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Photonuclear Neutron Production in OpenMC: Verification Against MCNPX, FLUKA, and a First-Collision Analytical Solution

T0 review · 2 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read OpenMC's photonuclear branch reproduces MCNPX's integrated neutron yields to within 0.7% across six broomstick benchmarks.

desk verdict Useful, well-scoped verification of the unofficial OpenMC photonuclear branch, but the headline 0.7% agreement is not tied to reported statistical uncertainties and the paper ships no reproducible inputs. read the letter →

arxiv 2607.26045 v1 pith:N52GTEFC submitted 2026-07-28 physics.app-ph

Lorenzo Loi , Andrea Missaglia , Carolina Introini , David Breitenmoser , Shaun D. Clarke , Sara A. Pozzi , Antonio Cammi This is my paper · ORCID
classification physics.app-ph PACS 25.20.-x02.70.Uu28.20.-v
keywords photonuclearreactionsOpenMCMonteCarloverificationphotoneutronproductionMCNPXFLUKAdatabroomstickbenchmark
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper verifies the photonuclear capability of an unofficial OpenMC development branch. Using six 'broomstick' benchmarks—2H, 9Be, and 238U targets hit by monoenergetic 5 or 15 MeV photons and by a continuous 1–20 MeV LINAC-like spectrum—it finds that OpenMC and MCNPX agree within about 0.7% on integrated neutron yield when both use the same ENDF7u data. A first-collision analytical solution confirms the yields for the light nuclides, while FLUKA, using its own photonuclear models, lands 6–9% away in the monoenergetic cases and within about 4% for the continuous source. The paper's second point is that integral agreement does not imply spectral agreement: the 2H monoenergetic case shows similar totals but visibly different neutron energy spectra. A reader should care because it clears the integrated-yield barrier to adopting the photonuclear branch while mapping where further work—spectra, kinematics, nuclear data—still sits.

What carries the argument

The broomstick benchmark: an extremely long, infinitesimally thin cylinder (radius 1e-6 cm, lengths 3000 cm for 2H, 1500 cm for 9Be, 400 cm for 238U) aligned with a pencil photon beam. This geometry suppresses secondary transport, so the outward neutron current through the lateral surface can be compared directly with first-collision production. The analytical solution computes Y_n = ∫ (dNγ/dEγ) [1−exp(−Σtot L)] w(Eγ) dEγ, where w(Eγ) = Σn/Σtot is the expected number of neutrons produced per first photon interaction, with Σn the macroscopic neutron-production cross section (including multiplicities) and Σtot the total photon interaction cross section. In the axially thick limit the bracket b

What would settle it

A decisive check would be to rerun the 238U benchmarks with a shorter target length (so Σtot L is no longer ≫1) and compare against the full Eq. (5) rather than the axially thick limit; if OpenMC and MCNPX stop tracking the analytical prediction in exactly the way the factor 1−exp(−Σtot L) departs from 1, the 'current equals first-collision production' identification is the fragile step. Alternatively, an experimental 2H photodisintegration spectrum at 5 MeV would discriminate between ENDF7u's reported kinematic bug and the other models, since the paper attributes the spectral discrepancy to a

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Extended reading notes

Core claim

The central claim is that, under common ENDF7u photonuclear data, the OpenMC photonuclear branch's integrated neutron-production response is statistically indistinguishable from MCNPX's: the two codes agree within 0.7% across all six benchmark configurations. The paper argues this verifies the branch's handling of the common evaluated cross sections, reaction multiplicities, source weighting, and integrated neutron tallies for the tested nuclides and spectra. It also establishes a boundary: agreement in total yield does not certify agreement in the emitted-neutron spectrum, demonstrated most sharply by the monoenergetic 2H case, where OpenMC and MCNPX get the same total but different spectra

Load-bearing premise

The load-bearing premise is the 'infinitesimal radius' broomstick condition—radius 10^-6 cm—which guarantees that every neutron created in the first collision exits through the lateral surface without secondary transport, so the tallied outward current equals first-collision production; the paper also assumes for all cases, including 238U, that the axial interaction factor 1−exp(−Σtot L) is effectively unity, yet it does not report the numerical check.

