Cumulative Fission Yields Research Articles

Bayesian approach to energy dependence of fission product yields of 235U by data augmentation

ABSTRACT We utilized a two hidden-layer Bayesian neural network (BNN) model along with data augmentation (DA) to predict the energy dependence of fission product yields (FPY). In the BNN model, the JENDL-5 FPY data are separated into 80 % for training and 20 % for validation. Additionally, the training data are combined with experimental cumulative fission yields and calculated values by five Gaussian model. The number of units in each layer and activation function were selected carefully to reproduce the global and fine structure of the FPY data. Through comparing the results with and without DA, we found that DA is particularly valuable for specific nuclides. The evaluation results with DA demonstrate reliable and accurate predictions of the energy dependence of fission product yields of 235U.

Cumulative fission yields of short-lived fission products from 235U and 239Pu measured by HPGe gamma-ray spectroscopy

In this study, we present a preliminary investigation focused on determining cumulative fission yields for short-lived fission products. Our analysis involves examining gamma spectra from the irradiated samples of 235U and 239Pu using the High Flux Isotope Reactor. The motivation stems from the observed discrepancy in the antineutrino energy spectrum within the range of 5 to 7 MeV. While several hypotheses have been proposed, a thorough analysis of fission yields provides an additional way of gaining insight into this unexplained phenomenon. Our study suggests that the measured gamma rays from 100Nb, 140Cs and 95Sr are consistent with the expected values. However, 93Rb, 96Y, 97Y and 142Cs cannot be quantified due to insufficient statistics, interference from other gamma rays and the Compton scattering background. Additionally, the calculated cumulative fission yields based on the measured 140Cs and 95Sr are found to be consistent with the JEFF3.3 fission yield library. The present work shows that the potential of improving gamma-ray spectroscopy in the fission yields as a means to improve our understanding of the antineutrino spectrum.

Measurement of Mass‐Independent Perturbations of Cadmium in Nuclear Debris Samples

The isotopic composition of cadmium in nuclear debris was measured by multi‐collector inductively coupled plasma‐mass spectrometry (MC‐ICP‐MS). Mass‐independent perturbations due to fission product decay on the isotopes of Cd were observed. Relative fission yields for masses 111, 112, 114 and 116 were determined in each sample of nuclear debris and compared with reported values found in irradiated plutonium and uranium fuels. Mass spectrometry measurements of the valley fission product endpoints are extremely challenging due to the low cumulative fission yields and small amounts of each isotope that are produced. To overcome these challenges, a new purification method for Cd was developed and validated by examination of a number of geological reference materials.

The Extension of the Hauser-Feshbach Fission Fragment Decay Model to Multi-chance Fission and its Application to 239Pu

The Hauser-Feshbach fission fragment decay model, HF3D, calculates the statistical decay of fission fragments through both prompt and delayed neutron and γ-ray emissions in a deterministic manner. While previously limited to the calculation of only first-chance fission, the model has recently been extended to include multi-chance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input prescission quantities–fission probabilities, pre-fission neutron energies, and the average energy causing fission– and post-scission quantities–yields in mass, charge, total kinetic energy, spin, and parity. From those fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions. The evaporation of the prompt neutrons and γ rays is calculated through the Hauser-Feshbach statistical theory, taking into account the competition between neutron and γ-ray emission, conserving energy, spin, and parity. The delayed emission is taken into account using time-independent calculation using decay data. This whole formulation allows for the calculation of prompt neutron and γ-ray properties, such as multiplicities and energy distributions, both independent and cumulative fission yields, and delayed neutron observables, in a consistent framework. Here, we describe the implementation of multi-chance fission into the HF3D model, and show an example of prompt and delayed quantities beyond first-chance fission, using the example of neutron-induced fission on 239Pu. This expansion represents significant progress in consistently modeling the emission of prompt and delayed particles from fissile systems.

