Nuclear data evaluation for decay heat analysis of spent nuclear fuel over 1–100 k year timescale

Accurate nuclear data are essential in the evaluation of decay heat from spent nuclear fuel (SNF). The accuracy of such data was assessed using an approach that compares values reported in different evaluated libraries and determines whether discrepancies reflect inaccuracies in primary data. A short list of 43 isotopes which are most significant to SNF decay heat calculations over 1–100 k years was produced by combining generic reactor inventory code with decay heat analysis for undifferentiated SNF. Decay properties (half-lives and decay energies) and neutron interactions (cross section and fission yields) were compared from 6 evaluated libraries. Fission product (FP) discrepancies identified are 90Sr half-life, where inclusion of a single measurement significantly reduces the evaluated value; 95mNb beta energy, where DDEP evaluation omits the decay to the 95Mo ground state; 99Tc beta energy, where evaluations differ by approximately 10% with a variety of shape factors used; 126Sb/126mSb beta (JEF2.2/3.1.1/3.3) and electron energies (JEFF3.1.1), where intensity differences are reported; and 137Cs beta energy, where ENDF/B-VIII.0 and JEF3.3 evaluations use incorrect shape factors. For actinides, the major discrepancies identified were 237Np alpha energy (JEF2.2/3.1.1) and 225Ac electron energies (ENDF/B-VIII.0) but overall show less discrepancies during long-term disposal (0.1–100 ky) compared to FP’s during interim storage (1–100 years). Further assessments of the 90Sr half-life and the best shape factor for the 99Tc beta decay are needed to improve future decay heat analyses, which are important for designing future stores and evaluating schemes for possible heat recovery.


Introduction
In specific circumstances, confidence in the precision and accuracy of nuclear data is critical to develop reactor models and understand the curation of radioactive wastes over long timescales. Unsurprisingly, modeling decay heat from spent nuclear fuel (SNF) may be considered essential to underpin safe storage and disposal of radioactive waste. In addition, the possibility that heat generated by radioactive waste could be recoverable to offset carbon costs associated with long-term management also requires accurate decay heat models. In both cases, it is important to assess nuclear data confidence levels. For decay heat modeling, the half-lives, decay energies and intensities are the quantities requiring assessment, where modeling of SNF includes the calculation of inventories produced during and after reactor operation then fission yields and neutron capture cross sections are also required.
Previous studies have propagated uncertainties in nuclear data from single evaluated libraries through decay heat analyses. A socalled pandemonium effect was identified in key fission product (FP) decay heat contributors during pre-and post-reactor operating times [1,2]. These systematic errors cause an underestimate in total gamma-ray energies and an overestimate in total beta energies [2] when a high-resolution germanium detector is used for data measurements. Propagation errors were also identified in FP gamma emissions for short cooling times (< 1 year) [3], fission yield data for long cooling times (< 1000 years) and cross-sectional data for longer cooling times (> 1000 years) [4]. These decay heat uncertainties were identified for a single library-ENDF/B-VII.1-by adopting a Monte Carlo Sampling Method [3,4], recognizing the importance of improved precision in decay heat calculations, especially for long term modeling. Comparisons of different libraries has identified significant variability for natural radionuclide decay data [5].
The work reported here applies the methodology of [5,6] to FP and actinides, comparing nuclear data in different evaluated libraries to identify where discordance between them might reflect issues with the primary data that would not be evident if only one library was used. In this work a simulation of typical SNF is used to identify those nuclides which are significant in contributing to the total decay heat at different stages of post-irradiation decay. For this manageable subset of the nuclides present in SNF, relevant nuclear data have been tabulated from six different evaluated libraries, any discrepancies noted and the nuclear data contributing to those discrepancies examined in more detail. It is not the intention of this work to produce comprehensive re-appraisals of existing a e-mail: h.doran.1@research.gla.ac.uk (corresponding author) data, rather to identify nuclides where inconsistencies lead to reduced confidence in evaluated data, and for those where this is significant for decay heat evaluation briefly discuss the data and suggest further work that could address issues identified.

