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arxiv: 2604.09935 · v1 · submitted 2026-04-10 · ⚛️ nucl-th

From credible shell model interactions to neutron-capture uncertainties

Pith reviewed 2026-05-10 16:13 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords neutron captureshell modelnuclear level densityradiative strength functionuncertainty quantificationaluminum-27Hauser-Feshbach model
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The pith

Shell-model calculations produce the first uncertainty-quantified neutron-capture cross section for aluminum-27, ranging from 5 to 25 percent with a non-Gaussian shape.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how shell-model structure calculations can supply nuclear level densities and radiative strength functions together with their uncertainties for use in statistical reaction modeling. These quantities are computed for 27Al with the USDBUQ500 interaction, which assigns constant 6 percent uncertainty to the level densities and 9 percent to the strength functions. When the values and their uncertainties are fed into the Hauser-Feshbach model, the resulting neutron-capture cross section carries an energy-dependent uncertainty of 5 to 25 percent whose distribution is non-Gaussian rather than symmetric. This supplies a concrete, first-principles route to error estimates for a reaction rate that matters for both astrophysics and nuclear technology applications.

Core claim

Using the USDBUQ500 shell-model interaction, nuclear level densities and radiative strength functions for 27Al are computed with constant uncertainties of 6 percent and 9 percent, respectively. When these are used in the Hauser-Feshbach statistical model, the neutron-capture cross section acquires an uncertainty of 5 to 25 percent, and the probability distribution of cross-section values is non-Gaussian.

What carries the argument

Uncertainty propagation from shell-model predictions of nuclear level densities and radiative strength functions through the statistical Hauser-Feshbach reaction model.

If this is right

  • Neutron-capture rates used in astrophysical network calculations can now carry quantified, non-Gaussian uncertainties derived from a microscopic model.
  • Shell-model interactions can be tested for their ability to reproduce not only discrete states but also the statistical properties that govern reaction rates.
  • The energy dependence of the cross-section uncertainty implies that error budgets in applications must be evaluated at each relevant energy rather than assumed constant.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same workflow could be applied to other light nuclei where shell-model spaces remain tractable, reducing reliance on purely phenomenological rate libraries.
  • A non-Gaussian distribution means that standard symmetric error propagation may underestimate the probability of extreme values in nucleosynthesis yields.
  • If the constant-percentage uncertainties found here prove general, they offer a simple scaling rule for estimating uncertainties in heavier systems before full calculations are feasible.

Load-bearing premise

Shell-model uncertainties in nuclear level densities and radiative strength functions remain constant at 6 percent and 9 percent and can be propagated through the Hauser-Feshbach model without introducing unaccounted-for uncertainties from the reaction model itself.

What would settle it

Direct comparison of the predicted cross section and its 5-to-25-percent uncertainty band against measured 27Al(n,gamma) data at energies relevant to stellar burning would confirm or refute the size and shape of the uncertainty.

Figures

Figures reproduced from arXiv: 2604.09935 by Konstantinos Kravvaris, Oliver Gorton.

Figure 2
Figure 2. Figure 2: The M1 RSFs computed with USDBUQ500 have a 9% uncertainty. For scale reference, the E1 RSF from the SMLO model used in YAHFC is given. 10−4 10−3 10−2 Cross section (b) Systematic models ENDF/B-VIII.0 USDBUQ500 1968,J.Colditz 1967,G.Peto 0 1 2 3 4 5 Neutron energy (MeV) 0 25 Unc. (%) +1σ −1σ 0.2 0.4 σ(2.7 < En < 3.2MeV) (mb) 0 500 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Neutron-capture cross section for 27Al. The lower panel shows the ±1σ variance (defined by 16-th and 84-th per￾centiles). The inset shows a histogram of the cross section en￾semble between En = 2.7 MeV and 3.2 MeV, with a markedly non-gaussian. The experimental data from [20] at 2.9 MeV and [19] at 3.0 MeV are shown in the main panel and the inset. 4 Discussion With the goal of better equipping astrophysic… view at source ↗
read the original abstract

Nuclear structure theory can provide nuclear astrophysics and nuclear technologies with bound state properties and transition rates. When describing nuclear reactions, the list can be extended to include statistical properties such as nuclear level densities (NLDs) and radiative strength functions (RSFs). We present the first uncertainty-quantified neutron-capture cross section for $^{27}$Al based on NLDs and RSFs computed with the shell model (SM). We find that the USDBUQ500 SM interaction predicts NLDs and RSFs with constant uncertainties of 6% and 9%, respectively. These, in turn, translate to a 5 to 25% uncertainty in the neutron-capture cross section, which exhibits a surprisingly non-Gaussian distribution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims to deliver the first uncertainty-quantified neutron-capture cross section on ^{27}Al by computing nuclear level densities (NLDs) and radiative strength functions (RSFs) directly from the shell model using the USDBUQ500 interaction. It reports that this interaction yields constant 6% uncertainty on the NLDs and 9% uncertainty on the RSFs; these uncertainties are then propagated through the statistical Hauser-Feshbach model to produce a 5–25% uncertainty band on the capture cross section whose distribution is non-Gaussian.

