pith. machine review for the scientific record. sign in

arxiv: 2602.05995 · v2 · submitted 2026-02-05 · ⚛️ nucl-ex · physics.app-ph

Recognition: 2 theorem links

· Lean Theorem

Westcott g Factors Extended to Arbitrary Neutron Energy Spectra

D.A. Matters , A.M. Hurst , T. Kawano
Authors on Pith no claims yet

Pith reviewed 2026-05-16 06:45 UTC · model grok-4.3

classification ⚛️ nucl-ex physics.app-ph
keywords Westcott g-factorneutron activation analysisPGAAneutron capture cross sectionENDF/B-VIII.1cold neutron beamsguided neutron beams
0
0 comments X

The pith

Westcott g-factors can now be calculated from any user-specified neutron energy spectrum rather than only Maxwellian distributions.

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

The paper develops a general method to compute Westcott g-factors that correct neutron-capture activation yields for non-1/v cross-section behavior when resonances overlap the incident neutron spectrum below about 5 eV. Traditional tables assumed a Maxwellian velocity distribution at a chosen temperature, but many current guided and cold-neutron beams have non-Maxwellian shapes that require spectrum-specific integration. Using ENDF/B-VIII.1 capture data, the authors tabulate g-factors over a wide range of Maxwellian temperatures and then apply the new arbitrary-spectrum procedure to measured flux distributions at the Budapest Research Reactor and the FRM II reactor. Open-source code is provided so that experimenters can repeat the calculation for any other measured spectrum.

Core claim

We present an approach for calculating g factors with user-specified neutron spectra, and we apply these methods to obtain Westcott g-factors for guided- and cold-neutron beams at the Budapest Research Reactor and the Forschungsreaktor München II reactor.

What carries the argument

The Westcott g-factor, obtained by integrating the energy-dependent capture cross section weighted by an arbitrary neutron flux distribution and then normalizing to the 2200 m/s cross section.

If this is right

  • g-factor tables for Maxwellian spectra are updated with current ENDF/B-VIII.1 data across a broad temperature range.
  • Specific numerical g-factors are supplied for the guided and cold beams at Budapest and FRM II.
  • Open-source software allows any user to compute g-factors for an arbitrary measured neutron spectrum.

Where Pith is reading between the lines

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

  • The same integration procedure could be applied to neutron spectra from spallation sources or other non-reactor facilities once their flux distributions are measured.
  • Elements whose capture resonances lie below 5 eV will show the largest correction differences when switching from Maxwellian to beam-specific spectra.

Load-bearing premise

The supplied neutron spectra for the Budapest and FRM II beams are accurate representations of the actual beams, and the ENDF/B-VIII.1 capture cross sections correctly describe the relevant low-energy resonances.

What would settle it

An activation-yield measurement for a resonance-affected target in one of the two beams that differs from the yield predicted by the new g-factor by more than the combined experimental and cross-section uncertainty.

Figures

Figures reproduced from arXiv: 2602.05995 by A.M. Hurst, D.A. Matters, T. Kawano.

Figure 1
Figure 1. Figure 1: Low-energy (𝐸 ≤ 5 eV) neutron-capture cross sections from ENDF/B-VIII.1 [18] for each of the isotopes listed in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Normalized neutron flux distributions 𝜙(𝑣) for guided cold- and thermal-neutron beams from the PGAA beamlines at the Budapest Research Reactor [34, 35] (a) and the FRM II reactor [37] (b), compared with Maxwellian and ideal-guide distributions 𝜙𝑇 (𝑣) defined with various average temperatures 𝑇 . It is evident from [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
read the original abstract

Westcott $g$ factors are used in Neutron Activation Analysis (NAA) and Prompt Gamma-ray Activation Analysis (PGAA) to evaluate the impact of non-$1/v$ behavior in the neutron-capture cross sections of certain nuclei on activation product yields. This non-$1/v$ behavior arises from the presence of neutron resonances in the neutron-capture cross sections that overlap with the source neutron spectrum at low ($<5$~eV) energies. Historically, Westcott $g$ factors that have been cataloged for NAA and PGAA applications are the result of calculations that assume a Maxwellian neutron velocity distribution with a given average temperature. In this study, we use this approach with updated neutron-capture cross sections from the Evaluated Nuclear Data File, version VIII.1 (ENDF/B-VIII.1) to tabulate Westcott $g$ factor values for a broad range of Maxwellian distribution temperatures, comparing the results against currently-available $g$ factors from International Atomic Energy Agency tables and other sources. It was discovered during this analysis that the use of guided thermal and cold-neutron beams at certain facilities necessitates an approach for evaluating Westcott $g$ factors based on arbitrary non-Maxwellian spectra. In this paper, we present an approach for calculating $g$ factors with user-specified neutron spectra, and we apply these methods to obtain Westcott $g$-factors for guided- and cold-neutron beams at the Budapest Research Reactor and the Forschungsreaktor M{\"u}nchen II reactor. Open-source software has been developed as part of this study that can be used to perform these calculations for applications in PGAA and NAA experiments

