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docs/2026_data_publication/bibliography.bib

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year = {2024},
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pages = {197},
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file = {Full Text PDF:/home/luke/snap/zotero-snap/common/Zotero/storage/Q8PQXJ6I/Leconte et al. - 2024 - Accurate measurements of delayed neutron data for reactor applications methodology and application.pdf:application/pdf},
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}
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}
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@techreport{nobreENDFBVIII12024,
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title = {{ENDF}/{B}-{VIII}.1},
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url = {https://www.osti.gov/biblio/2571019},
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doi = {10.11578/endf/2571019},
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abstract = {The ENDF/B-VIII.1 release is the newest evaluated nuclear data library produced, distributed, and recommended by CSEWG for use in nuclear science and technology applications. Among the many key advances, relative to the previous version ENDF/B-VIII.0, are: re-evaluation of 239Pu file by a joint international effort; updated 16,18O, 19F, 28-30Si, 50-54Cr, 55Mn, 54,56,57Fe, 63,65Cu, 139La, 233,235,238U, and 240,241Pu neutron nuclear data by the IAEA-coordinated INDEN collaboration; significant changes for 3He, 6Li, 9Be, 51V, 88Sr, 103Rh, 140,142Ce, Dy, 181Ta, Pt, 206-208Pb, and 234,236U neutron data; new nuclear data for the photo-nuclear, being 196 adopted from the IAEA2019 Photonuclear Data Library and one new file from JENDL-5; and new evaluations for the charged-particle and atomic sublibraries. Numerous thermal neutron scattering kernels were re-evaluated or provided for the very first time. Additionally, new covariance testing was implemented. ENDF/B-VIII.1 reduced bias in the simulations of many integral experiments with particular progress noted for fluorine, copper and stainless steel containing benchmarks. Data issues which had hindered the deployment of ENDF/B-VIII.0 for commercial nuclear power applications in high burn-up situations, were addressed. ENDF/B-VIII.1 data are distributed in both ENDF-6 and GNDS formats.},
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language = {English},
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urldate = {2026-04-03},
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institution = {Brookhaven National Lab},
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author = {Nobre, G. and Capote, R. and Pigni, M. and Trkov, A. and Mattoon, C. and Neudecker, D. and Brown, D. and Chadwick, M. and Kahler, A. and Kleedtke, N. and Zerkle, M. and Hawari, A. and Chapman, C. and Fleming, N. and Wormald, J. and Ramić, K. and Danon, Y. and Gibson, N. and Brain, P. and Paris, M. and Hale, G. and Thompson, I. and Barry, D. and Stetcu, I. and Haeck, W. and Lovell, A. and Mumpower, M. and Potel, G. and Kravvaris, K. and Noguere, G. and McDonnell, J. and Carlson, A. and Dunn, M. and Kawano, T. and Wiarda, D. and Al-Qasir, I. and Arbanas, G. and Arcilla, R. and Beck, B. and Bernard, D. and Beyer, R. and Brown, J. and Cabellos, O. and Casperson, R. and Cheng, Y. and Chimanski, E. and Coles, R. and Cornock, M. and Cotchen, J. and Crozier, J. and Cullen, D. and Daskalakis, A. and Descalle, M.-A. and DiJulio, D. and Dimitriou, P. and Dreyfuss, A. and Durán, I. and Ferrer, R. and Gaines, T. and Gillette, V. and Gert, G. and Guber, K. and Haverkamp, J. and Herman, M. and Holmes, J. and Hursin, M. and Jisrawi, N. and Junghans, A. and Kelly, K. and Kim, H. and Kim, K. and Koning, A. and Koštál, M. and Laramee, B. and Lauer-Coles, A. and Leal, L. and Lee, H. and Lewis, A. and Malec, J. and Damián, J. and Marshall, W. and Mattera, A. and Muhrer, G. and Ney, A. and Ormand, W. and Parsons, D. and Percher, C. and Pritychenko, B. and Pronyaev, V. and Qteish, A. and Quaglioni, S. and Rapp, M. and Ressler, J. and Rising, M. and Rochman, D. and Romano, P. and Roubtsov, D. and Schnabel, G. and Schulc, M. and Siemers, G. and Sonzogni, A. and Talou, P. and Thompson, J. and Trumbull, T. and Marck, S. and Vorabbi, M. and Wemple, C. and Wendt, K. and White, M. and Wright, R.},
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month = aug,
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year = {2024}
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}

docs/2026_data_publication/images/b80/section.tex

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\begin{figure}
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\centering
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\includegraphics[width=0.5\linewidth]{images/b80/pcc-bar.png}
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\caption{The ten largest uncertainty-weighted \glspl{PCC} $U_{i,v}$ sorted by \gls{DNP} and associated \gls{DNP} value from ENDF/B-VII.1 nuclear data.}
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\caption{The ten largest uncertainty-weighted \glspl{PCC} $U_{i,v}$ sorted by \gls{DNP} and associated \gls{DNP} value from ENDF/B-VIII.0 nuclear data.}
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\label{fig:b80-bar-uiv}
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\end{figure}
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docs/2026_data_publication/images/hybrid/section.tex

