Clean up and finish conclusion

Author: LukeSeifert

docs/2026_data_publication/bibliography.bib

@@ -59,13 +59,15 @@
 This is useful to note, as based on the uncertainty-weighted \glspl{PCC} calculated in Sections \ref{sec:b71} and \ref{sec:b80}, the emission probability data is the data in most need of updating.
 This is because the ENDF data has smaller relative uncertainties for the cumulative fission yields even though they do not agree well with the JEFF-3.1.1 and JENDL-5 cumulative fission yields.
 
-Table \ref{tab:total-delnu-compare-net} shows how total delayed neutron yields from the literature calculated using summation approaches or from experimental data compare with the results from this work.
-Among the values shown in Table \ref{tab:total-delnu-compare-net}, the outliers are the ENDF/B-VII.1 and ENDF/B-VIII.0 $\nu_d$ values.
+Table \ref{tab:total-delnu-compare-net} shows a small collection of total delayed neutron yields from the literature calculated using summation approaches or from experimental data compare with the results from this work.
+There are many existing analyses that calculate and measure the total delayed neutron yield, with various collections available in the literature \cite{d2002review, rudstam2002delayed, huynh2014calculation, parish1999status, blachot_status_1990, waldo1981delayed}.
+Generally, there has been increasing agreement over time that the delayed neutron yield for thermal fission of $^{235}$U is approximately $0.01625 \pm 0.01$ \cite{leconte_accurate_2024}.
+Among the values shown in Table \ref{tab:total-delnu-compare-net} and based on the agreed upon $\nu_d$ value, the outliers are the ENDF/B-VII.1 and ENDF/B-VIII.0 $\nu_d$ values. 
+
 
 \begin{table}[!h]
     \centering
-    \caption{Total delayed neutron yields $\nu_d$ of 100 fissions from thermal fission of $^{235}$U (based on \cite{huynh2014calculation}).}
-    \begin{threeparttable}
+    \caption{Total delayed neutron yields $\nu_d$ from 100 thermal fissions of $^{235}$U.}
     \begin{tabular}{ll}
         \hline
        Data & $\nu_d$ $[-]$ \\
@@ -79,6 +81,7 @@
         Synetos and Williams \cite{synetos1983delayed} & $1.510 \pm 0.06$ \\
         Tuttle \cite{tuttle1975delayed} & $1.700 \pm  0.05$\\
         Waldo et al.\cite{waldo1981delayed} & $1.670 \pm 0.07$ \\
+        Rudstam et al. \cite{rudstam2002delayed} & $1.620$\\
         \hline
         IAEA/JENDL-5 \cite{DIMITRIOU2021144, iwamoto2023japanese} & $1.596 \pm 0.09$\\
         ENDF/B-VII.1 \cite{chadwick2011endf} & $1.906 \pm 0.11$\\
@@ -88,15 +91,54 @@
         \hline
     \end{tabular}
     \label{tab:total-delnu-compare-net}
-    \end{threeparttable}
 \end{table}
 
+\subsubsection{Nuclear Data Comparisons}
+
 The results thus far have indicated potential discrepancies in the ENDF cumulative fission yields for \glspl{DNP}.
 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.
 This analysis showed there are two \glspl{DNP} alone that account for 67\% of the delayed neutron yield difference: $^{86}$As and $^{137}$Sb.
 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 $191 \pm 32$ $pcm$.
+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}.
+This yield difference is smaller in ENDF/B-VII.1, but that is because the emission probability in ENDF/B-VII.1 is $0.12$ instead of $0.36$ as it is in ENDF/B-VIII.0.
 
 The $^{137}$Sb yield difference has several contributing components: the emission probability in JENDL-5 is $0.49 \pm 0.08$, while the emission probability in ENDF/B-VIII.0 is $1.0 \pm 0.0$\footnote{No uncertainty is given, so an uncertainty of $1 \times 10^{-12}$ is used.}; the half-life in JENDL-5 is $0.94 \pm 0.01$ seconds, while the half-life in ENDF/B-VIII.0 is $0.45 \pm 0.05$ seconds; and finally the cumulative fission yield in JENDL-5 is $(2.4 \pm 0.9) \times 10^{-5}$, while the cumulative fission yield in ENDF/B-VIII.0 is $(7 \pm 5)\times 10^{-4}$.
 There are other \glspl{DNP} that contribute to the total delayed neutron yield discrepancy between ENDF and the other data sets, such as the cumulative fission yield of $^{85}$As, the cumulative fission yield of $^{90}$Br, all of the data for $^{86}$Ge, the cumulative fission yield of $^{94}$Rb, the cumulative fission yield of $^{137}$I, the cumulative fission yield and half-life of $^{98m}$Y, and others.
 Of the \glspl{DNP} listed, only $^{94}$Rb and $^{137}$I have larger yields in JENDL-5 than in ENDF/B-VIII.0; most of the differences in the nuclear data for \glspl{DNP} lead to ENDF datasets having a larger delayed neutron yield. 
 
