Nuclear Reaction Data for Fission Products Off Stability

Alexander Voinov; Aman Sharma; David Brown; Emanuel Chimanski; Gustavo Nobre; Kyle Wendt; Shusen Liu

arxiv: 2606.03720 · v1 · pith:R3MW4BX4new · submitted 2026-06-02 · ⚛️ nucl-th

Nuclear Reaction Data for Fission Products Off Stability

Gustavo Nobre , Emanuel Chimanski , Aman Sharma , Alexander Voinov , Kyle Wendt , David Brown , Shusen Liu This is my paper

Pith reviewed 2026-06-28 07:53 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords neutron cross sectionsfission productsnuclear deformationmachine learningunstable nucleinuclear reactionsENDF/B

0 comments

The pith

Accounting for nuclear deformation and machine-learning constraints improves predictions of neutron cross sections on unstable fission products.

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

The paper seeks to generate better theoretical predictions for neutron-induced reactions on fission products that lie far from nuclear stability. Standard models rely on simplified assumptions about nuclear shape that leave unquantified effects on the resulting cross sections. By replacing those assumptions with explicit treatment of nuclear deformation and by using machine learning to tighten the choice of model parameters, the authors aim to produce more reliable cross-section values where direct measurements do not exist. These values matter for reactor burnup calculations, nuclear forensics, nonproliferation monitoring, and astrophysical nucleosynthesis networks. The work concentrates on the most abundant fission products from uranium-235 fission and outlines a path toward submitting updated evaluated files to the ENDF/B library.

Core claim

A more realistic reaction modeling approach that accounts for nuclear deformation, combined with machine learning to constrain parameters, can improve predictions of neutron-induced reaction cross sections for fission products off stability compared to usual simplified assumptions.

What carries the argument

Nuclear deformation incorporated into reaction modeling, with machine-learning methods used to constrain uncertain parameters.

If this is right

Evaluated nuclear data files can be prepared for the most abundant fission products off stability.
These files can be submitted for inclusion in the next major ENDF/B release.
Cross-section libraries used in reactor design, burnup analysis, and nonproliferation applications will rest on fewer untested simplifications.
The same modeling framework can be applied to other neutron-induced reactions on unstable nuclei.

Where Pith is reading between the lines

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

The method may reduce the size of uncertainty bands that currently arise from unvalidated shape assumptions in evaluated data.
It could be tested on a small set of nuclei for which limited experimental anchors already exist before scaling to completely unmeasured cases.
Similar deformation-plus-machine-learning adjustments might improve predictions for charged-particle reactions on the same nuclei.
The approach offers a route to quantify how much each modeling choice affects final cross sections for specific applications.

Load-bearing premise

That adding explicit nuclear deformation and machine-learning constraints will produce meaningfully more accurate cross sections without introducing new uncontrolled uncertainties.

What would settle it

New experimental measurements of a neutron-induced cross section on one of the selected unstable fission-product nuclei that can be compared directly with both the simplified and the deformation-plus-machine-learning predictions.

Figures

Figures reproduced from arXiv: 2606.03720 by Alexander Voinov, Aman Sharma, David Brown, Emanuel Chimanski, Gustavo Nobre, Kyle Wendt, Shusen Liu.

**Figure 1.** Figure 1: Chart of nuclides indicating the nuclei relevant to the project primary goal, with isotopes color-coded by relative probability of formation through 235U spontaneous fission. ments of main processing codes (NJOY [2], FUDGE [3], AMPX [4]). 2 Planned Methodology The modeling of neutron-induced cross sections is normally divided in three regimes, (i) thermal, (ii) resonance, and (iii) fast regions. In the f… view at source ↗

**Figure 2.** Figure 2: Chart of nuclides indicating the nuclei relevant to the project primary goal, with isotopes color-coded by the value of the ratio of the excitation energy of the first 4+ state by the first 2 + one (E4 + /E2 + ). This is an indication of deformation, as a value near 3.3 indicates a perfect rotor. well the total cross section for well-measured staticallydeformed nuclei and also how the elastic and inelasti… view at source ↗