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\begin{table}[!h]
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\centering
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\caption{Total delayed neutron yields $\nu_d$ from 100 thermal fissions of $^{235}$U.}
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\begin{threeparttable}
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\begin{tabular}{ll}
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\hline
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Data & $\nu_d$ $[-]$ \\
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IAEA/JENDL-5 \cite{DIMITRIOU2021144, iwamoto2023japanese} & $1.596 \pm 0.09$\\
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ENDF/B-VII.1 \cite{chadwick2011endf} & $1.906 \pm 0.11$\\
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ENDF/B-VIII.0 \cite{Brown20181} & $2.023 \pm 0.11$\\
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ENDF/B-VIII.1 \cite{nobreENDFBVIII12024}\tnote{*} & $2.023 \pm 0.11$\\
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JEFF-3.1.1 \cite{santamarina2009jeff} & $1.477 \pm 0.08$\\
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JENDL-5 \cite{iwamoto2023japanese} & $1.597 \pm 0.09$ \\
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\hline
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\end{tabular}
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\begin{tablenotes}
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\small
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\item[*] ENDF/B-VIII.1 did not resolved the delayed neutron yield discrepancy present in the previous ENDF versions.
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\end{tablenotes}
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\end{threeparttable}
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\label{tab:total-delnu-compare-net}
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\end{table}
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\subsubsection{Nuclear Data Comparisons}
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The results thus far have indicated potential discrepancies in the ENDF cumulative fission yields for \glspl{DNP}.
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To investigate this, cumulative fission yield differences between JENDL-5 and ENDF/B-VIII.0 are compared for the \glspl{DNP} with the largest delayed neutron yield $\nu_d(I)$ contribution differences.
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To investigate this, cumulative fission yield differences between JENDL-5 and ENDF/B-VIII.0\footnote{Analysis with ENDF/B-VIII.1 gives the same results.} are compared for the \glspl{DNP} with the largest delayed neutron yield $\nu_d(I)$ contribution differences.
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This analysis showed there are two \glspl{DNP} alone that account for 67\% of the delayed neutron yield difference: $^{86}$As and $^{137}$Sb.
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The $^{86}$As yield difference primarily comes from the cumulative fission yield difference, which is $540 \pm 90$ $pcm$ larger in ENDF/B-VIII.0 than JENDL-5, and leads to a delayed neutron yield difference of $191 \pm 32$ $pcm$.
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The discrepancy between the $^{86}$As in ENDF data has been reported on previously for ENDF/B-VII.0 and ENDF/B-VII.1, respectively \cite{foligno_new_2019, mills2014calculation}.
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docs/2026_data_publication/main.tex