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

0 major / 3 minor

Summary. The manuscript extends the definition of Westcott g-factors from Maxwellian spectra to arbitrary user-specified neutron energy spectra via direct numerical integration against ENDF/B-VIII.1 capture cross sections. It supplies updated g-factor tables for Maxwellian distributions over a range of temperatures, compares them to existing IAEA and literature values, and demonstrates the method on guided and cold neutron beams at the Budapest Research Reactor and FRM II, accompanied by open-source software for general NAA/PGAA use.

Significance. If the numerical implementation is correct, the work supplies a practical, reproducible tool for handling non-Maxwellian spectra that are now routine at modern neutron facilities. The release of open-source code and reliance on standard evaluated nuclear data libraries are clear strengths that support verification and reuse. The central claim rests on standard Westcott integrals rather than new physics or fitted parameters.

minor comments (3)
  1. [Abstract] Abstract: the sentence beginning 'It was discovered during this analysis' could be rephrased to state directly that non-Maxwellian spectra are required for the cited beams, avoiding any implication of an unforeseen result.
  2. [Method] The manuscript should specify the exact energy grid and interpolation method used for the numerical integration of the arbitrary spectra, even if the code is open-source.
  3. [Results] Table of Maxwellian g-factors: include a column or supplementary plot showing the percentage difference from the IAEA compilation for the most discrepant isotopes to make the update explicit.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive review and the recommendation to accept the manuscript. The assessment correctly identifies the core contribution as a practical, reproducible extension of the standard Westcott integral to arbitrary spectra using ENDF/B-VIII.1 data, together with the release of open-source code.

Circularity Check

0 steps flagged

No significant circularity; direct numerical integration of standard definition

full rationale

The paper computes Westcott g-factors by direct numerical integration of ENDF/B-VIII.1 capture cross sections against either Maxwellian spectra or user-supplied beam spectra. The definition itself is the classical ratio of the spectrum-weighted integral to the 1/v reference integral; no parameters are fitted from the target data, no self-referential equations appear, and no uniqueness theorems or prior self-citations are invoked to justify the method. Tabulated Maxwellian results are compared to IAEA tables for validation only. The central claim therefore reduces to standard numerical quadrature applied to externally supplied inputs rather than to any internal construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of the ENDF/B-VIII.1 library for low-energy capture cross sections and on the validity of the Westcott integral formalism when applied to non-Maxwellian spectra.

axioms (2)
  • domain assumption ENDF/B-VIII.1 neutron-capture cross sections are sufficiently accurate in the <5 eV resonance region
    Used directly as input for all g-factor integrals.
  • domain assumption The Westcott g-factor definition remains valid for arbitrary spectra
    Extended from its original Maxwellian derivation without additional proof in the abstract.

pith-pipeline@v0.9.0 · 5612 in / 1263 out tokens · 35712 ms · 2026-05-16T06:45:43.580297+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages

  1. [1]

    H. D. Choi, et al. (Eds.), Database of Prompt Gamma Rays from Slow Neutron Capture for Elemental Analysis, International Atomic Energy Agency, Vienna, Austria, 2007

    work page 2007

  2. [2]

    S. F. Mughabghab, Resonance Properties and Thermal Cross Sections𝑍=1-102, 6th Edition, Elsevier Science, 2018

    work page 2018

  3. [3]

    G. L. Molnár (Ed.), Handbook of Prompt Gamma Activation Analysis, Kluwer Academic, Dordrecht, the Netherlands, 2004

    work page 2004

  4. [4]

    C. H. Westcott, The specification of neutron flux and nuclear cross-sections in reactor calculations, Journal of Nuclear Energy 2 (1955) 59 – 76

    work page 1955

  5. [5]

    C. H. Westcott, Effective cross section values for well-moderated thermal reactor spectra, Tech. Rep. CRRP-960, Atomic Energy of Canada Limited, Chalk River, Ontario (1960)

    work page 1960

  6. [6]

    Byrne (Ed.), Neutrons, Nuclei, and Matter, Institute of Physics Publishing, Bristol and Philadelphia, 1994

    J. Byrne (Ed.), Neutrons, Nuclei, and Matter, Institute of Physics Publishing, Bristol and Philadelphia, 1994

    work page 1994

  7. [7]

    A. M. Hurst, N. C. Summers, L. Szentmiklósi, R. B. Firestone, M. S. Basunia, J. E. Escher, B. W. Sleaford, Determination of the effective sample thickness via radiative capture, Nuclear Instruments and Methods in Physics Research B 362 (2015) 38–44

    work page 2015

  8. [8]

