with a symmetry energy near 32.8 MeV and effective mass above 0.75 at saturation density reproduce the data best.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The optimal J and m* window may be an artifact of the non-interacting quasiparticle approximation for Qβ (Eq. 4), whose error likely depends on effective mass; blocked HFB checks are needed before adopting the claim.","rationale":"The reader's strongest claim is the J and m* selection rule. Its weakest point is indeed the approximate Qβ formula (Eq. 4), because every correlation and fit in Section III inherits any systematic error in those Qβ values. The paper's own text notes the approximation is used 'to avoid' the blocking/time-odd cost, but it does not quantify the accuracy. The concern is not that Eq. (4) is wrong in general; it is that its error may be correlated with effective mass and symmetry energy, the exact parameters the paper claims to constrain. The pairing rescaling of Eq. (8), which is linear in m*/m, is a partial mitigation but is fitted to empirical gaps for only 28 nuclei and does not address mean-field rearrangement. A fully blocked HFB comparison is expensive but feasible for a subset, and it would settle whether the optimal region shifts. Consequently the paper is a valuable correlation study whose conclusion should remain conditional pending that sensitivity check; the verdict is unchanged from the reader's CONDITIONAL.","tokens_in":17760,"tokens_out":6896,"duration_ms":72498,"concrete_test":"Compute Qβ for a representative subset of the 215 nuclei using Eq. (1) with fully blocked HFB (including time-odd fields), for functionals spanning the (J,m*/m) plane: SkT1*, LNS, KIDS0, SQMC650, SLy5, NRAPR, Zσ, and SK255. Compare Eq. (4) with the blocked result and refit the quadratic minimum of γ(Esym) and the m*/m≥0.75 split using the corrected Qβ values. If the optimal J moves outside 32.8±0.7 MeV, or if the small/large-m* ordering of γ changes, the central claim is an artifact of the quasiparticle approximation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that J=32.8±0.7 MeV and m*/m≥0.75 is the most likely parameter region for reproducing Qβ rests entirely on Qβ values from Eq. (4), Qβ≈ΔM_nH−λ_p+λ_n−E_{2qp,lowest}, not on the actual mass difference in Eq. (1). This non-interacting quasiparticle approximation replaces B(N,Z)−B(N−1,Z+1) with parent chemical potentials plus two-quasiparticle energies, neglecting mean-field rearrangement, blocking of the odd-odd daughter, and time-odd fields. The error is not expected to be constant across the 42 functionals: for low m*/m the single-particle spectrum near the Fermi energy is sparse, so both λ and E_{2qp} become more sensitive to level positions, and the pairing rescaling f(x) (Eq. 8), calibrated on only 28 nuclei, may not remove this bias. Since such an m*-dependent error feeds directly into γ, the apparent threshold at m*/m=0.75 and the quadratic minimum at J=32.8 could be artifacts of the approximation rather than properties of the functionals. The paper acknowledges the approximation but provides no estimate of its error or of its correlation with the two parameters being constrained.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies correlations between ground-state Q_beta values and nuclear bulk properties computed from 42 Skyrme energy-density functionals. The authors perform spherical Skyrme-Hartree-Fock-Bogoliubov calculations for 215 even-even nuclei, compute Q_beta using the non-interacting quasiparticle approximation of Eq. (4), and compare with AME2020 Q_beta values through the mean difference (mu) and RMS deviation (gamma). They report Pearson correlation coefficients among gamma, mu, symmetry energy, effective mass, and other properties, then fit quadratic curves to gamma as a function of Esym for a subsample of functionals with effective mass above 0.75. This fitting yields an optimal symmetry energy at saturation density of J = 32.8 +/- 0.7 MeV, and the paper's central claim is that functionals with m*/m >= 0.75 and J near this value are most likely to systematically reproduce experimental Q_beta values. The abstract and Section IV additionally present the m*/m threshold as a criterion for functional selection.","tokens_in":18099,"tokens_out":8763,"duration_ms":84105,"significance":"If the central claim is correct, the paper offers a practical, easy-to-use criterion for pre-selecting Skyrme functionals for beta-decay calculations, which would be valuable given the proliferation of parametrizations. The manuscript is transparent about its method: it tabulates properties of all 42 functionals, clearly defines the approximate Q_beta expression, and acknowledges the spherical-symmetry limitation. The analysis is reproducible in principle, and the paper contributes a new observational constraint on the symmetry energy at low density, albeit with the important caveats described below. The study is exploratory and does not provide a derivation of the