Bayesian approach to heterogeneous data fusion of imperfect fission yields for augmented evaluations

We demonstrate that Bayesian machine learning can be used to treat the vast amount of experimental fission data which are noisy, incomplete, discrepant, and correlated. To supply the application needs, the two-dimensional cumulative fission yields (CFY) of neutron-induced fission of $^{238}\mathrm{U}$ are evaluated for energy dependencies and uncertainty qualifications by cross-experiment data fusion. For independent fission yields (IFY) with very few experimental data, the heterogeneous data fusion of CFY and IFY is employed to interpolate the energy dependence. This work shows that Bayesian data fusion can facilitate the maximum utilization of imperfect raw nuclear data.

Stochastically estimated covariance matrices for independent and cumulative fission yields in the ENDF/B-VIII.0 and JEFF-3.3 evaluations

A Monte-Carlo method for the generation of correlation and covariance matrices for independent and cumulative fission yields has been developed. The method uses a constrained Monte-Carlo resampling structure in order to vary evaluated fission yield libraries in a way that meets basic conservation principles. This results in the generation of correlation/covariance matrices with limited model bias and uncertainty; the matrices are primarily reflective of the evaluated fission yield uncertainties and correlations that arise from the evaluation process. This method has been applied to generate correlation and covariance matrices for all of the fissioning systems of the ENDF/B-VIII.0 and JEFF-3.3 evaluations, marking the first time such matrices have been generated for all of these systems. These covariance matrices have been published online for immediate public use. These correlation and covariance matrices can be used to improve uncertainty estimation in calculations of reactor antineutrino emission rates, decay heat problems, and nuclear forensics.

Extension of the Hauser-Feshbach fission fragment decay model to multichance fission

The Hauser-Feshbach fission fragment decay model, $\mathtt{HF^3D}$, which calculates the statistical decay of fission fragments, has been expanded to include multi-chance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input pre-scission quantities - fission probabilities and the average energy causing fission - and post-scission quantities - yields in mass, charge, total kinetic energy, spin, and parity. From these fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions, allowing for the calculation of prompt neutron and $\gamma$ properties, such as multiplicity and energy distributions, both independent and cumulative fission yields, and delayed neutron observables. In this work, we describe the implementation of multi-chance fission into the $\mathtt{HF^3D}$ model, and show an example of prompt and delayed quantities beyond first-chance fission, using the example of neutron-induced fission on $^{235}$U. This expansion represents significant progress in consistently modeling the emission of prompt and delayed particles from fissile systems.

Mass yield distributions in the Th232(n,f) reaction with fast neutrons

The cumulative yields of 48 fission products in the mass range of 77--153 have been measured for the $^{232}\mathrm{Th}(n,f)$ reaction with the average neutron energies of 7.46, 13.4, and 18.0 MeV using an off-line \ensuremath{\gamma}-ray spectrometric technique. Fast neutron beams were generated using the $^{9}\mathrm{Be}(p,n)$ reaction with the proton energies of 25, 35, and 45 MeV from the MC-50 Cyclotron at the Korea Institute of Radiological and Medical Sciences. Post-neutron mass chain yields were obtained from the cumulative fission yields using the charge distribution correction of the medium energy. From the mass yield data, the peak-to-valley ratio, average light mass, and heavy mass, as well as the average neutron numbers were obtained. The fine structure of the mass yield distribution in the $^{232}\mathrm{Th}(n,f)$ reaction is explained by considering the nuclear structure effects such as the even--odd effect and shell closure proximity. The effect of deformed shells closure proximity arising due to the octupole deformation of fragments is discussed. The difference in the mass yield distribution between the $^{232}\mathrm{Th}(n,f)$ and $^{238}\mathrm{U}(n,f)$ reactions at various excitation energies is explained based on the different types of potential energy surfaces between the two fissioning systems. The role of excitation energy on the standard I and standard II asymmetric mode of fission is also discussed. In the $^{232}\mathrm{Th}(n,f)$ reaction with the excitation energies of 11--13 MeV, the onset of symmetric product yields, peak-to-valley ratio, average light mass, and heavy mass, as well as the average neutrons number have been observed, which are explained from the point of second chance fission.

