{"id":"0e28aa30-d9e3-4c99-bd13-010e1d8a1c00","arxiv_id":"2501.19185","paper_version":3,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In 150Nd, gamma-decay branching ratios imply a chi-squared width distribution with 1.93(12) degrees of freedom, rejecting the Porter-Thomas value of 1.","lead":"New photon-scattering measurements in the isotope 150Nd find that the spread of gamma-decay strengths between 5 and 7 MeV is 7 standard deviations away from the standard Porter-Thomas statistical prediction. The result points to a share of ordered, structure-driven decays in a region believed to be chaotic, with consequences for nuclear reaction calculations in astrophysics and nuclear technology.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Finite-number bias in the ratio of sums may inflate the inferred ν; the paper does not demonstrate that the effective number of excited states is large enough for the asymptotic mapping R_exp ≈ s.","rationale":"The reader identified the high-NLD/uniform-strength assumption as the weakest point. My concern is a more specific consequence of that assumption: the finite-number bias in the ratio of sums that defines the internal fluctuation ratio s. The paper's central quantitative claim—ν = 1.93(12) and a 7σ rejection of Porter-Thomas—depends on the equality R_exp ≈ s, which holds only in the limit of many excited states. The paper asserts a level density of ~10^3 levels/MeV for 1− states, but it does not provide an experimental determination or a sensitivity analysis. The Dicebox simulation validates the analysis chain under that assumed NLD, but cannot validate the NLD itself. If the true NLD is a factor of 2–3 lower, the finite-N bias would bring the Porter-Thomas prediction closer to the data, reducing the significance, though likely not erasing the deviation entirely. Because the quantitative significance and the extracted nonstatistical fractions depend on this unquantified systematic, acceptance should be conditional on the authors either demonstrating that N_eff is sufficiently large or providing a corrected analysis that includes the finite-N bias and its uncertainty. The paper is otherwise well-argued and transparent, with open data and a Monte Carlo validation of the formalism, so I do not see a reason for rejection, but the 7σ claim is not yet robust against this finite-N effect.","tokens_in":13641,"tokens_out":16258,"duration_ms":160474,"concrete_test":"Use the open TUdatalib dataset to determine the effective number of excited 1− states N_eff in each beam-energy setting above 5 MeV, e.g., from the ratio of the integrated ground-state yield to a typical ground-state width or from an independent resonance-spacing measurement. Then run a Monte Carlo of Eq. (4) with N_eff states, sampling partial widths from χ² distributions with ν=1, and compute the distribution of R_exp. If the observed 0.490 lies beyond the 95% quantile of this finite-N Porter-Thomas distribution, the rejection stands; otherwise its significance is reduced. Alternatively, re-run the Dicebox simulation with NLD lowered by factors of 2 and 3 and check whether the simulated R_exp band shifts toward 0.490.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Equation (5) maps the measured branching ratio to ν via the asymptotic relation s = ν/(ν+2). This relation is exact only for the expectation of the ratio of sums in Eq. (4) when the number of excited states N is large enough that the ratio converges to its ensemble mean. For finite N, the ratio R_exp is a biased estimator of s: for Porter-Thomas partial widths (ν=1) and constant total widths, the bias is positive, roughly 2.2/N. The paper quotes a 1− level density of about 10^3 levels/MeV and a beam energy spread near 100 keV, giving N≈100 and a bias of order 0.02, which is comparable to the quoted uncertainty of 0.016. If the actual NLD is a factor of two to three lower (still plausible in the model), the bias rises to 0.04–0.07, a substantial fraction of the observed excess of 0.157 over the Porter-Thomas value 1/3. The Dicebox simulation reproduces R_sim ≈ 0.31, but it uses the same model NLD to generate its level schemes, so it cannot validate the NLD itself. The paper reports no finite-N correction and no systematic uncertainty from this effect, so the quoted ν = 1.93(12) and the 7σ rejection of Porter-Thomas are likely overestimated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a