symmetry energy; rather, it identifies a region of parameter space favored by Q_beta data under specific modeling assumptions. Given the strong dependence of the conclusions on the unquantified approximation in Eq. (4) and on the statistical treatment, the paper needs major revision before the claim can be considered robust.","major_comments":[{"comment":"","section":"Section II, Eq. (4)"},{"comment":"","section":"Section III.A and Section III.B"},{"comment":"","section":"Section II (spherical assumption) and Section IV"}],"minor_comments":[{"comment":"","section":"Abstract"},{"comment":"","section":"Fig. 5 caption"},{"comment":"","section":"Table I"},{"comment":"","section":"Section III.C"},{"comment":"","section":"General"},{"comment":"","section":"Section III.A"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and presents a useful exploratory study, but the central claim needs stronger support. The most important issue is the unquantified Q_beta approximation in Eq. (4), which may correlate with effective mass and thereby distort the extracted parameter window. The authors are likely able to address this with a moderate amount of additional computation (blocking or comparison with full binding energies for a subset of nuclei). The statistical weaknesses (no numerical Pearson values, arbitrary threshold, incomplete error budget) are also fixable. I do not see a fundamental flaw that would require rejection, provided the authors can demonstrate the robustness of the conclusion to the approximation and to the statistical choices."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth reading if you work with Skyrme EDFs for beta decay. What is genuinely new: it extends the known symmetry-energy/Q_beta correlation from odd-A nuclei to 215 even-even nuclei across 42 functionals, adds a density-dependent analysis, and shows that functionals with m*/m > 0.75 have systematically lower RMS deviations. The empirical pairing-scaling relation f(x) is also a useful practical result. The Table I compilation of functional properties plus gamma values is a handy reference.\n\nThe soft spots, in proportion. The central claim—that J = 32.8 ± 0.7 MeV and m*/m ≥ 0.75 is the most likely parameter window—is not as solid as the abstract implies. The optimal J comes from fitting a quadratic to gamma versus Esym using the same experimental Q_beta data the paper claims to describe. That is a fitted minimum, not an independent validation. The quoted uncertainty covers only the least-squares fit, not systematic errors from the model or the data selection. The m*/m ≥ 0.75 split is a hand-chosen grouping, and no significance tests are given for the Pearson coefficients. None of this kills the paper, but it means the conclusion is a heuristic, not a constraint.\n\nThe stress-test concern about Eq. (4) has real teeth. Replacing the actual mass difference with chemical potentials plus the lowest two-quasiparticle energy ignores blocking and time-odd fields, and the error is likely not constant across the functional set. For low-m* functionals the single-particle spectrum near the Fermi energy is sparse, so both lambda and E_2qp become more sensitive to level positions; the pairing rescaling f(x), calibrated on only 28 nuclei, may well leave a residual bias that tracks m*. If that is the case, the apparent threshold at 0.75 could be an artifact of the approximation rather than a real property of the functionals. The paper acknowledges the approximation but gives no estimate of its error or its correlation with the constrained parameters. A blocked HFB calculation for even-even parents, or at least a subset of nuclei, would be the natural check; without it, the central parameter window should be treated as a working hypothesis.\n\nWho gets value: practitioners who need to pick a Skyrme functional for r-process or beta-decay simulations. They should read this as a map of which functionals tend to do well, not as a rigorous determination of nuclear matter properties. The paper is honest about its spherical-shape limitation and cites prior work fairly. I would send it to peer review because the question matters and the study is transparent, but I would ask for sensitivity analyses and an out-of-sample functional test before endorsing the conclusion.","headline":"A transparent Skyrme-EDF correlation study with a plausible but under-supported central parameter window; the quasiparticle approximation may be shaping the result.","tokens_in":18594,"tokens_out":1864,"would_cite":false,"duration_ms":21674,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["21.60.Jz","21.65.Ef","23.40.