**Figure 3.** Figure 3: Comparison of 98Zr(n,total) cross section between a more realistic couple-channel calculation and a spherical one. TENDL also plotted as reference. wick, A.C. Kahler, N.A. Kleedtke et al., ENDF/BVIII.1: Updated Nuclear Reaction Data Library for Science and Applications, Nuclear Data Sheets 210, 1 (2026), special Issue on Nuclear Reaction Data. https://doi.org/10.1016/j.nds.2026.04.001 [2] R. MacFarlane, D… view at source ↗

read the original abstract

Neutron cross sections on fission products are relevant to a wide range of applications, including nuclear nonproliferation and forensics, spent-fuel assay, reactor burnup and design, as well as astrophysics. Evaluated nuclear data libraries generally fulfill application needs for isotopes on or near stability, however, for unstable fission products, theoretical descriptions of neutron-induced reactions often constitute the only available source of information. These models often make use of simplified assumptions, leading to unquantified impacts on predicted cross sections. In this work, we discuss possible approaches to addressing these issues, particularly by leveraging machine-learning methods, improved predictive reaction modeling, and experimental data to better constrain model parameters. Our goal is to eventually produce evaluated files for the most-produced nuclei off stability in the fission process of $^{235}$U and submit them to the ENDF/B for consideration in the future ENDF/B-IX.0 release. Here we present the methodology and discuss preliminary results comparing usual simplified approaches with a more realistic one accounting for nuclear deformation.

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.

Desk Editor's Note private letter to a colleague

The paper sketches a plan to fold nuclear deformation and ML parameter tuning into reaction models for unstable fission products, but the gains stay untestable without benchmarks.

read the letter

The core point is that this work flags the reliance on simplified models for neutron reactions on fission products far from stability and proposes to replace them with deformation-aware calculations plus machine learning to tighten parameters. They target the most abundant off-stability products from 235U fission and aim to deliver ENDF/B files. That is a concrete, application-driven goal.

What stands out is the recognition that current libraries leave large unquantified uncertainties precisely where data are needed for reactors, nonproliferation, and astrophysics. The preliminary model-to-model comparisons they show are a reasonable first step to illustrate the difference deformation makes.

The limitation is straightforward: no measured cross sections exist for these nuclei, so the comparisons cannot show which prediction is more accurate. Adding deformation and ML increases the number of adjustable pieces; without an external check, it is not clear whether uncertainty shrinks or simply moves. The abstract and stress-test note both flag this, and nothing in the described approach supplies an independent test.

The paper is aimed at nuclear data evaluators and reaction theorists who already work with Hauser-Feshbach codes and optical-model fits. Someone already tracking fission-product evaluations would find the methodology discussion useful as a status report on an ongoing effort.

It is worth sending to referees. The problem is real, the tools are standard, and the community needs documented attempts to improve these files even when full validation is out of reach.

Referee Report

1 major / 0 minor

Summary. The manuscript describes an approach to improve theoretical modeling of neutron-induced reaction cross sections for unstable fission products by incorporating nuclear deformation and using machine learning methods to constrain model parameters. It presents the methodology and preliminary results comparing this to usual simplified assumptions, with the goal of producing evaluated nuclear data files for the most-produced off-stability nuclei from 235U fission for submission to ENDF/B.

Significance. This work has the potential to fill important gaps in nuclear reaction data for applications in nonproliferation, spent fuel assay, reactor design, and astrophysics. The use of ML for parameter constraint and deformation modeling is a novel direction that, if successful, could lead to more accurate predictions where experimental data is unavailable.

major comments (1)

[Abstract] The central claim that a more realistic deformation-accounting approach combined with ML yields meaningfully better cross sections rests on preliminary model-to-model comparisons (as described in the abstract). No experimental benchmarks exist for these nuclei, so the manuscript must explicitly discuss how improvement versus uncertainty reduction is established; this is load-bearing for the claim of improved predictions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review. The single major comment is addressed below; we agree it requires explicit clarification in the manuscript and will revise accordingly.

read point-by-point responses

Referee: [Abstract] The central claim that a more realistic deformation-accounting approach combined with ML yields meaningfully better cross sections rests on preliminary model-to-model comparisons (as described in the abstract). No experimental benchmarks exist for these nuclei, so the manuscript must explicitly discuss how improvement versus uncertainty reduction is established; this is load-bearing for the claim of improved predictions.