Editorial extensions

If this is right

  • OpenMC's photonuclear branch can be trusted for integrated neutron-yield estimates in the tested energy–nuclide combinations, with the same caveats that apply to MCNPX-based results.
  • Users needing neutron energy or angular distributions should not rely on integral verification: the 2H monoenergetic case shows that identical totals can hide different spectra.
  • Nuclear-data choice matters more than code choice in several configurations: switching OpenMC from ENDF7u to IAEA/PD-2019 changed yields by up to 11.3%, larger than the code-to-code spread.
  • FLUKA's native-model results are within about 6–9% (monoenergetic) and about 4% (continuous) of the analytical reference, narrowing under broadband averaging even though local models differ.
  • The first-collision analytical solution is a practical reference for separating implementation errors from evaluated-data differences in photonuclear code verification.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the same six benchmarks could serve as regression tests if the photonuclear branch is ever proposed for integration into the official OpenMC distribution.
  • Beyond the paper: the 2H spectral mismatch points to a library-level kinematic issue (the paper cites an NJOY processing bug in older evaluations), implying that other codes using ENDF7u may also mis-sample spectra at 5 MeV even when yields are correct.
  • Beyond the paper: extending the broomstick design to angular-distribution scoring or to additional nuclides (e.g., 197Au, 63Cu) would test whether the 0.7% agreement holds beyond the three selected materials.
  • Beyond the paper: a quick analytic check of 1−exp(−Σtot L) over the 238U spectra would bound the residual bias in the analytical reference; the paper leaves that check unquantified.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper reports a verification study of an unofficial photonuclear development branch of OpenMC using six single-collision broomstick benchmarks. Targets are 2H, 9Be, and 238U, each exposed to a monoenergetic photon beam (5, 5, and 15 MeV, respectively) and to a continuous 1–20 MeV Kramers bremsstrahlung spectrum. OpenMC is compared with MCNPX under the same ENDF7u photonuclear data, with FLUKA using its native photonuclear models, and with a first-collision analytical solution for integrated neutron yield. Additional OpenMC runs with IAEA/PD-2019 quantify nuclear-data sensitivity. The principal finding is that OpenMC and MCNPX agree within about 0.7% in integrated neutron yield for all six configurations, while FLUKA and IAEA/PD-2019 deviate by larger amounts. The paper concludes that the branch reproduces integrated neutron production in the tested idealized geometries, while energy-differential spectra remain model- and data-sensitive.

Significance. This is a timely and appropriately scoped verification of a capability that is not yet in the official OpenMC distribution. The use of a common evaluated library for the primary OpenMC–MCNPX comparison is a sound way to separate implementation differences from data differences, and the chosen nuclides exercise distinct photonuclear mechanisms (two-body disintegration, multi-body breakup, actinide multi-channel/fission competition). The work also usefully demonstrates that integral agreement does not imply spectral agreement, and it quantifies sensitivity to the underlying nuclear-data evaluation. The paper is honest about the verification/validation distinction and about the idealized nature of the broomstick geometry. If the central quantitative claim is supported by reported statistical uncertainties, the paper will be a useful reference for the community; as it stands, that support is missing.

