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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Cluster dynamics simulation of xenon diffusion during irradiation in UO 2

Diffusion of fission gas in UO 2 nuclear fuel impacts several important performance metrics, such as fission gas release, swelling, and thermal conductivity. Current empirical models of fission gas release have significant uncertainty, some of which derives from the bulk diffusion rate and its dependence on, for example, fuel chemistry and irradiation. In this work, we have applied the previously-developed Free Energy Cluster Dynamics (FECD) methodology in the code Centipede to calculate xenon cluster concentrations in UO 2 under intrinsic (high temperature) and irradiation-enhanced (intermediate temperature) conditions in order to develop a model of the xenon diffusion coefficient based on the atomic scale mechanisms responsible for transport. While the diffusion mechanism for xenon in UO 2 is adequately described by the Xe + U 2 O vacancy cluster for intrinsic conditions, a similar process is not capable of capturing measured in-pile fission gas diffusivity at intermediate temperatures. Therefore, a different diffusion mechanism must dominate under this regime. Using calculated atomistic data, we have shown that irradiation-enhanced diffusion at intermediate temperatures occurs via the larger Xe + U 4 O y vacancy clusters, which have lower migration barriers and increase in concentration by several orders of magnitude compared to intrinsic conditions. This mechanism is enabled by the increased uranium vacancy concentration under irradiation due to Frenkel pair production. In addition, the fast migration of uranium interstitials with two attached oxygen interstitials lowers the total uranium interstitial concentration through reactions with sinks. This allows the extended defects, such as Xe + U 4 O y vacancy clusters, to maintain high concentrations by limiting annihilation with attached vacancies. Furthermore, predictions using the Xe + U 4 O y diffusion mechanism are in good agreement with experiment, albeit with some differences in the Arrhenius slope, which we believe may be related to either experimental or model parameter uncertainty. Lastly, an analytical expression suitable for application in fuel performance simulations was derived to capture the predictions of the Centipede simulations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

AGR-5/6/7 Final Release-to-Birth Ratio Data Analysis

AGR-5/6/7 is the last of a series of Advanced Gas Reactor (AGR) experiments conducted in the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL) in support of development and qualification of tristructural isotropic (TRISO) low-enriched fuel for use in the high-temperature gas cooled reactor (HTGR). AGR configuration and irradiation conditions are based on prismatic HTGR technology that is distinguished primarily through the use of helium coolant, a low-power-density ceramic core capable of withstanding very high temperatures, and TRISO-coated particle fuel. The AGR tests provide valuable irradiation-performance data to support fuel process development, qualify fuel for normal operation and accident conditions, and support development and validation of fuel performance and fission-product (FP) transport models and codes. Each AGR test consists of multiple independently controlled and monitored capsules containing fuel compacts placed in a graphite cylinder shrouded by a steel shell. Release-to-birth ratios (R/B) for fission-gas isotopes released from each capsule are calculated from release rates, measured by germanium detectors in the Fission Product Monitoring System (FPMS) installed downstream from each capsule, and birth rates calculated using numerical models of FG generation. The R/Bs are a critical measure of the ability of the fuel kernel, the particle coating layers, and the compact matrix to retain fission-gas atoms, preventing their release into the sweep-gas flow, and the impact of initially defective particles and/or particle-coating failures that occur during irradiation. For fission-gas isotopes, particle failure is defined as failure of all coating layers, allowing gaseous fission atoms to escape from a particle. During the first five cycles (162B ? 165A), R/Bs were stable in the 10-8?10-6 range, and no in-pile particle failures were observed, based on the gross gamma counts. The maximum R/B value of around 2 ? 10-6 for Kr-85m resulted from the presence of as-fabricated exposed kernels (based on the high exposed kernel fraction), the dispersed uranium, and high fuel particle temperatures in Capsule 1. Comparison of capsule-measured R/Bs from these early cycles to predictions using the previously developed AGR R/B model demonstrated FG release from the AGR-5/6/7 TRISO fuel was comparable to that of previous experiments. In addition, the Kr-85m R/B per-exposed-kernel values are comparable to R/B values obtained in AGR-3/4 irradiation experiment and four irradiation experiments performed during 1980s: (1) HRB-17/18, (2) COMEDIE-BD1, (3) HFR B1, and (4) HRB-21. In contrast, all measured R/B values are lower than predictions by the commonly used Richards and German models, which are intentionally conservative. A large number of in-pile particle failures occurred in Capsule 1 by the end of Cycle 166A. During the final four cycles (166A ? 168A), apparent damage to the Capsule 1 gas line appeared to cause FG leakage from that capsule into the other four capsules, resulting in an increase in fission gas (FG) detected in the effluent for all capsules. Isolation of the Capsule 1 gas line during the last three cycles also prevented measurement of its FG release. Thus, R/Bs in all capsules after Cycle 166A are highly uncertain because of undefined amount of leakage from Capsule 1, especially for long-lived isotopes. A few hundred in-pile particle failures were estimated for Capsule 1 before the end of Cycle 166A, but the total number of failures is unknown due to the lack of FG release data in the later cycles. Based primarily on evidence from the gross gamma counts during Cycle 168A, approximately 15 particles failed in Capsule 3 and four particles failed in Capsule 2. In-pile failures in Capsule 3 were anticipated because this capsule was designed to operate beyond the HTGR normal operating temperature range. In contrast, no in-pile failures were identified in the top two capsules (4 and 5) based on the absence of the typical spikes in gross gamma counts and low failure estimates using the AGR model, developed in INL/EXT-14-32970, for R/B of the short-lived isotopes (Kr-89 and Xe-137) with minimal leakage from Capsule 1.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Transmission electron microscopy with in-situ ion irradiation: Facilities and community