Identification of radionuclides for further investigation
A simulation code developed and validated for modeling the irradiation of 235U with thermal neutrons [7,8], modified to approximate fast neutron interactions and actinide production, was used to simulate a typical SNF inventory and model the decay over 100k years. For this purpose, the fuel was 1t of natural uranium with an irradiation period (1934 d or 5.3 y) and power output (3.62 MWth) typical of Magnox reactors. Other fuel and thermal reactor types will produce slightly different inventories, but the radionuclides contributing to the majority of the total decay heat are not expected to vary significantly. Inventory outputs were generated at different decay times (1,5,10,50, 100, 500, 1 k, 5 k, 10 k, 50 k and 100 k years) to simulate an activity value per radionuclide. Mean energy values were obtained by considering the radiation energy and intensity data for each radionuclide. From this, a summation of the activity and mean energy values was performed to compute the decay heat produced by all radionuclides in the simulated fuel. The simulation code and the decay heat calculations use data from the JEF2.2 library [9]. For each time period a decay heat vs cooling time plot was generated, allowing the identification of nuclides that contribute 99% of the total heat at that decay time. Given the approximations in the simulation code, and the potential for different inventories of different fuels and reactor designs, any nuclide close to this threshold was also included in the list of nuclides of interest. This list was compared to other studies, and any other nuclides identified as significant decay heat contributors by other authors were also included in this analysis.

Nuclear data comparative assessment
For all the radionuclides identified as significant decay heat contributors, nuclear data were tabulated from six evaluated libraries. For this work, the nuclear data comprised of half-lives, mean decay energies, independent and cumulative fission yields and thermal neutron capture cross sections. The libraries interrogated were JEF2.2, JEFF3.1.1, JEFF3.3, ENDF/B-VIII.0, ENSDF and DDEP. Data from the first four of these were extracted using the JANIS 4.1 tool, ENSDF data were extracted using the NucDat 2.8 tool [10], and DDEP data were taken from LNHB [11]. For nuclides with short-lived decay products, the total energy is calculated including radiation from the decay products in equilibrium.

Results and discussion
3.1 Percentage decay heat contributors Figure 1 illustrates a decay heat vs cooling time curve for one ton (1 t) of fuel on a log-log scale accompanied by a stacked percentage histogram in Fig. 2 displaying dominant radionuclides, across a cooling period 1-100 k years. There are 23 parent nuclides which contribute to 99% of the heat production at any time during the decay between 1 y and 100 ky and are plotted in Fig. 2. In green/turquoise, FP's such as 95Zr, 106Ru, 134Cs, 137Cs and 90Sr dominate over 80% of the total decay heat for initial cooling times of 1-10 years, followed by 90Sr and 137Cs making up the bulk of FP heat up to 100 years. This FP list supports other literature, suggesting that FP's dominate the decay heat process during the interim storage and transportation period [3,12,13]. In particular, a similar investigation for light-water reactor (LWR) designs was proposed by [13], identifying all FP's highlighted in Fig. 2, also identifying 90Y, 144Pr, 137mBa (which in this work have been included within the decay energy of their longer-lived parents). In orange/red, actinides such as 239Pu, 240Pu and 241Am dominate the total decay heat percentage between cooling times 100-100 k years. In particular, the highest percentage seen are 98% for 239Pu at 50 k years, 31% for 240Pu at 5 k years and 40% for 241Am at 500 years. This was also seen in [12] for PWR SNF at burnup 50 MWd/tHM, where the decay chains of 239Pu, 240Pu and 241Am reach their maximum decay heat for these cooling times. Actinides 241Pu, 242Am and 244Cm were also identified in [13] for total decay heat contributions of ≥ 99% for a cooling period between 2 and 100 years. These additional nuclides which prior literature suggest are important have also been included within this analysis. Finally, nuclear data from an additional seventeen short-lived daughter products were added to the discrepancy analysis, assuming that these are in equilibrium with their corresponding parent nuclides identified in Fig. 2 and hence will pose some importance in decay heat contributions. In total, 43 nuclides were identified for further examination. An *parent radionuclides that incorporate energies from shortlived daughter products, e.g., 137Cs*, includes 137Cs and its short-lived daughter product 137mBa 3.2 Nuclear data for identified nuclides of interest

Half-life
The half-lives for the nuclides of interest from the six evaluated libraries are given in Table 1. Note that the half-lives of shorter-lived decay products that are expected to be in equilibrium with a longer lived parent are not considered significant, and so are not listed. There are several isotopes where the half-life given in one library is inconsistent with the other evaluations. These are: -90Sr, half-life reported by JEF2.2 is 0.2-0.3 years longer than other libraries with a larger quoted uncertainty, and ENSDF is 0.1y longer than the other four libraries. -126Sn, half-life reported by JEF2.2 is less than half that of the other libraries, with no quoted uncertainty.

