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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Random Variation of ACRR Core Report

The research presented in this paper is to be a contribution to a larger research project. The project was designed to test the safety standards of Sandia National Laboratories' ACRR. The MCNP model of the ACRR core is being used to simulate the environment. To test the safety standards, the dimensions and density of the fuel in the core were varied randomly. Each rod had its own dimension and density assigned to it randomly. Ten different cases of the ACRR core were randomly created. The different cases were studied using 640-group neutron fluxes. The fluxes were compared to see how the variations affected the system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

(U) Energy-Dependent Perturbations of Scattering Cross Sections Using the PERT Card in MCNP6.2

The PERT card is used for first- and second-order perturbations of material densities, isotope densities, and isotope cross sections in the MCNP6.2 Monte Carlo code. Using the PERT card for firstand second-order sensitivities is straightforward. Reference 2 only looked at density perturbations with no energy dependence. This report looks at the sensitivity of a response to scattering cross sections as a function of energy and finds that there is a bug in the PERT capability. The SENSMG multigroup neutron sensitivity code was recently given the capability of computing sensitivities to user-specified reactions whose cross sections are available in a user-supplied NJOY output file. SENSMG uses the PARTISN multigroup discrete ordinates code for the transport. The NJOY-reaction capability is similar to that of SUSD3D, which also uses PARTISN for the multigroup transport. The PERT bug was identified by comparing MCNP6.2 outputs with SENSMG outputs. The next section of this report describes the test problem. Section III presents the MCNP6.2 PERT bug and proposes a solution. Section IV is a summary and conclusions. The SENSMG and MCNP input files are listed in the appendix.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2020

A Mercury Model of the Molly-G Fast Burst Reactor (FBR)

In order to design neutron irradiation experiments at a given nuclear reactor, one requires a representative neutron spectrum for the configuration of the reactor that will exist during the experiment. This usually implies modeling the operation of the reactor using a neutron transport code. Since the modeling of pulsed neutron reactors is quite complex, requiring coupled modeling of neutronics and thermo-structural response, the typical methodology employs analysis of the neutron spectrum which is obtained from a static keff calculation. While this time-independent Eigenfunction is not truly representative of that during a reactor pulse, we postulate that it is a reasonable representation for our purposes. The Nuclear Survivability (NS) Program at LLNL is considering fielding such experiments at the Molly-G (‘Molybdenum Godiva-II’) Fast Burst Reactor (FBR) at the White Sands Missile Range (WSMR). The goal of these experiments is to (a) test / proof / calibrate diagnostics, and (b) test the efficacy of neutron shield configurations, before fielding at other nuclear reactors, such as the Annular Core Research Reactor (ACRR) at SNL/NM. After attempting to secure either drawings or a copy of an existing MCNP model of the Molly-G FBR from various institutions, it was decided to develop a new model for use with the Mercury Monte Carlo transport code. The model described herein will be used to design these experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

AWCC Simulations

Neutron well counters provide a means to measure fissile mass by detecting coincident neutrons, which is a unique signature to fission. For coincidence counting, mass is determined using a calibration curve established with items that have the same material characteristics. Multiplicity analysis solves the point model equations for mass using known detector parameters. In both cases, mass measurements may exhibit a bias due to item characteristics and should be corrected for. Experiments can be done to estimate bias and material effects, but they require having both the well counter and the material well defined. In pursuit of estimating measurement bias and uncertainty in a High Efficiency Neutron Counter (HENC), an MCNP simulation was matched to measurements performed with an Active Well Coincidence Counter (AWCC) to de ne a neutron source term. The neutron source term will be used to predict measurement performance of similar material types in a HENC.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Characterization of Partial Charge Collection Induced by Neutron Damage in High-Purity Germanium Detectors