Quantification techniques of mass-separation and ion yield for the detection of radioactive isotopes

This research demonstrates two methods of quantifying ion yield efficiency using an inductively coupled plasma mass spectrometer. The mass spectrometer is used as a means of separation where individual decay mass-chains are isolated (i.e., implanted) onto a conductive substrate. Quantifying the ion yield of this recovery process is crucial to understanding the abundance of the separated isotope present in the unseparated starting sample. The first method measured the accumulated charge directly incident on the conductive substrate in real-time while the second method performed a full chemical analysis of the substrate after dissolution. Our previous results demonstrated and compared these quantification methods with a multi-element standard of stable isotopes. This research expands on previous results and utilizes the stable mass ion yield to quantify trace amounts of the (radioactive) isotope of interest present in the sample. The mass-separated radioactive isotopes were fission products produced from thermal neutron irradiation of a highly enriched 235U foil. Five peak-yield mass chains were targeted. The results indicate good correlation between the two methods of measuring the ion yield and imply that coupling this method with traditional radiometric counting can result in an accurate means of quantifying radioactive isotopes. The final results we report here are within 1-sigma of the published cumulative fission yields.

Feedback from experimental isotopic compositions of used nuclear fuels on neutron cross sections and cumulative fission yields of the JEFF-3.1.1 library by using integral data assimilation

Comparisons of calculated and experimental isotopic compositions of used nuclear fuels can provide valuable information on the quality of nuclear data involved in neutronic calculations. The experimental database used in the present study − containing more than a thousand isotopic ratio measurements for UOX and MOX fuels with burnup ranging from 10 GWd/t up to 85 GWd/t − allowed to investigate 45 isotopic ratios covering a large number of actinides (U, Np, Pu, Am and Cm) and fission products (Nd, Cs, Sm, Eu, Gd, Ru, Ce, Tc, Mo, Ag and Rh). The Integral Data Assimilation procedure implemented in the CONRAD code was used to provide nuclear data trends with realistic uncertainties for Pressurized Water Reactors (PWRs) applications. Results confirm the quality of the 235U, 239Pu and 241Pu neutron capture cross sections available in the JEFF-3.1.1 library; slight increases of +1.2 ± 2.4%, +0.5 ± 2.2% and +1.2 ± 4.2% are respectively suggested, these all being within the limits of the quoted uncertainties. Additional trends on the capture cross sections were also obtained for other actinides (236U, 238Pu, 240Pu, 242Pu, 241Am, 243Am, 245Cm) and fission products (103Rh, 153Eu, 154Eu) as well as for the 238U(n,2n) and 237Np(n,2n) reactions. Meaningful trends for the cumulative fission yields of 144Ce, 133Cs, 137Cs and 106Ru for the 235U(nth,f) and 239Pu(nth,f) reactions are also reported.

Systematics of Nd cumulative fission yields for neutron-induced fission of 235U, 238U, 238Pu, 239Pu, 240Pu and 241Pu

Systematics of cumulative fission yields of the neodymium isotopes for the thermal and fast neutron fission of 235U, 238U, 238Pu, 239Pu, 240Pu and 241Pu were obtained by combining integral results from the PROFIL experiments with theoretical calculations from the GEF code. The systematic behavior with the neodymium mass number (A = 143, 145, 146, 148, 150) deduced from the experimental trends is consistent with the smooth variation predicted by the GEF calculations, excepted for the 238U(n,f) reaction. For this system, isotopic and isotonic effects in fission-fragment shell structures are not adequately taken into account in the theoretical calculation. The obtained results also confirm the weak energy dependence of the Nd cumulative fission yields in the energy range of interest for thermal and sodium fast reactors. They suggest an energy dependency comparable to the experimental uncertainty which lies below 3%, for the 235U, 239Pu and 241Pu fissile isotopes.

Geant4 simulation of 238U(n,f) reaction induced by D-T neutron source

Knowledge of actinides (n,f) fission process induced by neutron is of importance in the field of nuclear power and nuclear engineering, especially for reactor applications. In this work, fission characteristics of 238U(n,f) reaction induced by D-T neutron source were simulated with Geant4 code from multiple perspectives, including the fission production yields, total nubar, kinetic energy distribution, fission neutron spectrum and cumulative γ-ray spectrum of the fission products. The simulation results agree well with the experimental nuclear reaction data (EXFOR) and evaluated nuclear data (ENDF). Mainly, this work was to examine the rationality of the parametric nuclear fission model in Geant4 and to direct our future experimental measurements for the cumulative fission yields of 238U(n,f) reaction.