-s"],"model":"deepseek-v4-flash","headline":"Beta-decay Q-values favor Skyrme functionals with symmetry energy 32.8 ± 0.7 MeV and effective mass at least 0.75.","keywords":["Q_beta values","Skyrme energy-density functionals","symmetry energy","effective mass","beta decay","Hartree-Fock-Bogoliubov","r-process nucleosynthesis","Pearson correlation"],"falsifier":"Redo the analysis on a subset of the 215 nuclei using HFB calculations with explicit blocking and deformation, for example in the A ≈ 100–150 region: if the RMS minimum moves away from J = 32.8 ± 0.7 MeV or the m*/m ≥ 0.75 advantage disappears, the claimed window is an artifact of Eq. (4) and the spherical assumption. A cheaper check is to compute Q_beta for the same nuclei with two functionals that share J ≈ 32.8 MeV but have m*/m below 0.75, using full blocking, and see whether their gamma drops to the level of SkT1*.","tokens_in":17581,"feed_emoji":"⚛️","tokens_out":7110,"duration_ms":60501,"temperature":0.7,"pith_summary":"This paper tries to identify which nuclear bulk properties control how well a Skyrme energy-density functional reproduces measured beta-decay Q-values, and to turn that into a practical selection criterion. By computing Q_beta for 215 even-even nuclei with 42 Skyrme functionals under spherical symmetry, it finds that the average error correlates with the symmetry energy at low densities, while the scatter of errors is smaller for functionals with effective mass m*/m at or above 0.75. The paper concludes that a saturation symmetry energy of 32.8 ± 0.7 MeV together with m*/m ≥ 0.75 is the window most likely to reproduce experimental Q_beta systematically. If true, this gives a cheap, physics-based filter for choosing functionals before expensive beta-decay or r-process calculations.","feed_headline":"Beta-decay Q-values favor a 32.8 MeV symmetry energy","feed_subtitle":"Across 42 functionals and 215 nuclei, the data pick out a narrow symmetry-energy and effective-mass window.","key_machinery":"The engine of the analysis is the non-interacting quasiparticle approximation for Q_beta, Q_beta ≈ ΔM_nH − λ_p + λ_n − E_{2qp,lowest}, which replaces the odd-daughter binding-energy difference with Fermi energies and the lowest two-quasiparticle energy, so that only even-even spherical Skyrme-HFB calculations are needed. A pairing scaling factor f(x), fit linearly to the effective mass x = m*/m, is tuned to reproduce empirical pairing gaps from the three-point mass difference, removing pairing as a source of variation across functionals. The argument then runs on Pearson correlation coefficients between Q_beta errors and bulk parameters — symmetry energy Esym(rho) at 0.34, 0.76, 1.00, and 1.50 rho0, effective mass, saturation density, and incompressibility — followed by a quadratic fit of the RMS deviation gamma versus Esym(rho) that yields the optimal symmetry-energy value at each density. This machinery isolates the symmetry-energy and effective-mass dependence that otherwise would be entangled with pairing strengths and single-particle level densities.","core_discovery":"The central claim is that experimental Q_beta values themselves select a narrow range of Skyrme functional parameters: a symmetry energy J = 32.8 ± 0.7 MeV at saturation density and an effective mass m*/m ≥ 0.75. This emerges from a Pearson-correlation analysis and a quadratic least-squares fit of the RMS deviation gamma against the symmetry energy at several densities; the minimum of gamma sits at 16.9 ± 0.4 MeV at 0.34 rho0, 27.2 ± 0.3 MeV at 0.76 rho0, 32.8 ± 0.7 MeV at rho0, and 40.4 ± 6.5 MeV at 1.50 rho0, with the low-density constraints much sharper. The paper also establishes that the mean deviation mu is positively correlated with low-density symmetry energy and essentially uncorrelated with effective mass, whereas gamma is negatively correlated with effective mass. Functionals such as LNS, the SkT family, KIDS0, KIDSA, SQMC650, and SQMC700 fall in the preferred window and give the smallest deviations; SkT1* has the lowest gamma among all 42. The message is that Q_beta data can constrain the symmetry energy below saturation, provided the effective mass is kept above 0.75.","pith_inferences":["A practical workflow suggested but not stated by the paper: screen any candidate Skyrme functional by its saturation J and m*/m before committing to QRPA beta-decay calculations; this could save the cost of full strength-function calculations for functionals that fail the Q_beta window.","The apparent effectiveness of the m*/m ≥ 0.75 cut may be partly an artifact of Eq. (4): low effective mass gives sparse single-particle spectra, and the non-interacting quasiparticle approximation may mishandle blocking in exactly those cases; testing a few m*/m ≤ 0.75 functionals with explicit blocking would show whether the cut persists.","Because beta-decay half-lives scale steeply with Q_beta, the 0.7 MeV uncertainty in the preferred symmetry energy translates into substantially larger uncertainties in half-lives; the correlation found here could be recast as a direct constraint on half-life predictions for r-process waiting-point nuclei."],"forward_implications":["A functional with J near 32.8 ± 0.7 MeV and m*/m > 0.75 is expected to reproduce measured Q_beta for even-even nuclei with RMS deviation around or below 1.3 MeV; SkT1* is