    Krtička, T

    D.A.Matters,A.G.Lerch,A.M.Hurst,L.Szentmiklósi,J.J.Carroll,Z.Révay,J.W.McClory,S.R.McHale,R.B.Firestone,B.W.Sleaford, M. Krtička, T. Belgya, Investigation of186Re via radiative thermal-neutron capture on185Re, Physical Review C 93 (2016) 054319

    work page 2016

  9. [9]

    A. M. Hurst, A. Sweet, B. L. Goldblum, R. B. Firestone, M. S. Basunia, L. A. Bernstein, Z. Révay, L. Szentmiklósi, T. Belgya, J. E. Escher, I. Harsányi, M. Krtička, B. W. Sleaford, J. Vujic, Radiative-capture cross sections for the139La(𝑛, 𝛾)reaction using thermal neutrons and structural properties of140La, Phys. Rev. C 99 (2019) 024310

    work page 2019

  10. [10]

    H.D.Choi,R.B.Firestone,M.S.Basunia,A.Hurst,B.Sleaford,N.Summers,J.E.Escher,Z.Révay,L.Szentmiklósi,T.Belgya,M.Krtička, Radiative capture cross sections of155,157Gd for thermal neutrons, Nuclear Science and Engineering 177 (2014) 219–232

    work page 2014

  11. [11]

    B. Pritychenko, Tables of neutron thermal cross sections, Westcott factors, resonance integrals, Maxwellian averaged cross sections, astrophysicalreactionrates,and𝑟-processabundancescalculatedfromtheENDF/B-VIII.1,JEFF-3.3,JENDL-5.0,BROND-3.1,andCENDL- 3.2 evaluated data libraries, Atomic Data and Nuclear Data Tables 163 (2025) 101708. D.A. Matters et al.:...

    work page 2025

  12. [12]

    R. B. Firestone, Renormalization of pile oscillator thermal neutron capture cross section data, Tech. Rep. INDC(USA)-109, International Atomic Energy Agency, Vienna, Austria (October 2021)

    work page 2021

  13. [13]

    Trkov, et al., IRDFF-II: A new neutron metrology library, Nuclear Data Sheets 163 (2020) 1–108

    A. Trkov, et al., IRDFF-II: A new neutron metrology library, Nuclear Data Sheets 163 (2020) 1–108

    work page 2020

  14. [14]

    R. B. Firestone, Database of prompt gamma rays from slow neutron capture for elemental analysis, (International Atomic Energy Agency, Vienna, 2006). URLhttps://www-nds.iaea.org/pgaa/egaf.html

    work page 2006

  15. [15]

    A. M. Hurst, R. B. Firestone, E. V. Chimanski, pyEGAF: An open-source Python library for the evaluated gamma-ray activation file, Nuclear Instruments and Methods in Physics Research A 1067 (2023) 168715

    work page 2023

  16. [16]

    A. M. Hurst, pyEGAF (PyPI package). URLhttps://pypi.org/project/pyEGAF/

    work page

  17. [17]

    D. A. Brown, 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 Sheets 148 (2018) 1–142

    work page 2018

  18. [18]

    G.Nobre,D.Brown,R.Arcilla,R.Coles,B.Shu,ProgresstowardstheENDF/B-VIII.1release,EuropeanPhysicsJournalWebofConferences 294 (2024) 04004

    work page 2024

  19. [19]

    Kawano, DeCE: the ENDF-6 data interface and nuclear data evaluation assist code, Journal of Nuclear Science and Technology 56 (11) (2019) 1029 – 1035

    T. Kawano, DeCE: the ENDF-6 data interface and nuclear data evaluation assist code, Journal of Nuclear Science and Technology 56 (11) (2019) 1029 – 1035

    work page 2019

  20. [20]

    Kawano, DeCE (GitHub repository)

    T. Kawano, DeCE (GitHub repository). URLhttps://github.com/toshihikokawano/DeCE

    work page

  21. [21]

    Brown, B

    D. Brown, B. Beck, C. Mattoon, T. Bailey, I. Thompson, J. L. Conlin, W. Haeck, M. White, M. Paris, M. Fleming, et al., Specifications for the Generalised Nuclear Database Structure (GNDS)-version 1.9, Tech. Rep. Technical Report NEA–7519, Organisation for Economic Cooperation and Development (2020)

    work page 2020

  22. [22]

    D. A. Matters, A. M. Hurst, Westcott factors (GitHub repository). URLhttps://github.com/DMatters/WestcottFactors

    work page

  23. [23]

    D. A. Matters, A. M. Hurst, WestcottFactors (PyPI package). URLhttps://pypi.org/project/westcott/

    work page

  24. [24]