new nuclear resonance fluorescence (NRF) method for probing fluctuations of partial gamma-decay widths below the neutron separation threshold. Using quasimonochromatic, linearly polarized photon beams at HIγS in a high-resolution mode, the authors measure the average branching ratio of 1− states in 150Nd decaying to the 2+1 state versus the 0+1 ground state over the excitation-energy range from 5 to 7 MeV. They observe a constant value R_exp = 0.490(16). Assuming partial widths that are χ2-distributed with ν degrees of freedom, they map this ratio through an internal fluctuation ratio s = ν/(ν+2) to ν = 1.93(12), rejecting the Porter-Thomas distribution (ν = 1) at 7 standard deviations. They validate the mapping with a Dicebox simulation that yields R_sim ≈ 0.31, consistent with s = 1/3 for Porter-Thomas statistics. The deviation is interpreted as evidence for nonstatistical gamma decay, with estimated nonstatistical contributions between 9.4(10)% and 94(10)% depending on the assumed K-quantum number of the decaying states.","tokens_in":13880,"tokens_out":7791,"duration_ms":74578,"significance":"If the result holds, this is the first experimental determination of partial-width fluctuations below the neutron separation threshold in a deformed nucleus, a region previously inaccessible to such studies. The claim is significant for RMT-based statistical nuclear models and for the widespread assumption of Porter-Thomas fluctuations in Hauser-Feshbach calculations. The paper's strengths include a new observable that is robust to photon-strength-function assumptions (a steep PSF would only increase the extracted ν), explicit validation of the formalism with an independent Monte Carlo cascade code, and open data availability. The interpretation in terms of K-quantum-number survival is appropriately framed as one possible explanation, and the paper clearly identifies the assumption of high level fragmentation as a limitation below 5 MeV.","major_comments":[{"comment":"The central mapping ⟨R_exp⟩ ≈ s in Eq. (6) and the resulting ν = 1.93(12) from Eq. (5) assume that the ratio of sums in Eq. (4) has converged to its ensemble mean. The manuscript states that a convergence analysis is in the Supplemental Material but does not report its quantitative outcome in the main text or include a finite-N systematic in the quoted uncertainty of 0.016. With a beam energy spread below 130 keV and a quoted 1− level density of about 10^3/MeV, the effective number of excited states is N ~ 100, for which the finite-N bias of the ratio estimator for Porter-Thomas widths is of order 2/N ~ 0.02, comparable to the quoted total uncertainty. If the true level density is a factor of two to three lower (still plausible for the back-shifted Fermi gas), the bias would rise to 0.04–0.07, a substantial fraction of the observed excess of 0.157 over s = 1/3. The authors should report the convergence curves, state the finite-N bias for the experimental N and beam profile, and include this effect either as a correction or as a systematic uncertainty in the quoted ν and significance.","section":"Discussion"},{"comment":"The statement that the statistical-model simulation results are 'not sensitive to the PSF and NLD model parameters' is stronger than what the visible analysis demonstrates. The Dicebox simulation uses the same back-shifted Fermi gas parameters from Ref. [76] to generate the level scheme, so it cannot by itself validate the NLD; it only shows that for the assumed NLD the extraction yields s ≈ 1/3. Because the finite-N bias depends directly on the actual number of levels excited in the beam window, a sensitivity scan over NLD parameters (for example, varying the level density by a factor of two to three) is needed to support the claim that the mapping is robust. Without such a scan, the quoted ν should carry an additional systematic uncertainty reflecting the NLD uncertainty.","section":"Discussion"}],"minor_comments":[{"comment":"The phrase 'degree of freedom of ν = 1.93(12)' should read 'degrees of freedom' for consistency with standard terminology for χ2 distributions.","section":"Abstract and Summary"},{"comment":"The notation '⟨⟨R_exp⟩⟩' in the paragraph on the K = 0 decomposition is inconsistent with the single-angle-bracket notation used elsewhere; this appears to be a typographical error.","section":"Discussion"},{"comment":"The