major comments (2)
  1. [III.B / Fig. 5 / Sec. II.B] The central claim, “OpenMC and MCNPX agreed within approximately 0.7%,” is not accompanied by any statistical uncertainty. Section II.B says that uncertainties correspond to the standard errors of the respective tally estimators, but no standard errors are given, plotted, or used to test whether 0.7% is statistically distinguishable from zero. For a low-yield configuration such as 9Be at 5 MeV (integrated yield on the order of 1e-3 per source photon), 1e8 source photons imply a Poisson relative error of roughly 0.3–0.5%; a 0.7% code difference is then on the order of 1–2 sigma. The same issue affects the energy-resolved comparison in Fig. 4, where low-count bins could be statistically indistinguishable. Please report per-bin and integrated relative errors (or confidence intervals) for all codes and all configurations, and state explicitly whether the quoted 0.7% is the observed differenc
  2. [II.C, Eqs. (7)–(11)] The paper itself states that the axially thick approximation underlying Eqs. (8) and (11) “must therefore be established by evaluating the finite-length interaction factor,” but no such evaluation is reported for any target. This matters for the analytical reference, especially for 238U, where L is only 400 cm and the factor 1−exp(−Σtot L) is not identically unity. The reader is asked to accept that the approximation is exact without a quantitative check. Please report either the minimum value of the finite-length factor over the contributing photon-energy range or the resulting correction to Yn for each case, even if the correction is negligible.
minor comments (5)
  1. [Abstract / Sec. II.C] The analytical solution is explicitly constructed from the same ENDF7u data used by OpenMC and MCNPX. Although Sec. II.C acknowledges this, the abstract and title present the analytical solution as a separate verification reference. Please qualify it as a consistency check of the implementation under a shared data library rather than an independent verification of the yield.
  2. [Sec. II.C, Eq. (2)] The photofission multiplicity νf is said to be energy dependent, but no explicit prescription or source for νf(Eγ) is given. Since the 238U cases rely on this quantity, a brief definition or citation would help.
  3. [Sec. II.B / Reproducibility] For a verification of an unofficial development branch, the exact code state matters. Please provide the specific commit hash (or version) of the Stein photonuclear branch used for all OpenMC calculations, and state whether the input decks are available in a repository.
  4. [Fig. 5] Several deviation labels are difficult to read (e.g., “1.87e-02%” and “3.64e-04%”), and the plot mixes different marker styles across panels. A small table of the integrated yields and deviations with uncertainties would be clearer than the crowded figure.
  5. [Sec. IV / Limitations] The FLUKA comparison combines implementation, model, and data differences. The paper states this correctly, but the conclusion should avoid implying that FLUKA provides an independent verification of OpenMC; it is better described as a cross-model plausibility check.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the analytical solution is a same-data consistency check, explicitly disclosed, while the core verification rests on independent code-to-code comparisons with MCNPX and FLUKA.

full rationale

The paper's central claim is a code-implementation verification: OpenMC and MCNPX use the same ENDF7u photonuclear data but are independent Monte Carlo implementations, and their sub-percent agreement tests whether the unofficial OpenMC branch processes the common evaluated cross sections consistently. This is not circular because the comparison is between two separate transport codes, not between a fitted model and its training target. The first-collision analytical solution is derived in the paper from the same ENDF7u cross sections used by OpenMC and MCNPX, and the paper explicitly states this: 'The photonuclear cross sections used in the analytical solution were taken from the ENDF7u evaluation adopted in the common-data OpenMC–MCNPX comparison. Consequently, the analytical result provides an additional check of the evaluated-data calculations, but it is not expected to reproduce the native FLUKA photonuclear model channel by channel.' This is a transparent internal consistency check, not a disguised external prediction; the paper does not claim the analytical solution independently validates the nuclear data. The FLUKA comparison uses independent native photonuclear models, and the IAEA/PD-2019 sensitivity study is explicitly separated from code verification. The only self-citation, reference [17], is a disclosed preliminary conference paper and is not load-bearing for the derivation; it is cited for context and for the statement that no prior peer-reviewed verification existed. The acknowledgment that the finite-length approximation 'must therefore be established' is an honest limitation and a correctness/completeness issue, not a circularity. Missing statistical uncertainties in the 0.7% claim are a statistical-reporting concern, not a circular-derivation concern. No step in the derivation reduces to its own inputs by construction.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No parameters were fitted to Monte Carlo results; the analytical solution uses evaluated cross sections and multiplicities directly. The benchmark geometry involves hand-chosen dimensions, of which the radial limit is the most consequential. The main assumptions are the single-collision escape of secondaries and the use of ENDF7u as a common data reference; the paper discloses that this makes the analytic solution a consistency check rather than an external benchmark.