Alpha decay energies
For mean alpha decay energies (

Mean beta decay and electron energies
The mean beta energies for the radionuclides of interest are given in Table 3, omitting those where the mean beta energy is less than 1 keV. There are several isotopes where the mean energy in one or more evaluated library is inconsistent with the other evaluations, which are: -85Kr, where the JEFF3.1.1 value is about 10% lower than the other evaluations.
-89Sr, where the JEFF3.3 value is slightly lower and the ENSDF slightly higher.
-90Y, where the DDEP value is slightly lower than the other evaluations.
-95mNb, where JEF2.2 does not report a mean energy, but a calculation of the difference between the reported total light particle energy and the discrete electron energies is more than twice the values in JEFF(3.1.1 and 3.3), ENDF/B-VIII.0 and ENSDF; and DDEP is less than half of these.   The total of auger and conversion electrons (CE) for each isotope of interest are given in Table 4, omitting those where the total energy is less than 0.

Mean gamma and X-ray energies
The mean gamma ray energies for the isotopes of interest are given in Table 5. Note a threshold of 1 keV was set for radionuclides displayed in Table 5 The mean X-ray energies for the isotopes of interest are given in Table 6. Note a threshold of 0.1 keV was set for radionuclides displayed in Table 6, to omit less significant X-ray energy values. This part of the analysis reveals a significant number of radionuclides with X-ray variation between the evaluated libraries, which are:

Fission yields
The cumulative fission yield is also an important variable to assess when comparing confidence levels in decay heat measurements for waste management and heat production. The cumulative yields following thermal fission of 235U are shown in Table 7 where it can be seen that the fission yields are consistent across all libraries. Cumulative fission yields for 239Pu are similarly consistent across all evaluations and are shown in Table 10 within "Appendix". Referring to Table 7, it is noted that the uncertainties reported for 90Y and 91Y in the ENDF/B-VIII.0 library by JANIS are anomalously high, and as these should be almost identical to the cumulative yields of the parent isotopes where the uncertainties are approximately 1% in both cases, which clearly reflects an error somewhere.
Independent thermal fission yield data from 235U and 239Pu were also taken from the chosen libraries. Note that the ENSDF library gives independent fission yields, but not cumulative yields, and although these could be calculated by summing the independent yields for nuclides in the decay chains this has not been done as it would be expected that the results would be very similar to the values from the other evaluations. The DDEP library only reports decay data and does not include fission yields. Independent thermal fission yield data for both 235U and 239Pu are tabulated within "Appendix" in Tables 11 and 12, respectively, where the analysis of these are beyond the scope of the paper.

Thermal capture cross-sectional assessment
Neutron capture processes inside a reactor are also important to consider when assessing decay heat confidence levels. This process is a primary and secondary mode of production for actinides and fission products, respectively, as well as the activation of non-fuel elements within a reactor (which are not considered here). Table 8 lists the thermal neutron capture cross sections for the isotopes of interest (which relate to burn-up reducing their concentrations within a reactor) and also for the N-1 isotopes where the cross sections are > 1 b and are likely to be present in significant quantities (which relate to production of the isotopes of interest within a reactor). There are several examples where the cross sections tabulated vary by an order of magnitude or more between different  137Cs (624 ± 53.9)×10 −2 (622 ± 6.9)×10 −2 evaluations. The different evaluations give values for these cross sections without a stated uncertainty, and no information on the primary data used to produce these values. Therefore, as the information needed to assess the primary data is not readily available within the evaluated libraries, further examination of these differences have not been attempted and is beyond the scope of this paper. However, there is clearly a need to resolve the significant differences between these evaluations and determine cross sections that can be used with confidence.