the best single case.","Experimental Q_beta values constitute a new low-density constraint on the symmetry energy: the analysis pins Esym(0.34 rho0) ≈ 16.9 ± 0.4 MeV and Esym(0.76 rho0) ≈ 27.2 ± 0.3 MeV, tighter than at saturation density.","Functionals with m*/m ≤ 0.75 systematically give larger Q_beta errors, with deviations concentrated near magic and semi-magic nuclei such as 22O, 30,32Ne, 56Ca, 132,134,136Sn, and 208,210,216,218Pb.","For full beta-decay half-life predictions, the Q_beta window must be combined with a separate criterion for the Gamow-Teller strength function: the paper notes that among the preferred functionals, LNS, SQMC650, and SQMC700 also have large Landau parameter G'_0, whereas the SkT family does not.","The optimal symmetry energy is sharply determined only below saturation; above rho0 the quadratic curves flatten, so Q_beta alone cannot constrain high-density symmetry energy."],"supporting_citations":[{"why":"Supplies the AME2020 evaluated Q_beta values for the 215 even-even nuclei used as the reference data set.","marker":"[40]"},{"why":"Introduces the non-interacting quasiparticle approximation, Eq. (4), that the paper uses to compute Q_beta from Skyrme-HFB Fermi energies and two-quasiparticle energies.","marker":"[42]"},{"why":"Establishes the earlier correlation between proton-neutron Fermi-energy difference, separation-energy difference, and symmetry energy that motivates looking for a Q_beta-symmetry energy link.","marker":"[38]"},{"why":"Shows a dependence of Q_beta on symmetry energy for odd-A nuclei, which the paper extends to even-even nuclei.","marker":"[39]"},{"why":"Provides the recommended set of Skyrme functionals from which most of the 42 parameter sets are taken.","marker":"[43]"},{"why":"Defines the empirical pairing gaps from the three-point mass difference used to calibrate the pairing scaling factor.","marker":"[52]"},{"why":"Supports the linear dependence of the pairing scaling factor on effective mass used in Eq. (8).","marker":"[53]"}],"fun_headline_variants":["Beta decay pins symmetry energy to 32.8 MeV","Q_beta data pin down J=32.8 MeV, m*/m≥0.75","Beta-decay values select a narrow Skyrme window","32.8 MeV symmetry energy emerges from beta-decay fit","Effective mass and symmetry energy fixed by Q_beta"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result rests on the non-interacting quasiparticle approximation for Q_beta (Eq. 4) together with the assumption that all 215 nuclei are spherical; if that approximation distorts Q_beta in a way that depends on symmetry energy or effective mass, the preferred window J = 32.8 ± 0.7 MeV and m*/m ≥ 0.75 could be shifted or spurious.","fun_headline_variants_meta":{"raw":{"variants":["Beta decay pins symmetry energy to 32.8 MeV","Q_beta data pin down J=32.8 MeV, m*/m≥0.75","Beta-decay values select a narrow Skyrme window","32.8 MeV symmetry energy emerges from beta-decay fit","Effective mass and symmetry energy fixed by Q_beta"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001327,"raw_usage":{"total_tokens":5491,"prompt_tokens":1124,"completion_tokens":4367,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":740,"completion_tokens_details":{"reasoning_tokens":4277}},"tokens_in":740,"tokens_out":4367,"duration_ms":29551,"temperature":1.0,"reasoning_tokens":4277,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:13:59.149551+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Redo the analysis on a subset of the 215 nuclei using HFB calculations with explicit blocking and deformation, for example in the A ≈ 100–150 region: if the RMS minimum moves away from J = 32.8 ± 0.7 MeV or the m*/m ≥ 0.75 advantage disappears, the claimed window is an artifact of Eq. (4) and the spherical assumption. A cheaper check is to compute Q_beta for the same nuclei with two functionals that share J ≈ 32.8 MeV but have m*/m below 0.75, using full blocking, and see whether their gamma drops to the level of SkT1*.","supporting_citations":[{"cited_title":"Huang, M","cited_arxiv_id":null,"evidence_quote":"Supplies the AME2020 evaluated Q_beta values for the 215 even-even nuclei used as the reference data set."},{"cited_title":"PearsonAll.out","cited_arxiv_id":null,"evidence_quote":"Introduces the non-interacting quasiparticle approximation, Eq. (4), that the paper uses to compute Q_beta from Skyrme-HFB Fermi energies and two-quasiparticle energies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the earlier correlation between proton-neutron Fermi-energy difference, separation-energy difference, and symmetry energy that motivates looking for a Q_beta-symmetry energy link."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows a dependence of Q_beta on symmetry energy for odd-A nuclei, which the paper extends to even-even nuclei."},{"cited_title":"Satu la, J","cited_arxiv_id":null,"evidence_quote":"Supports the linear dependence of the pairing scaling factor on effective mass used in Eq. (8)."}],"review_version":1}