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\begin{document}
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\title{Investigation of Delayed Neutron Precursor Data Uncertainties for Microscopic and Summation Calculations} %title of paper
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\title{Investigation of Delayed Neutron Precursor Data Uncertainties for Microscopic Calculations} %title of paper
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% Use the \addAuthor macro to add authors in the order they should appear. The second argument corresponds to
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% the affiliation declared below.
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This approach uses experimental data for individual \glspl{DNP} combined together computationally.
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One strength of this approach is that it provides insight into how each individual \gls{DNP} contributes to the \gls{DNP} group parameters.
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However, this strength is also a weakness, as it relies on the nuclear data for every \gls{DNP} individually, which means a few large uncertainties in the various \glspl{DNP} can lead to uncertain results for the \gls{DNP} group parameters.
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There is also a related, and similar approach, called the summation approach.
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This approach uses the same data, and is used for calculation of summed parameters such as the total delayed neutron yield $\nu_d$ and the average half-life $\bar\tau$.
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The microscopic approach can also be used for calculation of summed parameters such as the total delayed neutron yield $\nu_d$ and the average half-life $\bar\tau$ directly from the \glspl{DNP} data, generally referred to as conducting a summation, or aggregate, calculation.
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There have been investigations in the literature that use the microscopic and summation approaches to evaluate sensitivities and compare different datasets \cite{foligno_summation_2018, foligno_new_2019, mills2014calculation}.
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There have been investigations in the literature that use the microscopic approach to evaluate sensitivities and compare different datasets \cite{foligno_summation_2018, foligno_new_2019, mills2014calculation}.
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Although these analyses are informative and show many of the differences between datasets, they do not discuss the importance of \glspl{DNP} in regards to their effect on the calculated \gls{DNP} group parameters but instead based on their contribution to the total delayed neutron yield.
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Generally the larger the delayed neutron yield of a \gls{DNP}, the more important it is, but these analyses do not investigate how the uncertainty in each \gls{DNP} propagates through to calculated \gls{DNP} group parameters.
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\subsection{Microscopic and Summation Calculations}
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For the microscopic and summation methods, there are two distinct solution methods.
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The summation method is the simpler of the two, and simply involves summing the nuclear data to calculate the total delayed neutron yield and average half-life.
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The microscopic method is more in-depth, as it is used to calculate the \gls{DNP} group parameters, which give time-dependency and can be used to calculate the total delayed neutron yield and average half-life.
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Within the microscopic approach, there are two distinct processes that can be used.
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The summation calculation is the simpler of the two, and simply involves summing the nuclear data to calculate the total delayed neutron yield and average half-life.
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The full microscopic approach is used to calculate the \gls{DNP} group parameters, which give time-dependency and can be used to calculate the total delayed neutron yield and average half-life from the \gls{DNP} group parameters as well as the \gls{DNP} nuclear data.
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Equations \eqref{eq:summation-tdny} and \eqref{eq:avg-hl} are the equations for the total delayed neutron yield and average half-life, respectively, calculated using the summation approach as:
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Equations \eqref{eq:summation-tdny} and \eqref{eq:avg-hl} are the equations for the total delayed neutron yield and average half-life, respectively, from the summation calculation as:
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\begin{equation}
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\nu_d = \sum_{i=1}^I P_{n,i} CFY_i,
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\label{eq:summation-tdny}
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\label{eq:avg-hl}
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\end{equation}
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The uncertainties for each calculation can be propagated as shown in Equations \eqref{eq:summation-tdny-delta} and \eqref{eq:avg-hl-delta} as:
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The uncertainties for each calculation are propagated as shown in Equations \eqref{eq:summation-tdny-delta} and \eqref{eq:avg-hl-delta} as:
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\begin{equation}
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\Delta \nu_d^2 = \sum_{i=1}^I (\Delta P_{n,i} CFY_i)^2 + (P_{n,i} \Delta CFY_i)^2,
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\label{eq:summation-tdny-delta}
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The standard deviation propagated in the summation calculation are given by the dataset used, and any values without a standard deviation or a standard deviation of 0 use a value of $10^{-12}$.
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The microscopic approach enables calculation of time-dependent parameters by calculating the delayed neutron count rate from each \gls{DNP} after irradiation of a fissile nuclide.
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The solver first calculates the concentration of each \gls{DNP}, followed by the delayed neutron count rate, and finally uses the Scipy optimize module to calculate the six \gls{DNP} group parameters that optimally fit that delayed neutron count rate \cite{scipy}.
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The solver first calculates the concentration of each \gls{DNP}, followed by the delayed neutron count rate, and finally uses the SciPy optimize module to calculate the six \gls{DNP} group parameters that optimally fit that delayed neutron count rate \cite{scipy}.
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To calculate sensitivities and propagate uncertainties, a Monte Carlo sampling technique is used \cite{foligno_new_2019}.
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The solution is calculated with tolerances of $10^{-11}$ for ten randomly sampled initial conditions for the nominal nuclear data, which is then passed as an initial guess for each of the sampled Monte Carlo solves.
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The concentrations have the uncertainty propagated using the uncertainties package, and then in the count rate calculation the concentration $N_i$, half-life $\tau_i$, and emission probability $P_{n,i}$ are sampled using a normal distribution with a different random value for each \gls{DNP}.
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This work is also verified with the total delayed neutron yield $\nu_d$ from Leconte et al. from JEFF-3.1.1 cumulative fission yields combined with ENDF/B-VII.1 emission probabilities and half-lives.
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Specifically, this work calculates a value of $0.0157 \pm 0.0008$, which exactly agrees with the results from Leconte et al. \cite{leconte2020new}.
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Finally, there is also agreement with Huynh et al. using the JEFF-3.1.1 data to calculate the total delayed neutron yield of $0.0148 \pm 0.0008$ \cite{huynh2014calculation}.
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The verification uses the results from summation calculations, but each section demonstrates that the summation calculation results offer agreement within uncertainty bounds between the \gls{DNP} group parameter evaluated values and the summation calculation values.
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For the first set of results, additional information will be included that is not included in the other sections.
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Specifically, the delayed neutron count rate will be provided as well as a comparison to the count rate from calculated from other \gls{DNP} group parameters in the literature.

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