Authors: We agree that the distinction between demonstrated improvement and reduced model uncertainty must be stated explicitly, given the absence of experimental benchmarks for these unstable nuclei. In the revised manuscript we will (1) qualify the abstract language to emphasize that the reported comparisons are between modeling frameworks rather than against data, (2) add a dedicated paragraph in the introduction or results section explaining that the deformation-accounting approach reduces systematic bias associated with the spherical approximation while the ML step constrains parameter ranges within each framework, and (3) note that any claim of “better” cross sections remains provisional until future measurements become available. These additions will make the evidential basis of the central claim transparent without overstating the current results. revision: yes

Circularity Check

0 steps flagged

No circularity: methodology draws on external data and standard models

full rationale

The paper presents a methodology for constraining reaction model parameters via machine learning and experimental data on or near stability, then applies the resulting models to off-stability fission products. No derivation step, equation, or claim reduces a prediction to a fitted input by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames a known result. The central comparison is between simplified and deformation-aware modeling approaches, with the goal of producing ENDF files; this chain remains open to external benchmarks and does not collapse into its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The work implicitly rests on standard nuclear reaction theory.

axioms (1)

domain assumption Standard nuclear reaction models (e.g., Hauser-Feshbach) apply to off-stability fission products.
Invoked when discussing theoretical descriptions of neutron-induced reactions.

pith-pipeline@v0.9.1-grok · 5716 in / 1060 out tokens · 18136 ms · 2026-06-28T07:53:58.915863+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

19 extracted references · 12 canonical work pages

[1]

Nobre, R

G.P.A. Nobre, R. Capote, M.T. Pigni, A. Trkov, C.M. Mattoon, D. Neudecker, D.A. Brown, M.B. Chad- 0.001 0.01 0.1 1 10 Einc. (MeV) 10σ Total (barns) TENDL-2025 EMPIRE - spherical model EMPIRE - coupled channels 98 Zr(n,total) Figure 3.Comparison of 98Zr(n,total) cross section between a more realistic couple-channel calculation and a spherical one. TENDL al...

work page doi:10.1016/j.nds.2026.04.001 2025
[2]

MacFarlane, D

R. MacFarlane, D. Muir, R. Boicourt, A. Kahler, J. Conlin, W. Haeck, Tech. Rep. LA-UR-17-20093, Los Alamos National Laboratory, NM, USA (2017)

2017
[3]

Mattoon, B.R

C.M. Mattoon, B.R. Beck, G. Gert, Managing and Processing Nuclear Data Libraries with FUDGE, EPJ Web of Conferences284, 14010 (2023). 10.1051/epjconf/202328414010

work page doi:10.1051/epjconf/202328414010 2023
[4]

Wiarda et al., Tech

D. Wiarda et al., Tech. Rep. ORNL/TM-2016/43, Oak Ridge National Laboratory, TN, USA (2016), available from Radiation Safety Information Compu- tational Center asCCC-834

2016
[5]

Mughabghab, Atlas of Neutron Resonances (Elsevier, 2018), ISBN 978-0-444-63786- 4,https://linkinghub.elsevier.com/ retrieve/pii/C2015000524X

S.F. Mughabghab, Atlas of Neutron Resonances (Elsevier, 2018), ISBN 978-0-444-63786- 4,https://linkinghub.elsevier.com/ retrieve/pii/C2015000524X

2018
[7]

Koning, D

A.J. Koning, D. Rochman, J.C. Sublet, N. Dzy- siuk, M. Fleming, S.v.d. Marck, TENDL: Com- plete nuclear data library for innovative nuclear sci- ence and technology, Nuclear Data Sheets155, 1 (2019), special Issue on Nuclear Reaction Data. https://doi.org/10.1016/j.nds.2019.01.002

work page doi:10.1016/j.nds.2019.01.002 2019
[8]

Trkov, P

A. Trkov, P. Griffin, S. Simakov, L. Greenwood, K. Zolotarev, R. Capote, D. Aldama, V . Chechev, C. Destouches, A. Kahler et al., IRDFF-II: A new neutron metrology library, Nuclear Data Sheets163, 1 (2020). 10.1016/j.nds.2019.12.001

work page doi:10.1016/j.nds.2019.12.001 2020
[9]

Otuka, E

N. Otuka, E. Dupont, V . Semkova et al., Towards a more complete and accurate experimental nu- clear reaction data library (EXFOR): International collaboration between nuclear reaction data centres (NRDC), Nuclear Data Sheets120, 272 (2014)

2014
[10]

Koning, J

A. Koning, J. Delaroche, Local and global nucleon optical models from 1 kev to 200 mev, Nuclear Physics A713, 231 (2003). https://doi.org/10.1016/S0375-9474(02)01321-0

work page doi:10.1016/s0375-9474(02)01321-0 2003
[11]

Nobre, A

G. Nobre, A. Palumbo, D. Brown, M. Herman, S. Hoblit, F. Dietrich, Towards a coupled- channel optical potential for rare-earth nu- clei, Nuclear Data Sheets118, 266 (2014). https://doi.org/10.1016/j.nds.2014.04.054

work page doi:10.1016/j.nds.2014.04.054 2014
[12]

