From credible shell model interactions to neutron-capture uncertainties
Pith reviewed 2026-05-10 16:13 UTC · model grok-4.3
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.
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
- 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
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.
Referee Report
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)
- [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.
- [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)
- 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
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
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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
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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
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
axioms (2)
- domain assumption USDBUQ500 shell-model interaction produces NLDs and RSFs whose uncertainties are constant at 6% and 9%
- domain assumption Statistical model propagation of NLD and RSF uncertainties yields the reported 5-25% cross-section uncertainty without additional model errors
Reference graph
Works this paper leans on
-
[1]
S. Goriely, S. Hilaire, S. Péru, K. Sieja, Gogny- HFB+QRPA dipole strength function and its applica- tion to radiative nucleon capture cross section, Phys- ical Review C: Nuclear Physics98, 014327 (2018). 10.1103/PhysRevC.98.014327
-
[2]
O.C. Gorton, K. Kravvaris, J.E. Escher, C.W. John- son, Radiative strength functions from the energy- localized brink-axel hypothesis, Phys. Rev. C pp. – (2026). 10.1103/kg6r-t5d1
-
[3]
V . Zelevinsky, M. Horoi, R.A. Sen’kov, Moments method for shell-model level density, Journal of Physics: Conference Series665, 012048 (2016). 10.1088/1742-6596/665/1/012048
-
[4]
O.C. Gorton, K. Kravvaris, Toward shell model in- teractions with credible uncertainties, Phys. Rev. C 112, 014302 (2025). 10.1103/fzxv-4q1r
-
[5]
M. La Cognata, S. Palmerini, P. Adsley, F. Ham- mache, A. Di Pietro, P. Figuera, R. Alba, S. Cherubini, F. Dell’Agli, G. Guardo et al., Exploring the astrophysical energy range of the 27almg reaction: A new recommended reac- tion rate, Physics Letters B826, 136917 (2022). 10.1016/j.physletb.2022.136917
-
[6]
W.E. Ormand, Tech. rep., Lawrence Livermore Na- tional Laboratory (LLNL), Livermore, CA (United States) (2021),https://www.osti.gov/biblio/ 1808762
work page 2021
-
[7]
A.J. Koning, J.P. Delaroche, Local and global nu- cleon optical models from 1 keV to 200 MeV, Nu- clear PhysicsA713, 231 (2003)
work page 2003
-
[8]
C.D. Pruitt, J.E. Escher, R. Rahman, Uncertainty- quantified phenomenological optical potentials for single-nucleon scattering, Phys. Rev. C107, 014602 (2023). 10.1103/PhysRevC.107.014602
-
[9]
J.E. Escher, J.T. Harke, F.S. Dietrich, N.D. Sci- elzo, I.J. Thompson, W. Younes, Compound-nuclear reaction cross sections from surrogate measure- ments, Reviews of Modern Physics84, 353 (2012). 10.1103/RevModPhys.84.353
-
[10]
J. Kopecky, M. Uhl, Test of gamma-ray strength functions in nuclear reaction model calcula- tions, Physical Review C41, 1941–1955 (1990). 10.1103/physrevc.41.1941
-
[12]
A. Gilbert, A.G.W. Cameron, A composite nuclear- level density formula with shell corrections, Cana- dian Journal of Physics43, 1446–1496 (1965). 10.1139/p65-139
-
[13]
R. Capote, M. Herman, P. Obložinský, P. Young, S. Goriely, T. Belgya, A. Ignatyuk, A. Koning, S. Hi- laire, V . Plujko et al., RIPL – reference input param- eter library for calculation of nuclear reactions and nuclear data evaluations, Nuclear Data Sheets110, 3107 (2009). 10.1016/j.nds.2009.10.004
-
[14]
R.A. Sen’kov, M. Horoi, High-performance algo- rithm to calculate spin- and parity-dependent nuclear level densities, Phys. Rev. C82, 024304 (2010). 10.1103/PhysRevC.82.024304
-
[15]
W.E. Ormand, B.A. Brown, Microscopic calcu- lations of nuclear level densities with the lanc- zos method, Phys. Rev. C102, 014315 (2020). 10.1103/PhysRevC.102.014315
-
[16]
B.A. Brown, W.A. Richter, New “USD” Hamil- tonians for the sd shell, Physical Review C: Nu- clear Physics74, 034315 (2006). 10.1103/Phys- RevC.74.034315
-
[17]
J.M.R. Fox, C.W. Johnson, R.N. Perez, Uncertainty quantification of an empirical shell-model interac- tion using principal component analysis, Physical Review C: Nuclear Physics101, 054308 (2020). 10.1103/PhysRevC.101.054308
-
[18]
D. Brown, M. Chadwick, R. Capote, A. Kahler, A. Trkov, M. Herman, A. Sonzogni, Y . Danon, A. Carlson, M. Dunn et al., ENDF/B-VIII.0: The 8th major release of the nuclear reaction data library with CIELO-project cross sections, new standards and thermal scattering data, Nuclear Data Sheets148, 1 (2018). 10.1016/j.nds.2018.02.001
-
[19]
G. Petö, Z. Miligy, I. Hunyadi, Radiative capture cross sections for 3 mev neutrons, Journal of Nu- clear Energy21, 797–801 (1967). 10.1016/0022- 3107(67)90089-5
-
[20]
J. Colditz, P. Hille, Measurement of some capture cross sections for fast neutrons, Oesterr. Akad. Wiss. Math.-Naturwiss. Kl., Anz. 105: 236-41(1968). (1967)
work page 1968
-
[21]
A. Kedia, J.M. Berryman, J.C. Garcia, J.E. Es- cher, O.C. Gorton, E.M. Holmbeck, G.C. McLaugh- lin, C.D. Pruitt, A. Sieverding, R. Surman, Corre- lated and uncorrelated monte carlo neutron capture rate variations in weakr-process simulations (2026), https://arxiv.org/abs/2602.12428
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