Whilst there is a clear scientific and technological need for the technical capabilities of transmission electron microscopes with in-situ ion irradiation, it also requires a collaborative community of international researchers to support such facilities in successfully meeting this demand. Instruments of this type serve to provide fundamental understanding of the mechanisms which drive changes in materials important to nuclear fission and fusion energy, the semiconductor industry, quantum information systems, space travel, astronomy, geology and many more applications. As these areas continue to evolve and the instrumentation possibilities expand, the capacity of in-situ ion irradiation facilities must also develop hand-in-hand with the user community to deliver an ever-greater diversity of high-fidelity extreme-environment experimentation. Future directions for the field, such as miniaturization from MEMS/microfluidic devices and advanced controls with ML-based analysis, continuously emerge to advance both the hardware and software which support the coupling of TEMs with ion beams. This review sets out to provide up-to-date insights into the community and advancement of current, and development of future, facilities which have the potential to further unlock access to the nanoscale exploration of coupled extreme environments crucial to many of the important science and engineering challenges we face today.

In-situ irradiation↗
DOE OSTI2020

Microstructure evolution in U-10Zr alloy irradiated by swift Xe ions at 700 °C

The post-irradiation examination (PIE) results of U-10Zr binary metallic fuel that was irradiated by 84 MeV Xe ions at 700 °C are reported here. The U-10Zr specimen was synthesized by homogenizing elemental U and Zr powders through arc-melting. The as-fabricated U-10Zr was dominated by the sub-micron acicular α+ δ phase. After being irradiated by 84 MeV Xe ions at 700 °C up to 2.19 ×10 17 ions/cm 2 fluence, the U-10Zr was speculated to evolve into micro-scale γ 1 + γ 2 phases as predicted by the U-Zr phase diagram. During post-irradiation cooling, the U-rich γ 1 phase was mainly transformed to the αphase, while the Zr-rich γ 2 phase was partially retained along with formation of hexagonal structure phase (δ or ω). Xe bubbles formed in the γ 1 and γ 2 phases have salient different morphologies, implying faster Xe diffusion in the γ 1 phase than the γ 2 phase. The quantitative bubble morphology data collected in this study can provide valuable references for the development and validation of fuel performance models for this fuel.