free parameters (1)
  • Broomstick target radius = 1e-6 cm
    Chosen by hand as an 'optimal lower limit' for the single-collision limit; it defines the geometry but is not fitted to any yield and cancels in the analytical w(E) expression for single-nuclide targets.
assumptions (5)
  • standard math First-collision balance and exponential attenuation (Eqs. 2-5) correctly describe the expected neutron production.
    Standard radiation-transport bookkeeping; used to build the analytical reference in Section II.C.
  • domain assumption Broomstick single-collision premise: the radial dimension is so small that neutrons and secondaries escape without further transport.
    Justifies equating the lateral-surface current with first-collision production; entered in Section II.A via the 1e-6 cm radius.
  • domain assumption Axially thick / finite-length factor is handled correctly: either 1−exp(−Σtot L) ≈ 1 or the exact finite-length expression is used.
    The analytical yield is sensitive to this factor for 238U because Σtot L is finite; Section II.C says the applicability must be established but does not report the check.
  • domain assumption ENDF7u evaluated photonuclear data are an adequate common reference for the code-implementation comparison.
    The same library is used for OpenMC, MCNPX, and the analytical solution; the paper separately notes known deficiencies in photonuclear evaluations via ref. [18].
  • domain assumption FLUKA's native photonuclear models constitute an independent model-based reference.
    Used to detect differences not attributable to common evaluated data; described in Section II.B.

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Cite this review

Pith. "Pith review of Photonuclear Neutron Production in OpenMC: Verification Against MCNPX, FLUKA, and a First-Collision Analytical Solution." pith.science (2026). https://pith.science/paper/N52GTEFC

@misc{pith2026260726045,
  author       = {Pith},
  title        = {Pith review of: Photonuclear Neutron Production in OpenMC: Verification Against MCNPX, FLUKA, and a First-Collision Analytical Solution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N52GTEFC}},
  note         = {Machine review of arXiv:2607.26045}
}
read the original abstract

The modeling of photonuclear reactions is increasingly important for applications involving high-energy photon fields, including accelerator-driven neutron sources, radiation shielding, medical physics, and fusion technologies. Although the Monte Carlo code OpenMC provides well-verified photoatomic transport capabilities, its photonuclear physics is currently available only in an unofficial development branch and requires independent verification before broader scientific use or possible integration into the official code distribution. This work presents a systematic verification of the OpenMC photonuclear implementation using six single-collision broomstick benchmarks based on 2H, 9Be, and 238U targets irradiated by monoenergetic 5 MeV and 15 MeV photons and by a continuous 1--20 MeV linear accelerator (LINAC)-representative spectrum. OpenMC was compared with MCNPX using common ENDF7u photonuclear data, with FLUKA using its native photonuclear models, and with a first-collision analytical solution for the integrated neutron yield. Calculations using the IAEA/PD-2019 library were also performed to quantify nuclear-data sensitivity. OpenMC and MCNPX agreed within 0.7% in integrated neutron yield for all benchmark cases when the same ENDF7u data were used. FLUKA, which relies on its own native photonuclear models rather than ENDF7u, differed from the analytical solution by approximately 6-9% for the monoenergetic cases and by no more than approximately 4% for the continuous-source cases. Changing the OpenMC library to IAEA/PD-2019 produced deviations of up to 11.3% from the ENDF7u-based analytical solution, with the sensitivity varying strongly by nuclide and source spectrum.

Figures

Figures reproduced from arXiv: 2607.26045 by the authors.