Radionuclides where discrepancies between libraries are observed
The observations quoted within this paper are summarized in Table 9, listing those radionuclides where there are observed discrepancies between evaluations. From the discrepancies in decay data given in Table 9, those isotopes that are most significant in nuclear waste management and heat production have been investigated in more detail below. Of the remaining isotopes the discrepancies are either very small or have relatively simple explanations. For 85Kr, the beta energy discrepancy follows the use of an allowed transition of the dominant ( > 99%) decay to the 85Rb ground state in JEFF3.1.1 whereas the other evaluations use a physically more reasonable first forbidden transition. For 106Rh, where the differences account for < 1 keV in electron energy, the DDEP evaluators do not include any conversion electrons and the ENSDF evaluators list 9, of which 5 are given with zero intensity, whereas the other evaluations include a much larger number of conversion electrons with greater intensities. The JEF2.2 evaluation conducted in 1982 for 154Eu used gamma energy and intensity data from [14]-the other evaluations include data from several more recent measurements and although the differences in gamma ray energies and intensities are small, the cumulative differences across over 100 emissions accounts for the approximate 20 keV difference between the JEF2.2 and later evaluations. For 229Th, the JEF2.2, JEFF3.1.1 and JEFF3.3 share the same 1980 evaluation, with ENDF/B-VIII.0 and ENSDF incorporating more recent experimental data. 237Np alpha decay data for JEF2.2 and JEFF3.1.1 have large uncertainties that are significantly reduced with more precise data in later evaluations.

90Sr
The data for 90Sr show discrepancies in both half-life and mean beta energies. For the half-life evaluations, Woods and Lucas [15] produced new data following the decay of a 500 MBq 90Sr over six years using IG25 ionization counters producing a half life of 10495 ± 4 d, and an evaluation producing a weighted mean with six previously published results giving a half-life of 10516 ± 21 d, this is noted by the DDEP [16] and ENDF/B-VIII.0 evaluators [17] who reject some previously published values on the same grounds as Woods and Lucas (1996). The DDEP evaluation also includes a value by Schrader (2004) [18] for 17 y of measurements on a 90Sr source giving a half-life of 10557 ± 11d (replacing previous published measurements of the half-life from the same source) which was not available to Browne [17].   The ENSDF value given here [19] uses a weighted mean from just three long-term measurements of 10527 ± 51 d measured over 11 y [20], 10561 ± 14 d measured over 33 y [21] and the 10557 ± 11 d of Schrader (2004) [18] giving a weighted mean of 10558 ± 11 d. These are all longer than the Woods and Lucas (1996) value, and hence, a longer half-life is determined compared to other evaluations which have included the 1996 value. The Woods and Lucas (1996) half-life is inconsistent with the Martin et al. (1994) and Schrader (2004) values, the differences between them being 66 ± 15 d and 62 ± 12 d, respectively [18,21]. This inconsistency should be examined in more detail before selecting an evaluation that either incorporates the Woods and Lucas (1996) value or rejects it. In addition to the application to time trajectory of heat generation from nuclear waste, the value of the half-life of 90Sr is also critical to many applications where this isotope is used as a calibration source (for example, in applying known doses for luminescence dating).
For the beta decay, all the evaluations use the same endpoint energy (546.0 ± 1.4 keV), however the JEFF3.1.1 evaluators calculate the mean energy using a shape 0 (allowed) transition. With the transition from the 0+ ground state of 90Sr to the 2-ground state of 90Y, this cannot be an allowed transition, and the use of first forbidden shapes by the other evaluations is appropriate. Thus, it is concluded that the low value of the mean beta energy in the JEFF3.1.1 evaluation is incorrect, and any of the values in the other libraries should be used.