36 MATERIALS SCIENCE↗
DOE OSTI2025

U-Pu and Ba-Cs isotopic measurements on Trinitite by laser ablation sampling on the Neoma MC-ICP-MS

In this study we present the results of combined U-Pu and Ba-Cs isotope measurements obtained by laser ablation (LA) sampling of two glassy debris fragments (‘Trinitite’) from the world's first atomic bomb detonation conducted in New Mexico on July 16, 1945. Our primary goal in conducting these measurements was to understand whether examination of the U-Pu and Ba-Cs systematics by direct sampling (e.g. without any chemical separation or purification prior to isotope ratio measurement) could yield meaningful information that would differentiate the Trinitite fragments from glassy material lacking a nuclear fission signature. These measurements were conducted on a ThermoFisher Scientific Neoma multi collector – inductively coupled plasma – mass spectrometer (MC-ICP-MS), which is a relatively new MC-ICP-MS platform, so we also examine the behavior of these isotope systems in standards sampled in solution and via LA. Unsurprisingly, the measurements made on purified solutions of the U, Pu, and Ba isotopic standards produce high precision isotope ratios. Furthermore, this extends to the U-Pu measurements made by LA sampling, with the expected degradation in precision and accuracy related to matrix effects and signal intensity fluctuation. However, the Ba-Cs data acquired by LA is of low precision across all of the matrices examined and bears evidence of complex mass fractionation that will require further investigation to resolve. In total, our results indicate that the observed U-Pu isotope data are of sufficient quality to accurately constrain the U and Pu isotopic composition of glass containing sub-ppm levels of these elements which in turn could be used to differentiate glass containing anthropogenic fission products from natural glass whereas the Ba-Cs LA data cannot be used for this purpose until further methodological refinement is performed.

Ba-Cs↗
DOE OSTI2025

Elucidating Quintet-State Dynamics in Singlet Fission Oligomers and Polymers with Tetracene Pendants

To unlock the potential of molecular engineering for practical quantum sensing and computing, it is essential to create and control pure magnetic states in molecular systems. Singlet fission (SF) in organic materials offers a promising approach by generating pairs of triplet excited states from photoexcited singlets. Here, in this work, we investigate SF in a polymer with strategically positioned tetracene pendant groups along a polynorbornene backbone and its oligomeric counterparts, facilitating intrapolymer through-space coupling. Using continuous-wave and pulsed time-resolved electron paramagnetic resonance (EPR) spectroscopy, we elucidate the spin dynamics and identify key intermediates, including the quintet state, that emerge during SF. Our findings reveal that exciton translational motion along the pendant groups enhances the dissociation of triplet pairs, with oligomer length playing a critical role in modulating spin state interconversion and exciton transport. Our results provide key insights into the SF mechanism in polymeric materials and highlight the role of oligomer length in modulating spin state interconversion and exciton transport. This work advances our understanding of SF in polymers, paving the way for their application in quantum information science and energy conversion technologies.

Bindra, Jasleen K. [Argonne National Laboratory (A↗
NASA NTRS2018

Gradient Field Imploding Liner Fusion Propulsion System: NASA Innovative Advanced Concepts Phase I Final Report

The advancement of human deep space exploration requires the continued development of energetic in-space propulsion systems, from current chemical engines to nuclear thermal rockets to future high energy concepts such as nuclear fusion. As NASA embarks on a program to develop near-term nuclear thermal propulsion, this NASA Innovative Advanced Concepts (NIAC) Phase I activity was funded to investigate the feasibility of an innovative approach toward highly energetic pulsed fusion propulsion. Previous concept studies have proposed the conversion of fusion energy for in-space propulsion, ranging from laser-ignited fusion systems such as Gevaltig and VISTA, to the British Interplanetary Society's Daedalus concept and its more recent incarnation under Project Icarus, to steady-state spherical torus fusion systems. Recent NIAC studies have also evaluated several innovative fusion concepts, including the acceleration and compression of field reversed configuration plasmas in time-changing magnetic fields, magnetically driven liners imploding onto plasma targets, and high current z-pinch compression of material liners onto fission-fusion fuel targets. While each of these studies firmly established the potential benefits of fusion systems for interplanetary travel, they also identified significant challenges in successfully engineering such systems for spacecraft propulsion. The concept outlined in this Technical Publication (TP) builds on the lessons learned from these prior activities, approaching the quest for fusion-powered propulsion through an innovative variation of magneto-inertial fusion concepts developed for terrestrial power applications.