This paper investigates the correlation of damage induced by neutron interactions and degradation in the spectra of HPGe detectors. As neutrons kinetically interact with germanium crystals, they create interstitial and vacancy defects within the lattice. These defects then interfere with the charge migration of electron-hole pairs and reduce resolution in the observed energy spectrum. The partial charge collection produces observable spectral changes by increasing the peak width and reducing resolution (full width half maximum). A detailed characterization using various check sources was performed before and after iterations of neutron exposure in order to observe the effects of the neutron damage. An additional set of measurements was performed along with characterizations to show the detector’s response at discrete locations on the HPGe crystal. This was done to observe how the spectrum changes when the gamma rays are isolated to regions of various thicknesses of germanium. In order to impart damage, the detector was placed inside a californium shuffler with the face of the detector against the guide tube for the 252 Cf source. For irradiation of the HPGe, the source was then positioned in front of the face of the detector using the stepper motor of the shuffler. The neutron exposure time intervals were recorded and increased based on the initial damage observed. An MCNP simulation was performed to estimate the amount of interactions that occurred in the germanium crystal to ensure enough damage had occurred. Studying the effects that neutron damage imparts on a bullet-type HPGe detector can help provide necessary data to estimate total neutron exposure limits, reduce the likelihood of decisions made on suspect data, and aid in diagnostics of a damaged detector.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Technical Interface Coordination with SHINE (FY2020 Summary)

In FY20, Los Alamos National Laboratory (LANL) performed technical interface coordination with SHINE including coordination of SHINE CFD and thermal hydraulics conference calls, national laboratory conference calls, and program management activities such as reporting and tracking requirements for current FY20 activities. SHINE did not request any general technology consultation support for emergent issues. LANL has participated in the bi-weekly conference calls with SHINE and other national laboratories regarding LANL’s current activities. Activities discussed include the Supo 3-D CFD model geometry validation, releasing the CFD-MCNP coupled codes for the generic solution vessel simulations, and the ANL bubble experiment #2 design, preparation, and collaboration.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2020

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than \building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of MCNP, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than "building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of MCNP, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers. In this paradigm, reduced complexity computational and analytical models still have an important purpose. The explicit form of an analytic solution is arguably the best way to understand the qualitative properties of simple models. In contrast to "building up" a complex problem through understanding simpler problems, results from detailed computational scenarios can be better explained by "building down" the complex model through simple models rooted in the fundamental or essential phenomenology. Simplified analytic and computational models can be used to 1) increase a user's confidence in the computational solution of a complex model, 2) confirm there are no user input errors, and 3) ensure essential assumptions of the simulation tool are preserved. This process of using analytic models to develop a more valuable analysis of simulation results is named the results analysis methodology. The utility of the results assessment methodology and a complimentary sensitivity analysis is exemplified through the analysis of the neutron flux in a dry used fuel storage cask. This application was chosen due to current scientific interest in used nuclear fuel storage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Comparison Study of Upper Subcritical Limits Derived Using Sensitivity/Uncertainty Tools Case Studies of Benchmarks and Applications

Neutron transport methods used to establish subcriticality require validation by comparison to critical experiments considered to be benchmarks. Whisper is a sensitivity/uncertainty analysis tool developed to assist with the task of validation in nuclear criticality safety. Details on the Whisper methodology can be found in References 1-3 on the MCNP ® reference collection website at https://mcnp.lanl.gov. Whisper-1.0 was originally developed in 2014 and used to assist with nuclear criticality safety validation at Los Alamos National Laboratory. Whisper was upgraded in 2016 to Whisper-1.1 and prepared for release with MCNP6.2. Whisper contains a library of over 1100 critical experiment benchmarks and quantifies neutronic similarity of an application to benchmarks in the library. Using highest similarity benchmarks, Whisper computes a calculational margin (CM) encompassing of the worst-case bias and bias uncertainty at a 99% confidence level for each application. In addition, portions of the margin of subcriticality (MOS) for nuclear data uncertainty and potential code errors are computed. The baseline upper subcritical limit (USL) computed by Whisper is comprised of the CM, MOS nuclear data , and MOS code errors . The Whisper baseline USL is absent a portion of the MOS due to the area of application, which is applied based upon judgment by the criticality safety analyst. An objective of this paper is to present the baseline USL, CM and portions of the MOS as computed by Whisper for comparison with similar sensitivity/uncertainty tools, such as those used by IRSN and ORNL. The initial comparison involves four critical experiment benchmarks: HEU-MET-FAST-013-001, HEU-SOLTHERM-001-008, PU-MET-FAST-022-001, AND PU-SOL-THERM-001-001, which have been: 1. modeled independently by LANL, IRSN, and ORNL based upon information provided in the ICSBEP Handbook, 2. are common in S/U libraries for LANL, IRSN, and ORNL, 3. span a range of energy spectrum and fissile material, and 4. taken as applications for the purposes of this study and therefore excluded from use as a benchmark for calculating the upper subcritical limit. Results presented in this paper have been computed using covariance data for all isotopes in ENDF/BVII.0 using a 44-group energy structure. Benchmarks in the Whisper library were run in MCNP6.2 using 100,000 neutrons per cycle, skipping 100 cycles for 500 active cycles. Reference 10 also compares the results for baseline USL with an order of magnitude greater neutrons, using the same total number of cycles with 1,000,000 neutrons per cycle. Subsequent to the results presented in Reference 10 changes were made to the benchmark library, as discussed in Reference 11. Newer results using the revised benchmark library are presented herein.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