Measurement of fission products yields in the quasi-mono-energetic neutron-induced fission of 232Th

The cumulative yields of various fission products in the 232Th(n, f) reaction at average neutron energies of 5.42, 7.75, 9.35 and 12.53 MeV have been determined by using an off-line γ-ray spectrometric technique. The neutron beam was produced from the 7Li(p, n) reaction by using the proton energies of 7.8, 12, 16 and 20 MeV. The mass chain yields were obtained from the cumulative fission yields by using the charge distribution correction of medium energy fission. The fine structure in the mass yield distribution was interpreted from the point of nuclear structure effect. On the other hand, the higher yield around mass number 133–134 and 143–144 as well as their complementary products were explained based on the standard I and standard II asymmetric mode of fission. From the mass yield data, the average value of light mass (〈AL〉), heavy mass (〈AH〉), the average number of neutrons (〈ν〉) and the peak-to-valley (P/V) ratios at different neutron energies of present work and literature data were obtained in the 232Th(n, f) reaction. The different parameters of the mass yield distribution in the 232Th(n, f) reaction were compared with the similar data in the 232Th(γ, f) reaction at comparable excitation energy and a surprising difference was observed.

Measurements of the effective cumulative fission yields of143Nd,145Nd,146Nd,148Nd and150Nd for235U in the PHENIX fast reactor

The effective Neodymium cumulative fission yields for 235 U have been measured in the fast reactor PHENIX relatively to the 235 U fission cross-section. The data were derived from isotope-ratio measurements obtained in the frame of the PROFIL-1, PROFIL-2A and PROFIL-2B programs. The interpretations of the experimental programs were performed with the ERANOS code in association with the Joint Evaluated Fission and Fusion library JEFF-3.1.1. Final results for 143 Nd, 145 Nd, 146 Nd, 148 Nd and 150 Nd were 5.61%, 3.70%, 2.83%, 1.64% and 0.66%, respectively. The relative uncertainties attached to each of the cumulative fission yields lie between 2.1% and 2.4%. The main source of uncertainty is due to the fluence scaling procedure (<2%). The uncertainties on the Neodymium capture cross-sections provide a contribution lower than 1%. The energy dependence of the fission yields was studied with the GEF code from the thermal energy to 20 MeV. Neutron spectrum average corrections, deduced from GEF calculations, were applied to our effective fission yields with the aim of estimating fission yields at 400 keV and 500 keV, as given in the International Evaluated Nuclear Data Files (JEFF, ENDF/B and JENDL). The neutron spectrum average correction calculated for the PROFIL results remains lower than 1.5%.

Cumulative fission yields of short-lived isotopes under natural-abundance-boron-carbide-moderated neutron spectrum

This work expands the availability of energy-resolved short-lived cumulative fission product yields for 235,238,233U, 239Pu, and 237Np subjected to a 2$ pulse in the Washington State University TRIGA reactor. A boron carbide capsule tailored the neutron spectrum, creating a spectrum with an average energy of 700 keV, similar to fast reactor spectra and approaching that of 235U fission. Unique gamma spectra were collected from 4 min to 1 week after fission using high purity germanium detectors. Measured cumulative fission product yields generally agree well with published fast pooled fission product yield values from ENDF/B-VII, though a bias was noted for 239Pu.

Determination of short-lived fission product yields with gamma spectrometry

The majority of fission yield measurements to date have examined cumulative yields of long-lived nuclides. We present a method for determining independent as well as cumulative fission yields using gamma spectrometry and a Bayesian inverse analysis. This paper outlines the impetus for new fission product yield measurements, the methodology developed to measure these and other nuclear parameters, and initial experimental results for long-lived nuclides and sensitivity analyses. In initial scoping measurements, the cumulative yield of $$^{140}$$ Ba was estimated as $$4.9966\pm 0.3309$$ %, and the independent yield of $$^{140}$$ La was estimated to be $$0.0045\pm 0.0022$$ %. These estimated values are commensurate with existing literature values.