Lapointe, M. R.↗
DOE OSTI2021

Nuclear Excitation and Fission Studies with Short Pulsed Laser-Driven High Energy Gamma Rays

We propose the development of a platform to study photon excitation of high Z nuclei utilizing a high energy (70 J) short pulsed (500 fs) laser to drive > 5 MeV γ-radiation. The laser beam will be focused onto a specially prepared foam or corrugated conveying target, where it generates relativistic MeV electrons via ponderomotive and wake-field acceleration mechanisms. γ-emission is produced in the form of bremsstrahlung in the same target or in a separated high-Z γ-production target hit by the accelerated MeV electrons. The high energy γ-rays will be utilized to provide nuclear state excitation in the short time domain. The γ platform will allow to investigate photo fission of high Z target material positioned in an auxiliary target chamber in the γ-ray beam path via the established gas transport scheme. The photo fission yield will provide furthermore diagnostic information on the produced γ-yield. In addition, γ-spectroscopy will be used to identify γ-lines for the diagnostic of the excited state population of high Z target nuclei. This research capability is relevant to the understanding of how nuclear excitation effects fission, in relevance to recent astrophysical observations on element nucleosynthesis. These processes involve neutron-rich fragments and processes such as fission recycling (e. g. in neutron stars outer crusts).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

An Autonomous Critical Data Extrapolator for the AGN-201m

Nuclear nonproliferation serves as a key goal, being undertaken by the International Atomic Energy Agency (IAEA). To recognize proliferation there are two pathways that states, who intend to use nuclear material for malicious purposes can take, diversion can misuse. Diversion is when fissile nuclear material is declared to the IAEA for non-weapon purposes, but then covertly removed. If the source of nuclear material, that is not declared and not fissionable, is placed inside the reactor core to create fissile material used to create weapons then the state is using the second pathway of proliferation, misuse. With the emerging development in areas of simulation and machine learning the creation of virtual models of reactor systems, digital twins, serve as a potential method to identify proliferation through detecting anomalous behavior in the reactor. A digital twin for a physical nuclear reactor has never been developed, as digital twins serve as an emerging technology. To investigate the process for development and use of a digital twin for a nuclear reactor Idaho State University’s AGN-201m serves as the nuclear reactor used for development of this digital twin. A data acquisition system has been installed to the reactor system allowing for the transfer of collected data from a reactor operation to Idaho National Laboratory’s Deeplynx data warehouse. When utilizing data to train reactor physics and machine learning models, a significant challenge encountered is the initial state of the data. Nuclear proliferation will have the capacity to be detected when the reactor immediately starts up, nor will it occur after the reactor shuts down. Generally, it will be detected when the reactor is operating at some desired power over a sufficient period for that specific reactor design. For the AGN-201m this will be when the reactor is critical (generally 1 mW or above) for a timespan that is within or less than the range of a regular business day. Datasets sent to Deeplynx have had to be manually cut to when the reactor is critical based on plots of power levels. This method is inefficient and laborious, especially when using multiple datasets at once to train a model. To provide a more streamlined approach an automated critical data extrapolator is developed, with capabilities of recognizing when the reactor operation first reaches criticality, and when the reactor undergoes a SCRAM and is shutdown.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

An Evaluation of a Neutron Time Correlated Interrogation Method for Measurement of Fissile Content in Research Reactor Spent Fuel Assemblies

There are many research reactors worldwide that have been, or are being converted from the use of high enrichment uranium (HEU) to low enrichment uranium (LEU, < 20% enriched). The verification of fissile content and initial enrichment of the spent fuel is needed for the effective safeguards of the fuel. The advanced experimental fuel counter (AEFC) was developed for the measurement of spent fuel rods and assemblies from research reactors for safeguards verification. This measurement system contains components for active neutron interrogation, passive neutron totals counting, neutron coincidence counting, and gross gamma-ray counting. This report presents the first application of the time correlated interrogation technique for the measurement of the 235 U content in research reactor spent fuel assemblies. The technique, called time correlated induced fission (TCIF), uses a 252 Cf neutron source to irradiate the fuel assembly, and the subsequent induced fission events in the fissile material are measured by coincidence counting. The doubles rates are enhanced by having the neutron trigger events from both the 252 Cf source and the induced fission neutrons in the same time gate in the coincidence analysis. The average neutrons per fission of the 252 Cf source is 3.76 and the induced fission neutrons for 235 U is 2.44, so the number of neutrons that are produced is higher than for random neutron interrogation. This high effective neutron number increases the multiplicity counting rates and reduces the statistical error. The background coincidence counts from the 252 Cf are reduced by the water in the sample cavity and the polyethylene surrounding the 3 He detector tubes. This method of active neutron interrogation has been applied to the measurement of spent research reactor (IRT) fuel assemblies. The advanced experimental fuel counter (AEFC) was used to compare the TCIF method with the typically used AmLi neutron interrogation source that emits neutrons that are random in time. The statistical uncertainty for the use of the random neutron source (AmLi) and the time correlated source ( 252 Cf) for spent fuel interrogations was evaluated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Cumulative short-lived photofission product yields for nuclear forensic application