Figure 1
Figure 1. Schematic representation of the photonuclear broomstick benchmark. A mono-directional [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Microscopic photoatomic and neutron-producing photonuclear cross sections for [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Expected number of neutrons produced per first photon interaction, [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Energy-resolved neutron yields for the six broomstick benchmarks: (a) [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: Integrated neutron-yield comparison for (a,b) the three monoenergetic benchmarks and [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]

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Reference graph

Works this paper leans on

47 extracted references · 8 canonical work pages

  1. [1]

    Werner, Christopher J and others , year=

  2. [2]

    and Hansen, Luisa F

    Cullen, Dermott E. and Hansen, Luisa F. and Lent, Edward M. and Plechaty, Ernest F. , title =. 2003 , month = may, doi =

    2003

  3. [3]

    Caldwell, J. T. and Dowdy, E. J. and Berman, B. L. and Alvarez, R. A. and Meyer, P. , title =. Physical Review C , volume =. 1980 , doi =

    1980

  4. [4]

    2000 , issn =

    Estimations of neutron yield from beryllium target irradiated by SPring-8 hard synchrotron radiation , journal =. 2000 , issn =. doi:https://doi.org/10.1016/S0168-9002(99)00706-8 , author =

    work page doi:10.1016/s0168-9002(99)00706-8 2000

  5. [5]

    Zilges and D.L

    A. Zilges and D.L. Balabanski and J. Isaak and N. Pietralla , keywords =. Photonuclear reactions—From basic research to applications , journal =. 2022 , issn =. doi:https://doi.org/10.1016/j.ppnp.2021.103903 , url =

    arXiv 2022

  6. [6]

    and Constantin, Paul

    Balabanski, Dimiter L. and Constantin, Paul. 80 years of experimental photo-fission research. Eur. Phys. J. A. 2024. doi:10.1140/epja/s10050-024-01264-z

    work page doi:10.1140/epja/s10050-024-01264-z 2024

  7. [7]

    Loi and A

    L. Loi and A. Missaglia and D. Alesini and H. Braun and A. Cammi , title =. Proceedings of PHYSOR 2026 International Conference , year = 2026, publisher =. doi:10.5281/zenodo.20804002 , url =

    work page doi:10.5281/zenodo.20804002 2026

  8. [8]

    and Gheorghe, I

    Filipescu, D. and Gheorghe, I. and Goriely, S. and Tudora, A. and Nishio, K. and Ohtsuki, T. and Wang, H. and Fan, G. and Stopani, K. and Suzaki, F. and Hirose, K. and Inagaki, M. and Lui, Y.-W. and Ari-izumi, T. and Miyamoto, S. and Otsuka, T. and Utsunomiya, H. , journal =. Giant dipole resonance photofission and photoneutron reactions in ^. 2024 , month =

    2024

Show all 47 references
  1. [9]

    Findlay ,doi=

    D.J.S. Findlay ,doi=. Applications of photonuclear reactions ,year=. Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms ,abstract=

  2. [10]

    Mahabub Morshed and Hamid Osman and Fawzi F

    Md Fakhar Uddin and Shirin Akter and Mahiuddin Ahmed and Bushra Nufrin Sattar and K.M. Mahabub Morshed and Hamid Osman and Fawzi F. Bokhari and Sultan J. Alsufyani and Shams A.M. Issa and Mayeen Uddin Khandaker , keywords =. Photoneutron production mechanisms, their characteri...

    2024

  3. [11]

    Tsechanski and A.F

    A. Tsechanski and A.F. Bielajew and J.P. Archambault and E. Mainegra-Hing , keywords =. Electron accelerator-based production of molybdenum-99: Bremsstrahlung and photoneutron generation from molybdenum vs. tungsten , journal =. 2016 , issn =. doi:https://doi.org/10.1016/j.nim...