footnote states that the total uncertainty of 0.016 is the sum of a statistical component of 0.006 and a systematic component of 0.010; linear addition rather than quadrature is unusual and should be justified or clarified.","section":"Footnote 71"},{"comment":"The description of the 1+ data points (open diamonds with 1σ uncertainties versus filled triangles as 2σ upper limits) would benefit from a brief explanation of how the upper limits were derived from the same fit decomposition, to aid reproducibility.","section":"Fig. 2 and accompanying text"}],"recommendation":"major_revision","confidential_remarks":"The paper's main conclusion — that the average branching ratio deviates from the Porter-Thomas expectation — is likely correct and is an important first result in this energy regime. The key risk is the finite-N bias in the ratio-of-sums estimator, which is not explicitly quantified in the main text. If the Supplemental Material already contains a rigorous convergence analysis, the revision should be straightforward: the authors need to summarize the quantitative outcome and fold it into the error budget. The open dataset and the Dicebox validation are notable strengths that support the credibility of the work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the punchline. This paper introduces a new observable for partial-width fluctuations below the neutron separation threshold: the average branching ratio of dipole states to the 2+1 ground-band member versus the ground state. The measurement in 150Nd between 5 and 7 MeV gives 0.490(16), which, under the chi-squared model, means ν=1.93(12) and a 7σ rejection of Porter-Thomas. The experimental work is genuinely careful: the new high-resolution HIγS mode, open data, Geant4 response matrices, Thomson subtraction, and a Dicebox simulation that recovers the PT expectation s≈1/3. The robustness to PSF assumptions is good—a steeper PSF would only increase the deviation. The paper is honest about the low-energy region where the method breaks down due to low level density.\n\nWhat is new here is the method itself, not just the result. It gives a handle on width fluctuations in a region where there were no data for deformed nuclei. The logic chain from branching ratio to ν is clean, and the nonstatistical decomposition into K=0/K=1 contributions is a reasonable interpretation, though it is scenario-based and should not be over-read.\n\nThe soft spot is the finite-N bias. The mapping R_exp ≈ s is asymptotic in the number of excited states N. The paper points to a convergence analysis in the Supplemental Material but does not state its conclusion in the main text. With a 1- NLD of ~10^3 levels/MeV and a beam spread near 100 keV, N is about 100; if the NLD is two to three times lower—still plausible—N is 30-50. The ratio-of-sums estimator has a positive bias of order 2.2/N for constant total widths (that's the stress-test estimate), which at N=30 gives ~0.07, nearly half the observed excess over 1/3. The Dicebox simulation uses the same model NLD to generate realizations, so it validates the formalism but not the NLD. The paper should report the actual convergence result and include a systematic uncertainty from NLD uncertainty. Without that, the 7σ is not fully supported.\n\nThis is not a fatal flaw. The method and data deserve serious refereeing. I'd ask the authors to make the finite-N analysis explicit and to add a systematic budget. If the supplement already does this, the paper is close to acceptable; if not, it needs another round. Either way, this is a paper to send out, not desk-reject.","headline":"A genuinely new probe of width fluctuations below the neutron threshold, with solid data and one important statistical assumption left under-verified in the main text.","tokens_in":14498,"tokens_out":5706,"would_cite":true,"duration_ms":55334,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A measurement in 150Nd shows gamma-decay widths below the neutron threshold deviate from the Porter-Thomas distribution by 7 standard deviations.","keywords":["Porter-Thomas distribution","partial transition widths","nuclear resonance fluorescence","150Nd","quasicontinuum","K quantum number","statistical model","gamma-ray branching ratio"],"falsifier":"A decisive check is to measure the same $1^-$ branching ratio in $^{150}\\mathrm{Nd}$ with the photon beam tuned to individual resolved