Experiments have long been carried out with linear accelerator (linac) produced bremsstrahlung X-rays to study high-energy photon-induced fission, known as “photofission”. One benefit of photofission, when compared with neutron-induced fission, is the ability to investigate fundamental physics of fission at excitation energies lower than what is possible with neutrons [1]. Absorption of an incident neutron results in a compound nucleus with an excitation energy at least equal to the neutron binding energy; thus, the lowest energy region of the fission barrier cannot be studied. Fission product yield distributions are dependent on the incident particle energy and the target nucleus mass. They are generally represented by a double-humped curve, with low and high mass “peaks” and an intermediate mass “valley”. As incident particle energy increases, the excitation energy of the nucleus increases, thereby increasing the overall yield of isotopes in the valley with respect to the two maxima or peaks of the fission product curve [3]. Photofission is most probable for incident photons around 14 MeV due to the giant dipole resonance. Induced photofission around this energy results in a fission product yield distribution that resembles 14 MeV DT neutron fission more than thermal or fast (500 keV) neutron fission. In post-detonation nuclear forensics, the peak-to-valley ratio of the fission product yield curve could be used for characterizing device type by providing an indication of the neutron energy spectrum that had induced fission (e.g., 500 keV vs. 14 MeV). The goal of this work is to improve nuclear data for isotopes of interest in nuclear forensics and special nuclear material (SNM) detection, specifically the fission product yield data via photofission experiments for the isotopes of 238U and 232Th. Photofission has been proposed as a less costly and more flexible production method for the valley isotopes that are representative of DT neutron fission product yield distributions, which would benefit nuclear forensics exercises in testing for analysis techniques. Natural uranium and thorium targets were irradiated with bremsstrahlung photons (nominal endpoint energies of 8, 14, and 20 MeV), generated via impingement of high-energy electrons on a tungsten electron-to-photon radiator. Gamma-ray spectroscopy was used to observe and identify the decay of the resulting fission products. The photofission yields of 102 fission products were measured for the set of the 238U and 232Th targets at the three bremsstrahlung X-ray endpoint energies 8, 14, and 20 MeV. These fragments included masses ranging from A=84 to A=144, with half-lives as short as 1.07 seconds.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2023

Quick Look Report of Godiva U233 shot March 2022 Data Collection Activities

This report discussing the March 2022 irradiation of U233 on the Godiva critical assembly using burst mode and subsequent analysis of the fission products starting at 65 minutes post irradiation, and ending 12 days later. The Short-Lived Fission Product Yield (SLFPY) project is one of many efforts under the Nuclear Physics Multi-Lab and related Venture Project. The objective of the SLFPY project is to provide improved measurements of fission product yields for select nuclides. The SLFPY project consists of measurement and analysis campaigns. To produce fission data, samples of actinide material are irradiated in a high-flux neutron environment. These samples are quickly placed in front of a detection system where both gamma singles and coincidence spectra are collected as a function of time. Gamma spectroscopy is performed on the irradiated material on site near the irradiation facility, starting as soon as feasible after the irradiation and continuing for 7 days or longer. Following the data collection, time-dependent fission yield analyses are performed using gamma-ray spectroscopy. This document summarizes the measurement campaign performed March 21 - April 4, 2022 where sub-gram quantities of 233 U nitrate (UO 2 (NO 3 ) 2 ) were irradiated in the Godiva reactor. The Godiva burst #2076 conducted under experiment IER 504 had a temperature change of +156 degrees Celsius, lasted 13.32 microseconds, and had a reactivity of $\$$1.089. The targets consisted of uranium oxide solution deposited in a quartz tube and packed with quartz wool. The flame-sealed quartz ampoules were used to contain the uranium samples for the irradiation and count activities. On March 22, 2022, at 10:27:00 a.m. the three uranium ampoules, along with a witness foil pack, were irradiated in the Godiva critical assembly using burst mode operations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Analysis of Using a Hybrid ZIRCEX Process to Generate High-Assay Low-Enriched Uranium (HALEU) - 20158