    2016 doi

  4. [12]

    Kharkiv Institute of Physics and Technology

    Neutron Source Facility of the National Science Center "Kharkiv Institute of Physics and Technology" at Kharkiv, Ukraine , author =. 2021 , number =

    2021

  5. [13]

    Loi and A

    L. Loi and A. Missaglia and C. Introini and F. C. Giacobbo and E. Padovani and A. Cammi , title =. Proceedings of PHYSOR 2026 International Conference , year = 2026, publisher =. doi:10.5281/zenodo.20803408 , url =

    2026 doi

  6. [14]

    H. A. Kramers , title =. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science , volume =. 1923 , publisher =. doi:10.1080/14786442308565244 , URL =

    1923 doi

  7. [15]

    Dietrich, S. S. and Berman, B. L. , title =. Atomic Data and Nuclear Data Tables , volume =. 1988 , doi =

    1988

  8. [16]

    Chadwick, M. B. and others , title =. Nuclear Data Sheets , volume =. 2011 , doi =

    2011

  9. [17]

    2015 , note =

    Annals of Nuclear Energy , volume =. 2015 , note =. doi:https://doi.org/10.1016/j.anucene.2014.07.048 , author =

    2015 doi

  10. [18]

    Shriwise and Songlin Liu , keywords =

    Xiaokang Zhang and Patrick C. Shriwise and Songlin Liu , keywords =. Implementation and verification of PyNE R2S with DAG-OpenMC , journal =. 2020 , issn =. doi:https://doi.org/10.1016/j.fusengdes.2020.111837 , url =

    2020

  11. [19]

    Nuclear Fusion , year=

    Development and validation of fully open-source R2S shutdown dose rate capabilities in OpenMC , author=. Nuclear Fusion , year=

  12. [20]

    2022 , month =

    Bae, Jin Whan and Peterson, Ethan and Shimwell, Jonathan , title =. 2022 , month =. doi:10.1088/1741-4326/ac5450 , url =

    2022 doi

  13. [21]

    A newly developed and verified transport capacity of Monte Carlo photon particles in RMC , journal =

    Hao Luo and Shanfang Huang and Kan Wang and Xiang Xiao , keywords =. A newly developed and verified transport capacity of Monte Carlo photon particles in RMC , journal =. 2024 , issn =. doi:https://doi.org/10.1016/j.cpc.2023.108935 , url =

    2024

  14. [22]

    2018 , doi=

    Implementation and Validation of Photon Transport in OpenMC , author=. 2018 , doi=

    2018

  15. [23]

    , title =

    Parsons, Donald Kent and Toccoli, Cecile A. , title =. 2020 , month =. doi:10.2172/1776727 , url =

    2020 doi

  16. [24]

    Nuclear Science and Engineering , year=

    Comparison of the TRIPOLI-4®, DIANE, and MCNP6 Monte Carlo Codes on the Barber & George Benchmark for Photonuclear Reactions , author=. Nuclear Science and Engineering , year=

  17. [25]

    2024 , url =

    Dave Heinrichs and Ed Lent , title =. 2024 , url =

    2024

  18. [26]

    2024 , howpublished =

    Guy Stein , title =. 2024 , howpublished =

    2024

  19. [27]

    Book Title in Italic , Url =

    Author, Emily Ford and Author, First Middle , Publisher =. Book Title in Italic , Url =

  20. [28]

    Conference Paper Title , Year =

    Author(s), Charles Darwin , Booktitle =. Conference Paper Title , Year =

  21. [29]

    Title , Volume =

    Author(s), Bee , Journal =. Title , Volume =

  22. [30]

    Kochunas, Brendan , Title =

  23. [31]

    Proceedings of the PHYSOR-2024 , title=

    A, Author and B, Author and C, Author and D, Author , year=. Proceedings of the PHYSOR-2024 , title=

    2024

  24. [32]

    Characterization of photoneutron fluxes emitted by electron accelerators in the 4–20 MeV range using Monte Carlo codes: A critical review , journal =