resonances rather than integrated humps, so the contributing level density can be counted directly; if the true number of contributing levels is far below the assumed $10^3$ per MeV, the deduced $\\nu = 1.93$ would collapse toward the Porter-Thomas value. Alternatively, the method applied to a spherical even-even nucleus with a low $2^+_1$ energy should give $R \\approx 1/3$ if the statistical model holds there.","tokens_in":13437,"feed_emoji":"⚛️","tokens_out":6973,"duration_ms":58108,"temperature":0.7,"pith_summary":"The paper introduces a method to test whether the partial gamma-decay widths of excited nuclear states follow the Porter-Thomas distribution, the statistical benchmark of chaotic quantum systems. Applied to $^{150}\\mathrm{Nd}$ between 5 and 7 MeV, it yields an average branching ratio of $0.490(16)$ for decays of $1^-$ states to the $2^+_1$ state versus the ground state. Under the standard assumption of $\\chi^2$-distributed partial widths, this corresponds to a fluctuation parameter $\\nu = 1.93(12)$, which rules out Porter-Thomas ($\\nu = 1$) by 7 standard deviations. The result matters because nuclear reaction codes used for astrophysics and reactor design rely on Porter-Thomas fluctuations when predicting gamma-decay rates.","feed_headline":"Gamma widths of 150Nd defy Porter-Thomas by 7 sigma","feed_subtitle":"A new branching-ratio method finds ν = 1.93, shaking the statistical model of nuclear decays.","key_machinery":"The central object is the average branching ratio $R_{\\rm exp}$, the ratio of energy-integrated nuclear resonance fluorescence cross sections for decays from photoexcited $J=1$ states to the $2^+_1$ state and to the ground state, corrected by the $E^3_\\gamma$ phase-space factor. In integral spectroscopy with a quasimonochromatic photon beam, this ratio is obtained by decomposing the scattered-photon spectrum into two humps without resolving individual transitions. For $\\chi^2$-distributed partial widths the ratio reduces to $s$ times a photon strength function ratio, and under the Brink-Axel hypothesis that ratio is near unity, so $R_{\\rm exp} \\approx s = \\nu/(\\nu+2)$. The derivation of this identity, including the convergence analysis when many states are summed, is what converts a single count-ratio measurement into a constraint on the width distribution.","core_discovery":"The central claim is that, in the energy region 5 to 7 MeV just below the neutron separation threshold of $^{150}\\mathrm{Nd}$, the ensemble of photoexcited $1^-$ states decays to the $2^+_1$ and ground states with an average branching ratio $R_{\\rm exp} = 0.490(16)$, whereas the Porter-Thomas hypothesis predicts about $1/3$. Relating $R_{\\rm exp}$ to the internal fluctuation ratio $s$ of $\\chi^2$-distributed partial widths through $s = \\nu/(\\nu+2)$ gives $\\nu = 1.93(12)$. A Monte-Carlo statistical-model simulation with the Dicebox code, which explicitly implements Porter-Thomas fluctuations, returns $R_{\\rm sim} \\approx 0.31$, confirming the derivation. The authors conclude that the excess branching is caused by nonstatistical gamma decay, with a contribution between $9.4(10)\\%$ and $94(10)\\%$ depending on whether the nonstatistical states carry $K = 0$ or $K = 1$ quantum numbers.","pith_inferences":["If the deviation stems from conserved $K$ quantum numbers, then measurements on spherical nuclei should recover the Porter-Thomas value $s \\approx 1/3$, providing a clean test of the interpretation.","The $9.4(10)\\%$ to $94(10)\\%$ nonstatistical contribution is a model-dependent bracket, not a unique determination; angular distribution data at more detector positions could in principle separate $K=0$ from $K=1$ components.","Extending the measurement toward the neutron separation threshold would map where, if anywhere, the statistical regime begins in this nucleus.","Since $\\nu$ is inferred through the $\\chi^2$ model, an independent determination of the full distribution of resolved partial widths would verify the deviation without that assumption."],"forward_implications":["Statistical-model reaction codes that assume Porter-Thomas widths will misestimate gamma-decay rates in the quasicontinuum of deformed nuclei.","Photon strength function extractions using the ratio or shape method must divide out the internal fluctuation ratio $s$, otherwise the inferred strengths are biased.","The new method works