HFIRCON Version 1.0.5 User Guide

The High Flux Isotope Reactor (HFIR) Controller (HFIRCON) code is a collection of python routines and C plugins that automate the workflow for fuel and single- or multicycle target depletion analyses for HFIR at Oak Ridge National Laboratory (ORNL). This code calls the LAVAMINT (LAVA Model Interrogator) parallel (MCNP) Monte Carlo N-Particle model interrogator to stochastically calculate cell volumes and bounding boxes, the ADVANTG (Automatic Variance Reduction Generation) code package for all variance reduction and source biasing calculations, the ORNL-Transformative Neutronics/MCNP5 transport solver for all transport solutions, and the MSX_DEPLETE module to perform all depletion calculations via the ORIGEN (Oak Ridge Isotope Generation) application programming interface. It also performs a robust set of postprocessing functions to automatically provide summaries of several key metrics that are common to a wide variety of typical HFIR design and safety-basis analyses.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Updates to Relevance Vector Machine: Multiclass Classification, Variable Selection, and Proof-of-Concept Application to Safeguards Fresh Fuel Verification using List-Mode Neutron Collar Data

To expand the capabilities of safeguards authorities to verify the integrity of fresh fuel assemblies, Oak Ridge National Laboratory has retrofit the existing electronics of the JCC-71 uranium neutron coincidence collar, which contains 18 3 He neutron detectors and an external 241 AmLi(α, n) neutron interrogation source arranged to surround a fresh nuclear fuel assembly. The new electronics system allows analysts to record list-mode neutron multiplicity data in addition to the singles and doubles rates that are currently measured. Based on previous proof-of-concept research, analysis of these new data will identify off-normal fuel configurations in an assembly and characterize or localize the specific partial fuel defects. The purpose of this report it to document the analysis algorithm development and then to demonstrate its capability for the safeguards verification of fresh fuel assemblies using list mode neutron collar data. To analyze the complex list-mode data collected with the upgraded uranium neutron collar, multivariate classification algorithms are being developed using a novel classification method, the relevance vector machine. This approach may be applied to multiclass problems to estimate the probability that test data belongs to one of many possible classes of data. In addition, our method identifies the most useful variables/channels for making predictions, which illuminates the basis for the model’s predictions, and this interpretability is largely unique among data analytics methods. Variable selection occurs during model training and parameter tuning and does not need any external hyperparameter tuning routines. Finally, we apply the modified relevance vector machine to a simulated dataset of list-mode neutron collar data generated with the radiation transport code MCNP. The method can correctly identify off-normal fuel configurations, categorize the data according to four fuel defect scenarios, and rank the channels in the data according to prediction utility. For nuclear safeguards applications, it is concluded that this method has the potential to increase the sensitivity and reliability to detect missing fuel rods from a standard 17 x 17 Pressurized Water Reactor (PWR) fresh fuel assembly. Within this analysis, “off-normal” (i.e., missing fuel rods) were correctly classified in 17 simulated test scenarios with one quarter (25%) of the fresh fuel rods missing using a training data set of 58 simulated measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

As-Run Neutronics Evaluation for the CSM-10584 Experiment in the ATR

This engineering calculations and analysis report (ECAR) documents the results of the Advanced Test Reactor (ATR) detailed Monte Carlo N-Particle (MCNP) code full-core model as-run physics analysis performed to support the Colorado School of Mines (CSM) experiment in the B-5 position.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Oak Ridge National Laboratory Shutdown Dose Rate Code Suite