+
+For summation calculations, microscopic evaluations of the \gls{DNP} group parameters, or any simulations of delayed neutron emission rates using individual \gls{DNP}, these differences in the nuclear data are relevant to consider and account for when using ENDF data.
+The difference between JENDL-5 and JEFF-3.1.1 was also investigated to determine which \glspl{DNP} have the largest effect leading to JEFF-3.1.1 under-predicting the total delayed neutron yield.
+There is a 120 $pcm$ difference between JENDL-5 and JEFF-3.1.1 total delayed neutron yields.
+As previously discussed in Section \ref{sec:jeff311}, JEFF-3.1.1 has only 136 \glspl{DNP} in its dataset, and 123 of those are present in JENDL-5.
+Those 123 that are in common have a total delayed neutron yield contribution in JEFF-3.1.1 that is 76 $pcm$ less than the same \glspl{DNP} in JENDL-5.
+The remaining 44 $pcm$ delayed neutron yield difference between JENDL-5 and JEFF-3.1.1 comes from the \glspl{DNP} the datasets do not have in common, as JENDL-5 has 257 \gls{DNP} with half-life, emission probability, and cumulative fission yield data while JEFF-3.1.1 has only 136.
+
+The difference between the JEFF-3.1.1 and JENDL-5 total delayed neutron yields does not come primarily come from one or two \glspl{DNP}, as was the case for the ENDF data difference.
+The top four \glspl{DNP} with the largest yield differences are $^{94}$Rb, $^{98m}$Y, $^{85}$As, and $^{89}$Br which are all present in both datasets and have both negative and positive differences\footnote{$^{94}$Rb is larger in JENDL-5 by 54 $pcm$, $^{98m}$Y is larger in JEFF-3.1.1 by 52 $pcm$, $^{85}$As is larger in JENDL-5 by 39 $pcm$, and $^{89}$Br is larger in JEFF-3.1.1 by 21 $pcm$.}.
+Instead, the difference comes from many small $\nu_d$ contributions from JEFF-3.1.1 that are smaller than those in JENDL-5.
+
+This is shown in Figure \ref{fig:hybrid-hist-jeff-jendl}, which shows the JENDL-5 delayed neutron yields subtracted from the JEFF-3.1.1 delayed neutron yields using histograms with bin widths of 10 $pcm$.
+Figure \ref{fig:hybrid-hist-jeff-jendl}(a) shows the histogram for the 123 \glspl{DNP} present in both datasets.
+This histogram shows in the two largest bins of 0 to 10 $pcm$ and -10 to 0 $pcm$ there are 62 \glspl{DNP} with an average $\Delta \nu_{d,i}$ of 0.90 $pcm$ contributing a total of 55.5 $pcm$, while there are 51 \glspl{DNP} with an average $\Delta \nu_{d,i}$ of -1.22 $pcm$ contributing a total of -62.2 $pcm$, respectively.
+The average $\Delta \nu_{d,i}$ when using the 123 \glspl{DNP} present in both datasets is -0.62 $pcm$, which comes from many small contributions as well as the seven \glspl{DNP} with a $\Delta \nu_{d,i}$ less than -10 $pcm$, though this is slightly offset by the three \glspl{DNP} with a $\Delta \nu_{d,i}$ greater than 10 $pcm$.
+Figure \ref{fig:hybrid-hist-jeff-jendl}(b) shows the histogram for the 280 unique nuclides between both datasets.
+This histogram shows in the two largest bins of 0 to 10 $pcm$ and -10 to 0 $pcm$ there are 85 \glspl{DNP} with an average $\Delta \nu_{d,i}$ of 0.66 $pcm$ contributing a total of 55.9 $pcm$, while there are 184 \glspl{DNP} with an average $\Delta \nu_{d,i}$ of -0.49 $pcm$ contributing a total of -90.7 $pcm$, respectively.
+The average $\Delta \nu_{d,i}$ when using the 280 \glspl{DNP} present in either dataset is -0.43 $pcm$, which comes from many small contributions as well as the seven \glspl{DNP} with a $\Delta \nu_{d,i}$ less than -10 $pcm$, though this is slightly offset by the three \glspl{DNP} with a $\Delta \nu_{d,i}$ greater than 10 $pcm$.
+The average is smaller in magnitude compared to using only the common \glspl{DNP} because there are many additional smaller contributions present when account for the many less impactful \glspl{DNP} present in JENDL-5 that are not present in JEFF-3.1.1.
+
+
+\begin{figure}[!ht]
+\centering
+\subfloat[The JEFF-3.1.1 \gls{DNP} $\nu_{d_i}$ minus the JENDL-5 \gls{DNP} $\nu_{d,i}$ for \glspl{DNP} present in both datasets.]{
+  \includegraphics[width=0.45\linewidth]{images/hybrid/yield_diff_hist_present_both.png}
+}
+\hspace{0.05\linewidth}
+\subfloat[The JEFF-3.1.1 \gls{DNP} $\nu_{d_i}$ minus the JENDL-5 \gls{DNP} $\nu_{d,i}$ for all \glspl{DNP} present in either dataset.]{
+  \includegraphics[width=0.45\linewidth]{images/hybrid/yield_diff_hist_all.png}
+}
+\caption{These histograms show the difference in the individual \gls{DNP} yield contribution $\Delta \nu_{d,i}$ between the JEFF-3.1.1 dataset and the JENDL-5 dataset using bin widths of 10 $pcm$. Using all \gls{DNP} present in either dataset results in an average delayed neutron yield contribution difference $\Delta \nu_{d,i}$ of -0.43 $pcm$, while using only \gls{DNP} present in both datasets results in an average delayed neutron yield contribution difference $\Delta \nu_{d,i}$ of -0.62 $pcm$.}
+\label{fig:hybrid-hist-jeff-jendl}
+\end{figure}
+
+\FloatBarrier