95mNb
The mean beta energy reported in the DDEP library is a lot lower than that reported in the other evaluations (8.3 keV vs 22 keV). For JEF2.2, the library lists the 5.6% beta-decay branch but it does not include any beta emissions in the library, and a mean energy has been calculated here from the difference between the mean energy for discrete electrons and the reported mean energy for all light particles. The mean energy for discrete electrons in JEF2.2 is reported lower than those within the other libraries, resulting in a higher mean beta energy. The discrepancy in the JEF2.2 value reflects incomplete data included in the evaluation and is not considered further here except to note that later and more complete evaluations are preferred. The incomplete data in JEF2.2 also contribute to the low total energy of other electron emissions. The low DDEP mean beta energy is almost entirely explained by the absence of the beta transition to the 95Mo ground state included in the other evaluations (for ENSDF this has an endpoint of 1160 keV, with a mean energy of 437.4 ± 0.2 keV and a 3.2 ± 1.0% intensity), with minor variations in mean energy and intensity of the other transitions. This is a first unique forbidden ( 1 − 2 → 5 + 2 ) transition, and there is no obvious reason why it would not occur with an intensity similar to that ascribed to it in ENSDF and other evaluations. The notes on the DDEP evaluation [22,23] do not explain why this transition has been omitted, and this appears to be an error in the DDEP evaluation. The variations in the total energy of discrete electrons reflects variations in the intensity of the dominant 216keV conversion electron with DDEP and JEFF3.3 evaluators giving this an intensity of 58.1 ± 0.6% and 58.0 ± 2.7%, respectively, with ENSDF, ENDF/B-VIII.0 and JEFF3.1.1 evaluators giving this a lower intensity of 55.9 ± 0.6%, 55.9 ± 1.0 % and 56.0 ± 1.7%, respectively.

99Tc
All evaluations agree that the beta emissions from 99Tc are dominated by the ground state to ground state transition with a maximum energy of 293.5-293.8 keV for all evaluations, except ENSDF which gives this as 297.5 ± 1.0 keV [24] and an intensity of 100% or very slightly lower. The major difference between the libraries is the choice of decay shape. The JEF2.2 and ENDF/B-VIII.0 evaluations use an allowed, non-unique transition shape but yield very different mean energies. The JEFF3.1.1 and 3.3 evaluations use a first forbidden unique shape and also yield different mean energies, and the ENSDF and DDEP evaluations use a second forbidden shape. The ENSDF evaluation uses an experimentally derived shape by Reich and Schüpferling [25], whereas the DDEP evaluator [26] uses a weighted evaluation of form factors from Feldman and Wu [27]. These form factors were recalculated by Lipnik and Sunier (1966), Snyder and Beard (1966) who were then recalculated by Behrens and Szybisz (1976), and Reich and Schüpferling (1974) [25,[28][29][30].

126Sn
The earlier evaluations of the 126Sn half-life use an estimation from [31] based on the thermal yield of 235U in the order of 10 5 y. This estimation has been supplanted by radiochemical analyses and specific activity measurements of 2.07 × 10 5 y [32] and 2.5 × 10 5 y [33] in the later evaluations.

126Sb and 126mSb
The

144Ce
For 144Ce, it is unclear where the beta energy discrepancy for the JEF3.3 evaluation arises as all the evaluations agree on the end-point energies and intensities of the three beta transitions. Though it is noted that the transitions reported through JANIS (for the JEF/JEFF and ENDF/B-VIII.0 evaluations) are allowed non-unique whereas DDEP lists them as first-forbidden non-unique. With the decays involving a parity change and I = 0 or 1, these should be first-forbidden decays. Differences in the assumed shape will result in different mean energies, but this does not explain the difference between the JEF3.3 and other evaluations if the same shapes are used. Given that the DDEP evaluators explicitly use a physically realistic first-forbidden decay it is reasonable to take this as the best value for the mean energy, as this is consistent with all other values apart from JEFF3.3 which looks erroneous.

137Cs
The mean beta energy reported by the JEFF3.3 and ENDF/B-VIII.0 evaluations is approximately 5% lower than that reported by the other libraries. The differences reflect significant variations in the treatment of the transition to the 137Ba ground state. This is a ( 7 + 2 → 3 + 2 ) second forbidden transition; however, the JEF2.2, JEFF3.1.1 and ENDF/B-VIII.0 libraries describe this as an allowed non-unique transition, and JEFF3.3 as a first forbidden transition. The ENSDF and DDEP evaluators use the LOGFT program to determine a mean energy of 416.26 ± 0.08 keV, whereas ENDF uses SPEBETA to give a mean energy of 271.0 ± 0.1 keV. The other evaluations are not explicit in how this mean energy was derived, but the JEF2.2 and JEFF3.1.1 values are consistent with ENSDF/DDEP, while the JEFF3.3 value is consistent with ENDF/B-VIII.0. Given the evidence that this is a second forbidden transition, the evaluations that use this shape function (or, produce mean energies consistent with this) are preferred, and the conclusion is that the 137Cs mean beta energies reported by JEFF3.3. and ENDF/B-VIII.0 are in error.