Significance. If the quoted constant percentages are rigorously extracted from the interaction (via ensemble or sensitivity methods) and the propagation step is free of unquantified reaction-model systematics, the work supplies a concrete, falsifiable example of carrying nuclear-structure uncertainties forward to a reaction observable. The reported non-Gaussian character of the final uncertainty would be a noteworthy result for nuclear astrophysics and technology applications.

major comments (2)
  1. [Abstract] Abstract: the central numerical claims—constant 6% NLD uncertainty and 9% RSF uncertainty from USDBUQ500—are stated without any derivation, ensemble definition, or sensitivity-analysis procedure. Because the subsequent 5–25% cross-section band and its non-Gaussian shape rest directly on these percentages, the absence of the extraction method is load-bearing.
  2. [Results / Propagation] The propagation step through the Hauser-Feshbach model must be shown explicitly (sampling strategy, assumed independence of NLD and RSF errors, energy range over which the 6% and 9% figures remain constant). Without this, it is impossible to confirm that the reaction model itself contributes no additional unquantified uncertainty.
minor comments (1)
  1. Define all acronyms (NLD, RSF, SM, USDBUQ500) at first use in the main text rather than relying solely on the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The feedback has identified opportunities to strengthen the presentation of our uncertainty quantification and propagation procedures. We address each major comment below and will incorporate revisions to improve clarity and completeness.

read point-by-point responses
  1. Referee: [Abstract] Abstract: the central numerical claims—constant 6% NLD uncertainty and 9% RSF uncertainty from USDBUQ500—are stated without any derivation, ensemble definition, or sensitivity-analysis procedure. Because the subsequent 5–25% cross-section band and its non-Gaussian shape rest directly on these percentages, the absence of the extraction method is load-bearing.

    Authors: We agree that the abstract would benefit from a concise indication of the uncertainty extraction method to make the central claims self-contained. The 6% NLD and 9% RSF uncertainties are obtained via sensitivity analysis of the USDBUQ500 interaction parameters and an associated ensemble of shell-model calculations, as detailed in the Methods section of the manuscript. We will revise the abstract to include a brief statement outlining this procedure, thereby supporting the reported translation to the 5–25% cross-section uncertainty band and its non-Gaussian character. revision: yes

  2. Referee: [Results / Propagation] The propagation step through the Hauser-Feshbach model must be shown explicitly (sampling strategy, assumed independence of NLD and RSF errors, energy range over which the 6% and 9% figures remain constant). Without this, it is impossible to confirm that the reaction model itself contributes no additional unquantified uncertainty.

    Authors: We concur that explicit details on the propagation are necessary for full reproducibility and to isolate the nuclear-structure contribution. The manuscript performs the propagation by sampling within the stated uncertainty bands and passing the varied NLDs and RSFs to the Hauser-Feshbach code; the 6% and 9% values are approximately constant over the excitation-energy range relevant to neutron capture on 27Al. We will expand the Results section to describe the Monte Carlo sampling strategy, justify the independence assumption between NLD and RSF uncertainties (arising from distinct shell-model observables), confirm the energy range, and explicitly state that no additional reaction-model systematics are folded into the reported band. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper computes NLDs and RSFs directly from the USDBUQ500 shell-model interaction and propagates the stated constant uncertainties (6% and 9%) through the Hauser-Feshbach statistical model to obtain the neutron-capture cross-section uncertainty band. The abstract and reader's summary present these percentages as outputs of the interaction itself rather than parameters fitted to the target cross-section data, with no equation shown that reduces the final uncertainty to a quantity defined by the same data. No load-bearing self-citation, self-definitional step, or ansatz smuggled via prior work is identifiable from the provided text that would collapse the central claim to its inputs by construction. The derivation remains self-contained as a forward computation from an independent nuclear-structure model.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review; the central claim rests on the credibility of the USDBUQ500 interaction and the assumption that its NLD/RSF uncertainties are constant and directly transferable to the capture cross section. No free parameters or invented entities are named in the abstract.

axioms (2)
  • domain assumption USDBUQ500 shell-model interaction produces NLDs and RSFs whose uncertainties are constant at 6% and 9%
    Stated as a direct prediction of the interaction in the abstract
  • domain assumption Statistical model propagation of NLD and RSF uncertainties yields the reported 5-25% cross-section uncertainty without additional model errors
    Implicit in the translation step described in the abstract

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Reference graph

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