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

@@ -119,4 +119,6 @@
 \label{fig:pcc-charts-jendl5}
 \end{figure}
 
-\FloatBarrier
+\FloatBarrier
+
+

docs/2026_data_publication/images/hybrid/yield_diff_hist_all.png

@@ -60,14 +60,14 @@ \section{Introduction}
 These effects are well understood and have been simplified using various approximations.
 For example, the delayed neutrons are treated as having six to eight sources, or \gls{DNP} groups, even though in reality there are hundreds of precursor nuclides that decay and emit these delayed neutrons \cite{brady1988evaluation}.
 
-There are several different methods for calculating these \gls{DNP} groups, and in this work the microscopic approach is of particular interest \cite{pfeiffer2002status, d2002review, rudstam2002delayed, wilson2002delayed, brady1989delayed, mills2014calculation, huynh2014calculation, foligno_new_2019}.
+There are several different methods for calculating these \gls{DNP} groups, and in this work the microscopic approach is of particular interest \cite{d2002review, rudstam2002delayed, wilson2002delayed, brady1989delayed, mills2014calculation, huynh2014calculation, foligno_new_2019}.
 This approach uses experimental data for individual \glspl{DNP} combined together computationally.
 One strength of this approach is that it provides insight into how each individual \gls{DNP} contributes to the \gls{DNP} group parameters.
 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.
 There is also a related, and similar approach, called the summation approach.
 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 $\bar\tau$.
 
-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}.
+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}.
 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.
 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.
 
@@ -81,7 +81,7 @@ \section{Methods}
 This section details the three stages to the analyses presented in this paper: the data treated as an input, the solver which calculates the data of interest, and the data analysis which details how the solver results are processed.
 The solver itself can be considered a converter of the \gls{DNP} nuclear data into six group \gls{DNP} parameters, which are then passed into data analysis calculations.
 
-\subsection{Data}
+\subsection{DNP Nuclear Data Treatment}
 
 There are two different sets of data used in this work: the nuclear data for each individual \gls{DNP} and the calculated \gls{DNP} group parameters that approximate those individual \glspl{DNP}.
 The $I$ \gls{DNP} have the following data:
@@ -115,9 +115,9 @@ \subsection{Data}
     & & & \multicolumn{3}{c}{Available Data}\\
     Data name & Year & Source & $\tau_i$ & $P_{n,i}$ & $CFY_i$\\
     \hline
-      \gls{IAEA} database & 2018 & \cite{DIMITRIOU2021144} & Yes & Yes & No\\
-      \gls{JEFF} 3.1.1 & 2017 & \cite{plompen2020joint} & Yes & Yes & Yes\\
       \gls{ENDF}/B-VII.1 & 2011 & \cite{chadwick2011endf} & Yes & Yes & Yes\\
+      \gls{JEFF} 3.1.1 & 2017 & \cite{plompen2020joint} & Yes & Yes & Yes\\
+      \gls{IAEA} database & 2018 & \cite{DIMITRIOU2021144} & Yes & Yes & No\\
       \gls{ENDF}/B-VIII.0 & 2018 & \cite{Brown20181} & Yes & Yes & Yes\\
       \gls{JENDL}-5 & 2021 & \cite{iwamoto2023japanese} & Yes & Yes & Yes\\
     \hline
@@ -128,7 +128,7 @@ \subsection{Data}
 The data of interest in these datasets are for the individual \gls{DNP} nuclear data.
 This data is passed into the solver, which then converts these data into \gls{DNP} group parameters for analysis and post-processing.
 