225Ac
The discrete electron energies calculated from the different evaluations differ markedly. JEF2.2 and JEFF3.1.1 use the same data and give a total energy of 27.6 ± 0.7 keV, JEFF 3.3 and DDEP give slightly lower energies of 20.1 ± 0.5 keV and 21.2 ± 0.5 keV, respectively, while the ENSDF value is much lower at 14.7 ± 1.4 keV and ENDF/B-VIII.0 is much higher with large uncertainties at 38.4 ± 14.7 keV. The ENSDF evaluation also reports a lower X-ray energy. It seems unlikely that the large and imprecise ENDF/B-VIII.0 is the best value for this energy; however, it would take further study to determine the best value.

Conclusions
An assessment was conducted on nuclear data to identify possible inconsistencies and discrepancies on isotopes that could influence decay heat calculations from RWM procedures. The assessment used a simple reactor inventory and decay model, combined with consideration of prior literature, to identify the nuclides that contribute to the majority of the decay heat (cumulatively > 99 %) at different stages of storage and disposal between 1 and 100 k years. This produced a list of 43 isotopes of interest, including short-lived decay products. The approach of [5,6] was then followed to compare the nuclear data for each of these isotopes as reported in six different semi-independent evaluations, where significant discrepancies were noted to explore further.
The main potential issues identified were: -90Sr, where the half-life values differ significantly depending on whether or not the evaluators include one of the experimental values which is significantly shorter than other measurements recorded over longer periods of time. The accuracy of these different long term measurements should be assessed to identify why there are discrepancies, and whether one or more of them include systematic errors. Further independent data on the half-life would also be of benefit. Since 90Sr is an isotope commonly used for various applications requiring a calibrated activity, an accurate value for the half-life is essential for these applications. -95mNb, where the beta decay energy reported by the DDEP evaluation appears to be in error, omitting beta decay to the 95Mo ground state. -99Tc, where the mean beta energy calculated by different evaluations varies with the assumed shape of the beta spectrum. The DDEP and ENSDF evaluations both use measured spectral shapes, but still differ by almost 10% in the mean energy reported. The shape of this decay spectrum needs further investigation, either through more thorough examination of the existing data or with additional experimental measurement. Other discrepancies were noted to be of lesser significance, including half-lives for 126Sn (where the JEF2.2 value is just an order of magnitude estimate); mean beta energies for 85Kr and 89Sr; energies for discrete electrons for 106Rh, 126Sn, 229Th and 237Np; and the gamma energies for 229Th.
Overall, FP's dominated the discrepancy analysis, which are defined as high decay heat contributors across the interim storage period (1 -100 years). Actinides, however, whose decay heat dominance is noticed at the long-term disposal timescale (0.1-100 ky), showed only potential discrepancies in 237Np alpha and 225Ac electron energies. Overall, consistency in mean alpha energies is seen across the evaluated libraries which could be due to better measurements or easier modeling capabilities. For FP's, the modeling capabilities are hindered by different shape factors in beta energies (seen for 99Tc) and limitations in detector measurements for both beta and gamma energies. These consistencies in alpha energies could ultimately ensure a higher accuracy in decay heat measurements, especially when radioactive waste awaits disposal into a future repository, versus during the interim storage period.

Data Availability Statement
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. This manuscript has associated data in a data repository. [Authors' comment: The datasets generated during and/or analyzed during the current study are available in the Enlighten repository, http://dx.doi.org/10.5525/gla.researchdata.1300.]

Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.
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A Appendices
A.1 Cumulative fission yield data due to 239Pu Table 10 depicts the cumulative fission yield data from the thermal fission of 239Pu. The data here show a similar relationship to 235U reported within the main body of the text.
A.2 Independent thermal fission yield data due to 235U and 239Pu Within the different evaluations there are often significant variations in the independent thermal fission yields reported; Tables 11 and 12 display these values for 235U and 239Pu respectively. In some cases, an order of magnitude difference can be seen.