    Adrien Sari , keywords =. Characterization of photoneutron fluxes emitted by electron accelerators in the 4–20 MeV range using Monte Carlo codes: A critical review , journal =. 2023 , issn =. doi:https://doi.org/10.1016/j.apradiso.2022.110506 , url =

    2023

  25. [33]

    Journal of Instrumentation , volume=

    A reconsideration of photoneutron production through a 5 MeV electron LINAC using MCNP and FLUKA , author=. Journal of Instrumentation , volume=. 2023 , publisher=

    2023

  26. [34]

    and Boicourt, R

    Macfarlane, Robert and Muir, Douglas W. and Boicourt, R. M. and Kahler, III, Albert Comstock and Conlin, Jeremy Lloyd , title =. 2017 , month =. doi:10.2172/1338791 , url =

    2017 doi

  27. [35]

    Pomraning, G. C. , Edition =. Linear Kinetic Theory and Particle Transport in Stochastic Mixtures , Year =

  28. [36]

    Adams, M. L. and Larsen, E. W. and Pomraning, G. C. , Journal =. Benchmark Results for Particle Transport in a Binary Markov Statistical Medium , Volume =

  29. [37]

    Zimmerman, G. B. and Adams, M. L. , Journal =. Algorithms for Monte-Carlo Particle Transport in Binary Statistical Mixtures , Volume =

  30. [38]

    Donovan, T. J. and Danon, Y. , Journal =. Application of Monte Carlo Chord-Length Sampling Algorithms to Transport Through a Two-Dimensional Binary Stochastic Mixture , Volume =. doi:https://doi.org/10.13182/NSE03-A2332 , Year =

    doi

  31. [39]

    , Keywords =

    Vasques, R. , Keywords =. A Review of Particle Transport Theory in a Binary Stochastic Medium , School =

  32. [40]

    Fichtl, E. D. , Keywords =. Stochastic Methods for Uncertainty Quantification in Radiation Transport , School =

  33. [41]

    Brantley, B. S. , title =. Proc. Int. Conf. on Mathematics, Computational Methods and Reactor Physics (M&C2009) , month =. 2009 , address =

    2009

  34. [42]

    Pautz, S. D. and Franke, B. C. , Institution =. The Levermore--Pomraning and Atomic Mix Closures for n-ary Stochastic Materials , Year =

  35. [43]

    Bohlen, T. T. and Cerutti, F. and Chin, M. P. W. and Fassò, A. and Ferrari, A. and Ortega, P. G. and Mairani, A. and Sala, P. R. and Smirnov, G. and Vlachoudis, V. , title =. Nuclear Data Sheets , volume =. 2014 , doi =

    2014

  36. [44]

    and Boehlen, T

    Battistoni, G. and Boehlen, T. and Cerutti, F. and Chin, P. W. and Esposito, L. S. and Fassò, A. and Ferrari, A. and Lechner, A. and Empl, A. and Mairani, A. and others , title =. Annals of Nuclear Energy , volume =. 2015 , doi =

    2015

  37. [45]

    and Clarke, Shaun D

    Pozzi, Sara A. and Clarke, Shaun D. and Walsh, William J. and Miller, Eric C. and Dolan, Jennifer L. and Flaska, Marek and Wieger, Benjamin M. and Enqvist, Andreas and Padovani, Enrico and Mattingly, John K. and Chichester, David L. and Peerani, Paolo , title =. Nuclear Instru...

    2012

  38. [46]

    and Cho, Y

    Kawano, T. and Cho, Y. S. and Dimitriou, P. and Filipescu, D. and Iwamoto, N. and Plujko, V. and Tao, X. and Utsunomiya, H. and Varlamov, V. and Xu, R. and Capote, R. and others , title =. Nuclear Data Sheets , volume =. 2020 , doi =

    2020

  39. [47]

    Pelowitz, D. B. , title =

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