-\subsection{Solver}
+\subsection{Microscopic and Summation Calculations}
 
 For the microscopic and summation methods, there are two distinct solution methods.
 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.
@@ -261,7 +261,7 @@ \subsection{Solver}
 These equations are approximate because the number of groups $K$ used is fewer than the total number of \glspl{DNP} $I$.
 To differentiate between the calculation of these parameters using $I$ \glspl{DNP} and $K$ groups, the parameters will be written as $\nu_d(I)$ and $\bar{\tau}(I)$ when calculated using $I$ \glspl{DNP} and $\nu_d(K)$ and $\bar{\tau}(K)$ when calculated using $K$ groups.
 
-\subsection{Data Analysis}
+\subsection{Sensitivity and Uncertainty Analysis}
 
 The \gls{PCC} is used to analyze the \gls{DNP} group parameters calculated from the solver for various unique combinations of sampled \gls{DNP} nuclear data and is calculated using the SciPy stats module \cite{scipy}.
 The \gls{PCC} measures the linear correlation between the \gls{DNP} data and the calculated \gls{DNP} group parameters.
@@ -358,6 +358,8 @@ \section{Results}
 They present a benchmark problem using JEFF-3.1.1 cumulative fission yields with ENDF/B-VIII.0 emission probabilities and half-lives, which is replicated in this work \cite{santamarina2009jeff, Brown20181}.
 The four groups in the study are \gls{CEA}, \gls{CIEMAT}, the \gls{JAEA}, and the University of Nantes, all of whom reported the same result of $0.01609 \pm 0.0008$ for the total delayed neutron yield from thermal fission of $^{235}$U.
 This agrees with the same result calculated in this work of $0.01609 \pm 0.0008$.
+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.
+Specifically, this work calculates a value of $0.0157 \pm 0.0008$, which exactly agrees with the results from Leconte et al. \cite{leconte2020new}.
 
 For the first set of results, additional information will be included that is not included in the other sections.
 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.
@@ -394,17 +396,23 @@ \subsection{JENDL-5}
 
 \subsection{Hybrid}
 
-\todo{Have a large table with all group parameters, yields, half-lives, etc. (maybe put full table in an appendix)}
-
 \input{images/hybrid/section}
 
 
 \section{Conclusions}
 
-\begin{itemize}
-    \item Summarize the main takeaways from the results (maybe a table indicating DNPs of interest for different datasets?)
-    \item Describe how improving these data will enable development of improved models of DNPs and kinetics models
-\end{itemize}
+This work presented analyses using the microscopic approach to compare \gls{DNP} nuclear data between the IAEA beta-delayed neutron emission database, ENDF/B-VII.1, ENDF/B-VIII.0, JEFF-3.1.1, JENDL-5, and hybrid datasets.
+These results, when compared with other summation calculations in the literature and experimental data, indicate that each dataset has specific \glspl{DNP} that have large relative uncertainties with a greater impact on the calculation of \gls{DNP} group parameters and delayed neutron emission rates than other \glspl{DNP}.
+Large differences in ENDF datasets that lead to discrepancies when comparing results with other summation calculations and experimental data are presented, specifically indicating problematic nuclides of $^{85}$As, $^{86}$As, $^{100}$Rb, $^{137}$Sb.
+The under-prediction of JEFF-3.1.1 for calculation of the total delayed neutron yield is also presented, indicating that the largest individual differences come from $^{94}$Rb, $^{98m}$Y, $^{85}$As, and $^{89}$Br; however, the majority of the difference comes from small contributions from many \glspl{DNP} both present in the dataset and lack of contribution from \glspl{DNP} missing from the dataset.
+The JENDL-5 dataset is shown to have good agreement with experiments and other calculations in the literature, including when using the IAEA beta-delayed neutron emission database.
+The \glspl{DNP} with the largest uncertainty-weighted sensitivities that affect delayed neutron emission rates and calculated \gls{DNP} group parameters are provided for each dataset evaluated in this work.
+A discussion on hybrid datasets is also provided, which provides evidence that cumulative fission yields in ENDF datasets contribute to larger delayed neutron yields than other results in the literature.
+
+The results in this work offer a new perspective for identifying \gls{DNP} in nuclear datasets that are in need of reduced uncertainties or lead to discrepancies with other results in the literature.
+These results can be leveraged to resolve nuclear data discrepancies and conduct experiments to improve the most relevant \gls{DNP} nuclear data.
+Through these targeted improvements to the nuclear data, future calculations using the individual \gls{DNP} nuclear data can be improved more rapidly.
+These improvements will improve the accuracy of transient simulations for nuclear reactors and enable more in-depth analyses on \gls{DNP} behavior.
 
 
 \pagebreak