    Matters, T

    D. Matters, T. Kawano, Fork to DeCE develop branch (GitHub repository). URLhttps://github.com/DMatters/DeCE_g-Factor/tree/develop

    work page

  25. [25]

    D. A. Brown, et al., ENDF-6 formats manual, Tech. Rep. BNL-224854-2023-INR, Cross Sections Evaluations Working Group (September 2023)

    work page 2023

  26. [26]

    McKinney, Data structures for statistical computing in Python, in: S

    W. McKinney, Data structures for statistical computing in Python, in: S. van der Walt, J. Millman (Eds.), Proceedings of the 9th Python in Science Conference, 2010, pp. 56 – 61

    work page 2010

  27. [27]

    Mattoon, B

    C. Mattoon, B. Beck, G. Godfree, Managing and processing nuclear data libraries with FUDGE, EPJ Web of Conferences 284 (2023) 14010

    work page 2023

  28. [28]

    Mattoon, For updating data and generating evaluations (FUDGE): LLNL code for managing nuclear data (GitHub repository)

    C. Mattoon, For updating data and generating evaluations (FUDGE): LLNL code for managing nuclear data (GitHub repository). URLhttps://github.com/LLNL/fudge

    work page

  29. [29]

    Virtanen, SciPy 1.0 Contributors, SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nature Methods 17 (2020) 261–272

    P. Virtanen, SciPy 1.0 Contributors, SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nature Methods 17 (2020) 261–272

    work page 2020

  30. [30]

    A.L.Nichols,D.L.Aldama,M.Verpelli,Databaseextensions,August2008,in:HandbookofNuclearDataforSafeguards,no.INDC(NDS)- 0534, IAEA, Vienna, Austria, 2008

    work page 2008

  31. [31]

    van Sluijs, A

    R. van Sluijs, A. Stopic, R. Jacimovic, Evaluation of Westcott𝑔(𝑡𝑛)-factors used in𝑘 0-NAA for "non-1∕𝑣"(𝑛, 𝛾)reactions, Journal of Radioanalytical and Nuclear Chemistry 306 (2015) 579–587

    work page 2015

  32. [32]

    N. E. Holden, Temperature dependence of the Westcott𝑔-factor for neutron reactions in activation analysis (IUPAC technical report), Pure and Applied Chemistry 71 (12) (1999) 2309–2315

    work page 1999

  33. [33]

    Chand, S

    M. Chand, S. Bagchi, B. H. Khan, Determination of Westcott𝑔-factors for the assay of non-1∕𝑣nuclides using𝑘0-NAA, Applied Radiation and Isotopes 217 (2025) 111666

    work page 2025

  34. [34]

    Belgya, Prompt gamma activation analysis at the Budapest Research Reactor, Physics Procedia 31 (2012) 99–109

    T. Belgya, Prompt gamma activation analysis at the Budapest Research Reactor, Physics Procedia 31 (2012) 99–109

    work page 2012

  35. [35]

    Belgya, Z

    T. Belgya, Z. Kis, L. Szentmiklósi, Neutron flux characterization of the cold beam PGAA-NIPS facility at the Budapest research reactor, Nuclear Data Sheets 119 (2014) 419–421

    work page 2014

  36. [36]

    Révay, T

    Z. Révay, T. Belgya, Z. Kasztovszky, J. L. Weil, G. L. Molnár, Cold neutron PGAA facility at Budapest, Nuclear Instruments and Methods in Physics Research B 213 (2004) 385–388

    work page 2004

  37. [37]

    P.Kudejova,G.Meierhofer,K.Zeitelhack,J.Jolie,R.Schulze,A.Türler,T.Materna,ThenewPGAAandPGAIfacilityattheresearchreactor FRM II in Garching near Munich, Journal of Radioanalytical and Nuclear Chemistry 278 (3) (2008) 691–695

    work page 2008

  38. [38]

    C. L. Dunford, Organisation for Economic Co-Operation and Development, Nuclear Energy Agency - OECD/NEA, Inter: ENDF/B thermal cross-sections, resonance integrals, g-factors calculation. URLhttps://inis.iaea.org/records/fqpqg-d3r21

    work page

  39. [39]

    C. L. Dunford, Evaluated nuclear data file, ENDF/B-VI, in: S. M. Qaim (Ed.), Nuclear Data for Science and Technology, Springer Berlin Heidelberg, Berlin, Heidelberg, 1992, pp. 788–792. D.A. Matters et al.:Preprint submitted to ElsevierPage 15 of 29 Westcott𝑔Factors Extended to Arbitrary Neutron Energy Spectra Appendix: Maxwellian and Ideal-Guide Spectrum ...

    work page 1992