Nobre, A

G.P.A. Nobre, A. Palumbo, M. Herman, D. Brown, S. Hoblit, F.S. Dietrich, Derivation of an optical po- tential for statically deformed rare-earth nuclei from a global spherical potential, Phys. Rev. C91, 024618 (2015). 10.1103/PhysRevC.91.024618

work page doi:10.1103/physrevc.91.024618 2015
[13]

Nobre, F.S

G.P.A. Nobre, F.S. Dietrich, M. Herman, A. Palumbo, S. Hoblit, D. Brown, Towards an optical potential for rare-earths through coupled channels, AIP Conference Proceedings1625, 45 (2014). 10.1063/1.4901763

work page doi:10.1063/1.4901763 2014
[14]

Herman, M., Nobre, G. P. A., Palumbo, A., Diet- rich, F. S., Brown, D., Hoblit, S., Coupled chan- nels optical model potential for rare earth nuclei, EPJ Web of Conferences69, 00007 (2014). 10.1051/epj- conf/20136900007

work page doi:10.1051/epj- 2014
[15]

Dietrich, I.J

F.S. Dietrich, I.J. Thompson, T. Kawano, Target- state dependence of cross sections for reactions on statically deformed nuclei, Phys. Rev. C85, 044611 (2012). 10.1103/PhysRevC.85.044611

work page doi:10.1103/physrevc.85.044611 2012
[16]

Hilaire, M

S. Hilaire, M. Girod, Large-scale mean-field calcula- tions from proton to neutron drip lines using the D1S gogny force, Eur. Phys. J. A33, 237 (2007)

2007
[17]

Herman, R

M. Herman, R. Capote, B. Carlson, P. Obložinský, M. Sin, A. Trkov, H. Wienke, V . Zerkin, EMPIRE: Nuclear reaction model code system for data evalua- tion, Nuclear Data Sheets108, 2655 (2007)

2007
[18]

Capote, M

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

work page doi:10.1016/j.nds.2009.10.004 2009
[19]

V onach, Extraction of level density information from non-resonant reactions, p

H. V onach, Extraction of level density information from non-resonant reactions, p. p. 247–290. (1983)

1983
[20]

Hambye, M

A.V . V oinov, T. Renstrøm, D.L. Bleuel, S.M. Grimes, M. Guttormsen, A.C. Larsen, S.N. Liddick, G. Perdikakis, A. Spyrou, S. Akhtar et al., Level den- sities of 74,76Ge from compound nuclear reactions, Phys. Rev. C99, 054609 (2019). 10.1103/Phys- RevC.99.054609

work page doi:10.1103/phys- 2019

[1] [1]

Nobre, R

G.P.A. Nobre, R. Capote, M.T. Pigni, A. Trkov, C.M. Mattoon, D. Neudecker, D.A. Brown, M.B. Chad- 0.001 0.01 0.1 1 10 Einc. (MeV) 10σ Total (barns) TENDL-2025 EMPIRE - spherical model EMPIRE - coupled channels 98 Zr(n,total) Figure 3.Comparison of 98Zr(n,total) cross section between a more realistic couple-channel calculation and a spherical one. TENDL al...

work page doi:10.1016/j.nds.2026.04.001 2025

[2] [2]

MacFarlane, D

R. MacFarlane, D. Muir, R. Boicourt, A. Kahler, J. Conlin, W. Haeck, Tech. Rep. LA-UR-17-20093, Los Alamos National Laboratory, NM, USA (2017)

2017

[3] [3]

Mattoon, B.R

C.M. Mattoon, B.R. Beck, G. Gert, Managing and Processing Nuclear Data Libraries with FUDGE, EPJ Web of Conferences284, 14010 (2023). 10.1051/epjconf/202328414010

work page doi:10.1051/epjconf/202328414010 2023

[4] [4]

Wiarda et al., Tech

D. Wiarda et al., Tech. Rep. ORNL/TM-2016/43, Oak Ridge National Laboratory, TN, USA (2016), available from Radiation Safety Information Compu- tational Center asCCC-834

2016

[5] [5]

Mughabghab, Atlas of Neutron Resonances (Elsevier, 2018), ISBN 978-0-444-63786- 4,https://linkinghub.elsevier.com/ retrieve/pii/C2015000524X

S.F. Mughabghab, Atlas of Neutron Resonances (Elsevier, 2018), ISBN 978-0-444-63786- 4,https://linkinghub.elsevier.com/ retrieve/pii/C2015000524X

2018

[6] [7]