for any stable isotope, offering a systematic probe of width fluctuations and $K$-quantum-number conservation below neutron thresholds.","The constant branching ratio from 5 to 7 MeV gives no evidence for a splitting of the pygmy dipole resonance into $K$ components in $^{150}\\mathrm{Nd}$."],"supporting_citations":[{"why":"Defines the Porter-Thomas distribution, the null hypothesis being tested.","marker":"[17]"},{"why":"The Hauser-Feshbach statistical model whose width fluctuation assumption is checked.","marker":"[23]"},{"why":"Supplemental material containing the derivation of $s = \\nu/(\\nu+2)$ and the convergence analysis.","marker":"[12]"},{"why":"The Dicebox Monte-Carlo code that validates the formalism and reproduces the Porter-Thomas prediction $R_{\\rm sim} \\approx 0.31$.","marker":"[72]"},{"why":"The HI\\gamma S photon source whose high-resolution mode enabled the separation of the two decay branches.","marker":"[50]"},{"why":"Provides the low-lying level scheme used to seed the statistical-model simulations.","marker":"[75]"},{"why":"The prior observation of branching-ratio variation across IVGDR components in $^{154}\\mathrm{Sm}$, which this result extends and contrasts with.","marker":"[67]"}],"fun_headline_variants":["150Nd defies Porter-Thomas by 7 sigma","Branching-ratio method finds nu=1.93, defying Porter-Thomas","Nonstatistical gamma decay in 150Nd challenges Porter-Thomas","7-sigma evidence against Porter-Thomas in 150Nd","New method reveals 150Nd decay branching deviates from Porter-Thomas"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The measured average branching ratio equals the ensemble-mean internal fluctuation ratio $s$ only if the 5 to 7 MeV region contains enough $1^-$ levels, on the order of $10^3$ per MeV, that the excitation strength is spread uniformly across the photon beam profile; the authors state this assumption fails below about 5 MeV, and a much smaller effective number of sampled levels would bias the inferred $\\nu$.","fun_headline_variants_meta":{"raw":{"variants":["150Nd defies Porter-Thomas by 7 sigma","Branching-ratio method finds nu=1.93, defying Porter-Thomas","Nonstatistical gamma decay in 150Nd challenges Porter-Thomas","7-sigma evidence against Porter-Thomas in 150Nd","New method reveals 150Nd decay branching deviates from Porter-Thomas"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000897,"raw_usage":{"total_tokens":3877,"prompt_tokens":972,"completion_tokens":2905,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":588,"completion_tokens_details":{"reasoning_tokens":2812}},"tokens_in":588,"tokens_out":2905,"duration_ms":20444,"temperature":1.0,"reasoning_tokens":2812,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T21:01:11.453734+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check is to measure the same $1^-$ branching ratio in $^{150}\\mathrm{Nd}$ with the photon beam tuned to individual resolved resonances rather than integrated humps, so the contributing level density can be counted directly; if the true number of contributing levels is far below the assumed $10^3$ per MeV, the deduced $\\nu = 1.93$ would collapse toward the Porter-Thomas value. Alternatively, the method applied to a spherical even-even nucleus with a low $2^+_1$ energy should give $R \\approx 1/3$ if the statistical model holds there.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Porter-Thomas distribution, the null hypothesis being tested."},{"cited_title":"It refers to Refs","cited_arxiv_id":null,"evidence_quote":"Supplemental material containing the derivation of $s = \\nu/(\\nu+2)$ and the convergence analysis."},{"cited_title":"Be ˇcv´aˇr, Nucl","cited_arxiv_id":null,"evidence_quote":"The Dicebox Monte-Carlo code that validates the formalism and reproduces the Porter-Thomas prediction $R_{\\rm sim} \\approx 0.31$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The HI\\gamma S photon source whose high-resolution mode enabled the separation of the two decay branches."},{"cited_title":"Basu and A","cited_arxiv_id":null,"evidence_quote":"Provides the low-lying level scheme used to seed the statistical-model simulations."},{"cited_title":"Kleemann et al., Phys","cited_arxiv_id":null,"evidence_quote":"The prior observation of branching-ratio variation across IVGDR components in $^{154}\\mathrm{Sm}$, which this result extends and contrasts with."}],"review_version":1}