The Oak Ridge National Laboratory (ORNL) shutdown dose rate (SDDR) code suite calculates gamma dose rates at a location of interest due to activation of materials. The code suite is based on the rigorous two-step (R2S) method that involves two radiation transport calculations: (1) neutron radiation transport to determine neutron fluxes in the material for which activation calculations will be performed and (2) gamma radiation transport to determine dose rates at a location of interest, due to material activation. The ORNL SDDR code suite is used to determine an importance function that characterizes the neutron’s importance to the final SDDR when the Monte Carlo radiation transport method is used. This report demonstrates how the ORNL SDDR code suite is implemented through the following codes: Monte Carlo N-Particle (MCNP) code Version 5-1.60, Oak Ridge Isotope Generator (ORIGEN), MSX suite of utilities, Neutron Activation Gamma Source Sampler (NAGSS), and Automated Variance Reduction Generator (ADVANTG). For this demonstration, the International Thermonuclear Experimental Reactor (ITER) SDDR benchmark problem is used and the dose rate result is compared to previously published work.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2020

Analysis with the ORIGEN Module of PNAR Spent Fuel Measurements for Nuclear Safeguards Applications

This report documents the analysis of the Passive Neutron Albedo Reactivity (PNAR) measurements for 23 boiling water reactor spent fuel assemblies that were performed in Finland under Action Sheet 65, which is an international collaboration on spent fuel safeguards verification methods in the context of the Finnish spent fuel encapsulation/repository system. PNAR measures the passive neutron and gamma emission rates from each of the spent fuel assemblies like a Fork detector, and it also measures the PNAR ratio, which is expected to correlate with the net neutron multiplication of the measured fuel assembly. The analysis was performed with the Oak Ridge Isotope Generation and Depletion (ORIGEN) Data Analysis Module, which was originally developed for predicting Fork detector spent fuel measurement signals in real time and has been integrated into the Integrated Review and Analysis Package developed by Euratom and the International Atomic Energy Agency. The module includes the ORIGEN burnup analysis code and integrates detector response functions pregenerated using the MCNP Monte Carlo transport code to predict the detector signals in several seconds per assembly. In this study, new response functions specific to the analyzed PNAR measurements were generated for the ORIGEN Module. The study also analyzes the impact of using detailed fuel design and operation information vs. standard safeguards information on the results calculated with the ORIGEN Module. Using detailed information reduced the standard deviation of the relative differences between calculated and measured neutron count rates among the 23 assemblies from ~10% to ~4%. The results obtained using standard safeguards information for these PNAR measurements were similar to those obtained for the Fork detector. A clear trend was found between the calculated net neutron multiplications and the measured PNAR ratios of the 23 assemblies. An uncertainty assessment of the calculations was also performed to estimate the potential impact of the accuracy and the completeness of declaration information on the calculated results for the count rates and net neutron multiplications. The ORIGEN Module predictions for PNAR signals and net neutron multiplication are expected to directly support the safeguards inspectors’ efforts to verify operator declarations of a spent fuel assembly in real time in safeguards practices.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Total Measurement Uncertainty in Neutron Coincidence Multiplicity Analysis

Neutron multiplicity counting is the most commonly used nondestructive assay technique for determining the plutonium mass within containers of scrap PuO 2 or mixed oxide (MOX). In multiplicity analysis, the 240 Pu eff mass, leakage multiplication, and alpha ratio (the ratio of [α, n]-to-spontaneous fission neutron production) are the three primary unknown sample properties. They must be determined simultaneously. To solve for these three unknowns in a multiplicity assay, three measured values are needed: the singles, doubles, and triples neutron count rates. While the analysis is limited to solving for three unknowns, there are many additional factors that impact the observed count rates and contribute to the measurement uncertainty. In this study we investigate the various uncertainty contributors for the multiplicity analysis through a combination of traditional uncertainty propagation techniques supplemented by Monte Carlo simulations to address the dependences not explicitly expressed by the point source model. Uncertainties arising from counting statistics, calibration parameters, calibration method, nuclear data, and various material characteristics (isotopic abundances, chemical form, density, and impurities) are considered. A Total Measurement Uncertainty (TMU) estimate is then developed from these uncertainty contributors. This study is confined to multiplicity analysis of items commonly encountered in international safeguards applications. That is, the study focused on Pu oxides and MOX materials for the masses ranging up to 4000 grams total Pu. Multiplicity measurements were simulated using MCNP V6 based on the Plutonium Scrap Multiplicity Counter (PSMC), Epithermal Multiplicity Counter (ENMC), Pyrochemical Multiplicity Counter, and Large Epithermal Multiplicity Counter (LEMC) for this study; however, this report focuses on the parameterization of the uncertainties for the PSMC. The performance differences between the PSMC and the other multiplicity counting systems are relatively small, primarily manifesting in the impact on measurement precision so that the evaluation developed for the PSMC can be applied to the other multiplicity counting systems. Finally an analysis tool, the Multiplicity TMU Estimator, was developed from this study to serve as an aid for evaluation of the total measurement uncertainty of multiplicity assay results obtained from the commonly used INCC acquisition and analysis software.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Calculated Gamma Output from a 6-kilogram Sphere of Neptunium