Koning, D

A.J. Koning, D. Rochman, J.C. Sublet, N. Dzy- siuk, M. Fleming, S.v.d. Marck, TENDL: Com- plete nuclear data library for innovative nuclear sci- ence and technology, Nuclear Data Sheets155, 1 (2019), special Issue on Nuclear Reaction Data. https://doi.org/10.1016/j.nds.2019.01.002

work page doi:10.1016/j.nds.2019.01.002 2019

[7] [8]

Trkov, P

A. Trkov, P. Griffin, S. Simakov, L. Greenwood, K. Zolotarev, R. Capote, D. Aldama, V . Chechev, C. Destouches, A. Kahler et al., IRDFF-II: A new neutron metrology library, Nuclear Data Sheets163, 1 (2020). 10.1016/j.nds.2019.12.001

work page doi:10.1016/j.nds.2019.12.001 2020

[8] [9]

Otuka, E

N. Otuka, E. Dupont, V . Semkova et al., Towards a more complete and accurate experimental nu- clear reaction data library (EXFOR): International collaboration between nuclear reaction data centres (NRDC), Nuclear Data Sheets120, 272 (2014)

2014

[9] [10]

Koning, J

A. Koning, J. Delaroche, Local and global nucleon optical models from 1 kev to 200 mev, Nuclear Physics A713, 231 (2003). https://doi.org/10.1016/S0375-9474(02)01321-0

work page doi:10.1016/s0375-9474(02)01321-0 2003

[10] [11]

Nobre, A

G. Nobre, A. Palumbo, D. Brown, M. Herman, S. Hoblit, F. Dietrich, Towards a coupled- channel optical potential for rare-earth nu- clei, Nuclear Data Sheets118, 266 (2014). https://doi.org/10.1016/j.nds.2014.04.054

work page doi:10.1016/j.nds.2014.04.054 2014

[11] [12]

Nobre, A

G.P.A. Nobre, A. Palumbo, M. Herman, D. Brown, S. Hoblit, F.S. Dietrich, Derivation of an optical po- tential for statically deformed rare-earth nuclei from a global spherical potential, Phys. Rev. C91, 024618 (2015). 10.1103/PhysRevC.91.024618

work page doi:10.1103/physrevc.91.024618 2015

[12] [13]

Nobre, F.S

G.P.A. Nobre, F.S. Dietrich, M. Herman, A. Palumbo, S. Hoblit, D. Brown, Towards an optical potential for rare-earths through coupled channels, AIP Conference Proceedings1625, 45 (2014). 10.1063/1.4901763

work page doi:10.1063/1.4901763 2014

[13] [14]

Herman, M., Nobre, G. P. A., Palumbo, A., Diet- rich, F. S., Brown, D., Hoblit, S., Coupled chan- nels optical model potential for rare earth nuclei, EPJ Web of Conferences69, 00007 (2014). 10.1051/epj- conf/20136900007

work page doi:10.1051/epj- 2014

[14] [15]

Dietrich, I.J

F.S. Dietrich, I.J. Thompson, T. Kawano, Target- state dependence of cross sections for reactions on statically deformed nuclei, Phys. Rev. C85, 044611 (2012). 10.1103/PhysRevC.85.044611

work page doi:10.1103/physrevc.85.044611 2012

[15] [16]

Hilaire, M

S. Hilaire, M. Girod, Large-scale mean-field calcula- tions from proton to neutron drip lines using the D1S gogny force, Eur. Phys. J. A33, 237 (2007)

2007

[16] [17]

Herman, R

M. Herman, R. Capote, B. Carlson, P. Obložinský, M. Sin, A. Trkov, H. Wienke, V . Zerkin, EMPIRE: Nuclear reaction model code system for data evalua- tion, Nuclear Data Sheets108, 2655 (2007)

2007

[17] [18]

Capote, M

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

work page doi:10.1016/j.nds.2009.10.004 2009

[18] [19]

V onach, Extraction of level density information from non-resonant reactions, p

H. V onach, Extraction of level density information from non-resonant reactions, p. p. 247–290. (1983)

1983

[19] [20]

Hambye, M

A.V . V oinov, T. Renstrøm, D.L. Bleuel, S.M. Grimes, M. Guttormsen, A.C. Larsen, S.N. Liddick, G. Perdikakis, A. Spyrou, S. Akhtar et al., Level den- sities of 74,76Ge from compound nuclear reactions, Phys. Rev. C99, 054609 (2019). 10.1103/Phys- RevC.99.054609

work page doi:10.1103/phys- 2019