Idaho National Lab (INL) is investigating the feasibility of providing High-Assay Low Enriched Uranium (HALEU) by recovering Highly Enriched Uranium (HEU) from spent nuclear fuel (SNF) and downblending the HEU with natural, low-enriched, or depleted uranium (NU, LEU, or DU). That investigation identified that significant quantities of HALEU could be produced with a Hybrid ZIRCEX process to further advanced reactor research while reducing INL's environmental liability. Many new advanced reactor designs are being developed with improved safety, efficiency, and economics. Most require nuclear fuel with U-235 enrichment between 5% and 20%, which is defined as HALEU. Although technically feasible, there is no current domestic capability to make HALEU in the US. While it is anticipated that industry will provide HALEU through commercial enrichment once advanced reactors mature, until a market is established, an interim source of HALEU is needed to enable research and demonstration. An interim source of HALEU could be provided by recovering the HEU in some DOE-managed SNF and downblending it to between 5% and 20% using the Hybrid ZIRCEX Process. ZIRCEX is a dry head-end process to remove cladding (zirconium or aluminum) from SNF. Drying of the SNF is needed prior to introduction to ZIRCEX. After cladding removal, uranium and fission products in the bed material are oxidized and elutriated. In a Hybrid ZIRCEX process, the HEU process stream is sent to a very compact, modular solvent extraction process for uranium purification. The uranyl nitrate from solvent extraction is denitrated and calcined to produce a HALEU product ready for fuel fabrication. The long-lived fission products from solvent extraction are immobilized in glass using a small in-can melt. By removing the cladding before dissolution, the volume of glass waste is reduced by a factor of up to 300 times (when compared to not removing the cladding from the fuel). Other radioactive wastes from the process could be disposed of as Class A or Class B low-level waste. In addition to producing HALEU for advanced reactors, consumption of SNF would reduce DoE's environmental liability. Incorporating low-enriched spent fuel (versus exclusive use of LEU, DU, or NU) into the downblending scheme could reduce the SNF inventory even further. Several downblending and enrichment scenarios using INL fuels were investigated in this study. The results of this analysis show that the Hybrid ZIRCEX process could make a significant contribution to needed HALEU feedstock and reduce the environmental liability of managing SNF at INL. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1978

Excess fission xenon at Apollo 16

Results are reported of stepwise heating analyses of Xe and Kr in four Apollo 16 low-grade breccias: 60019, 60225, 60275, and 67455. All four samples contain significant amounts of solar wind gases and at least three contain excess fission Xe. This observation indicates that the excess fission Xe effect is global rather than local, i.e., results from moon-wide redistribution of fission Xe rather than local redistribution in KREEP-rich Apollo 14 material. It is suggested that the excess fission Xe phenomenon represents a temporal variation in the amount of fission Xe available for redistribution, that it is prominent in samples from both highland sites simply because they are older than mare sites, and that samples from these sites had experienced at least some of their surface exposure at an early epoch.

Bernatowicz, T. J.↗
DOE OSTI2020

An Analytic Benchmark for the Solution to the Isotopic Fission Spectrum Mixture Problem

In neutron transport calculations, it is common to specify material compositions in terms of constituent isotopes. Material compositions may be described by isotope number densities and associated microscopic cross sections. For general reaction cross sections, the macroscopic cross sections of a composition are simply the summation of the sum of the products of isotope number densities and microscopic cross sections. A notable exception is the mixture of the neutron fission spectrum in fissile material. To demonstrate proper and improper mixture of the neutron fission spectrum, a zero-dimensional test problem is developed. Using the test problem, it is demonstrated that the improper mixing of the fission spectrum results in an eigenvalue error of approximately 65 pcm. Though this may seem small, any error in such a simple calculation is unacceptable. In similar infinite-homogeneous test problems, eigenvalue errors of more than 300 pcm have been observed. It is also shown that the error due to fission spectrum mixing can be exaggerated for computer program verification purposes. It is concluded that the proper mixture of the neutron fission spectrum is essential for accurate neutron transport simulations. The effect of improper neutron fission spectrum mixture is demonstrated and quantified and this test problem may be used for verification purposes in the future.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