We previously modeled a 6 kg neptunium sphere with pyDMTK 2.0.0b, a python-based intrinsic radiation (INRAD) modeling tool, on the MOONLIGHT machine. Here we report results from version 2.0.1b on SNOW, another TriLab Linux Capacity Cluster (TLCC) resource on the Laboratory’s Turquoise network. We also present gamma output from MCNP 6.2.0 in terms of discrete line strengths, full gamma spectra, and dose rate maps for visualization. Results from both models agree with recent gamma measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Performance Demonstration of Self-Powered Neutron Detectors for Steady-State Reactor Operations

The irradiation testing of sensors in reactors is a crucial step towards calibrating and qualifying sensors prior to their deployment in experiments. This report details the process toward qualifying and calibrating custom-designed rhodium-based self-power neutron detectors (Rh-SPNDs) for steady-state reactor irradiations. This process serves to both demonstrate the performance capabilities of Rh-SPNDs as well as to provide experimental data for development of a sensor sensitivity model. Two designs of Rh-SPNDs were tested in various reactors to demonstrate: detection resolution in a low neutron flux environment, a delayed-response compensation technique, output linearity in a large range of neutron flux, and measurement accuracy verified with dosimetry. The detection resolution and compensation technique was demonstrated in the AGN-201m reactor at Idaho State University. The irradiation confirmed the sensors’ capability to perform steady-state operations in a low neutron flux of ~2E8 n/cm 2 -sec. Sensor output linearity coupled with the delayed-response compensation was investigated at the neutron radiography reactor at Idaho National Laboratory. A Rh-SPND was irradiated to neutron fluxes ranging from 2E8 to 2E13 n/cm2-sec range. The measured data demonstrated a wide and linear range of operation with a measured linear sensitivity of 1.0129 ×10 -13 A/W with a correlation-squared value of r 2 =0.9927. The measurement accuracy was investigated at the Advanced Test Reactor Critical reactor. The SPNDs were inserted into a test vehicle with collocated flux wires. Two irradiations with different flux levels were performed, and the SPNDs relative measurement between the two irradiations was calculated to be 1.2613 ± 0.0153 for the small SPND design and 1.1809 ± 0.0108 for the large SPND design. Both SPND measurements fell between the co-axial dosimetry result, which reported 1.218 ± 0.047. Additionally, the preliminary MCNP model for calculating SPND sensitivity was developed in parallel to this work. Modeled neutron spectrum with measured magnitude was used for inputs to determine the simulated SPND output. The results showed an overestimation of signal strength by a factor of 5, which was expected because of model simplification. This leads to future modeling work to account for signal losses from additional physical properties, including high temperature environments for FY-21.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Radiation Transport Simulation of the Sulfur Counting System in the Radiation Metrology Laboratory (RML)

At the request of staff members from the Radiation Metrology Laboratory (RML), a series of Monte Carlo radiation transport calculations were performed using two different models of the detector geometry of the RMLs sulfur counting system. The fraction of electrons from each β-decay of 32 P in the sulfur pellet that enter the window of the sulfur counting system was calculated with both MCNP and ITS. In addition, the differential energy distributions of the electrons entering the counting system window were computed. There was significant agreement between the integral and differential quantities calculated by the two transport codes. Summary tables are for the integral efficiency values are found in the body of the report.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