Mass distribution in the quasi-mono-energetic neutron-induced fission of 232Th

The cumulative yields of various fission products in 232Th(n, f) with average neutron energies of 6.35, 8.53 and 10.09 MeV have been determined using an off-line \(\gamma\)-ray spectrometric technique. The neutron beam was produced from the 7Li(p, n) reaction. From the cumulative fission yields, the mass chain yields were obtained by using charge distribution correction of medium energy. The peak-to-valley (\(P/V\)) ratio, the average value of light mass (\(\langle A_{L}\rangle\)), heavy mass (\(\langle A_{H} \rangle\)) and the average number of neutrons (\(\langle\nu \rangle\)) at the three different neutron energies of the present work and at other energies from the literature in the 232Th(n, f) reaction were obtained from the mass yield data. The present and the existing literature data in the 232Th(n, f) reaction at various excitation energies were compared with similar data in the 238U(n, f) reaction. The fine structure in the mass yield distribution was interpreted from the point of nuclear structure effect such as shell closure proximity and even-odd effect. The role of standard I and standard II asymmetric mode of fission was discussed. The different types of mass-yield distributions between 232Th(n, f) and 238U(n, f) reactions were explained from different types of the potential energy between the two fissioning systems. The role of excitation energy was also investigated.

Calculation of Delayed Neutron Yields for Various Libraries

This paper presents the comparison between the total delayed neutron yields (νd¯) calculated and the recommended values proposed by Tuttle, the experimental data of Waldo and those of Benedetti. These data are given for thermal, fast, and high energy fission ranges. The calculation of total delayed neutron yields is performed either by the NJOY nuclear data processing system or by the summation method. The decay data found in the various evaluations as the delayed neutron branching ratios (Pn) and the cumulative fission yields (CY) can also be validated by delayed neutron yield calculation using the summation method. In the first method, where the treatment is performed by the NJOY system, the general purpose evaluation files (JEFF-3, JEF-2, ENDF/B-VII.0 and ENDF/B-VI.4 were considered. In the summation calculation, the data used are the delayed neutron branching ratios (also called delayed neutron emission probabilities) and the cumulative fission yields that are given for thermal, fast, high energy fission and spontaneous fission. These data are found in the Radioactive Decay Data and Fission Yield Data files (File 8) of nuclear data evaluations. In this study, we also perform a benchmark calculation with various libraries: JEF-2.2, JEFF3.1.1, ENDF/B-VII.0, ENDF/B-VII.1 and JENDL/FP-2011.

Estimation of 239Pu independent and cumulative fission product yields from the chain yield data using a Bayesian technique

The independent and cumulative fission product yields (FPYs) are obtained by using the Bayesian technique based on the evaluated mass chain yield, where required constraints such as the normalization can be straightforwardly included. We apply this technique to the 239Pu FPY data at neutron incident energies of 0.5, 2.0, and 14 MeV, where the most updated mass chain yield ENDF/B-VII.1 data are available. The obtained yield data are compared with the evaluated values by England and Rider in ENDF/B-VI, and differences from their values are investigated. We show that the modern decay data used, such as branching ratios to ground and metastable states, cause differences in the evaluated individual and cumulative fission yields.

MOX fuel effects on the isotope inventory in LWRs

Although today in most of the nuclear power reactors UO2 fuel is used, currently about 40 reactors in Europe are licensed to use MOX, and over 30 are making use of this right. While the typical isotopic compositions (mostly including only the minor actinides and the major fission products) of MOX fuel is well known and described in the literature, it is difficult to find detailed data how the concentrations change for the isotopes which are important in the source term (noble gases, iodine, cesium) with respect to Pu composition and Pu content. This paper presents the results of systematic calculations to determine how the isotopic composition of MOX fuel fed into PWRs and BWRs is changing during irradiation depending on the initial plutonium composition and content and the level of burnup. For most of the fission products the differences are in the range of a few percent. This is due to the fact that the results are for a given burnup and furthermore, the differences in the cumulative fission yields are only a few 10%. Differences larger than 10% at 50MWday/kgHM can be only found for a few isotopes, e.g. 135Xe, 149Sm, 151Sm, 155Gd, 157Gd. For comparison purposes, the isotope concentration ratios between MOX fuel and conventional UO2 fuel are also provided.