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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Enhancing quantum utility: Simulating large-scale quantum spin chains on superconducting quantum computers

We present the quantum simulation of the frustrated quantum spin- 1 2 antiferromagnetic Heisenberg spin chain with competing nearest-neighbor ( J 1 ) and next-nearest-neighbor ( J 2 ) exchange interactions in the real superconducting quantum computer with qubits ranging up to 100. In particular, we implement the Hamiltonian with the next-nearest neighbor exchange interaction in conjunction with the nearest-neighbor interaction on IBM's superconducting quantum computer and carry out the time evolution of the spin chain by employing the first-order Trotterization. Furthermore, our implementation of the second-order Trotterization for the isotropic Heisenberg spin chain, involving only nearest-neighbor exchange interaction, enables precise measurement of the expectation values of staggered magnetization observable across a range of up to 100 qubits. Notably, in both cases, our approach results in a constant circuit depth in each Trotter step, independent of the number of qubits. Our demonstration of the accurate measurement of expectation values for the large-scale quantum system using superconducting quantum computers designates the quantum utility of these devices for investigating various properties of many-body quantum systems. This will be a stepping stone to achieving the quantum advantage over classical ones in simulating quantum systems before the fault tolerance quantum era. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-Time Operator Evolution in Two and Three Dimensions via Sparse Pauli Dynamics

We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in one-dimensional (1D) spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model that is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources. Published by the American Physical Society 2025

Begušić, Tomislav (ORCID:0000000279424134)↗
NASA NTRS2010

Copoly(Imide Siloxane) Abhesive Materials with Varied Siloxane Oligomer Length

Incorporation of PDMS moieties into a polyimide matrix lowered the surface energy resulting in enhanced adhesive interactions. Polyimide siloxane materials were generated using amine-terminated PDMS oligomers of different lengths to study changes in surface migration behavior, phase segregation, mechanical, thermal, and optical properties. These materials were characterized using contact angle goniometry, tensile testing, and differential scanning calorimetry. The surface migration behavior of the PDMS component depended upon the siloxane molecular weight as indicated by distinct relationships between PDMS chain length and advancing water contact angles. Similar correlations were observed for percent elongation values obtained from tensile testing, while the addition of PDMS reduced the modulus. High fidelity topographical modification via laser ablation patterning further reduced the polyimide siloxane surface energy. Initial particulate adhesion testing experiments demonstrated that polyimide siloxane materials exhibited greater abhesive interactions relative to their respective homopolyimides.

Wohl, Christopher J.↗
DOE OSTI2021

Structure of the E. coli agmatinase, SPEB

Agmatine amidinohydrolase, or agmatinase, catalyzes the conversion of agmatine to putrescine and urea. This enzyme is found broadly across kingdoms of life and plays a critical role in polyamine biosynthesis and the regulation of agmatine concentrations. Here we describe the high-resolution X-ray crystal structure of the E . coli agmatinase, SPEB. The data showed a relatively high degree of pseudomerohedral twinning, was ultimately indexed in the P 3 1 space group and led to a final model with eighteen chains, corresponding to three full hexamers in the asymmetric unit. There was a solvent content of 38.5% and refined R/R free values of 0.166/0.216. The protein has the conserved fold characteristic of the agmatine ureohydrolase family and displayed a high degree of structural similarity among individual protomers. Two distinct peaks of electron density were observed in the active site of most of the eighteen chains of SPEB. As the activity of this protein is known to be dependent upon manganese and the fold is similar to other dinuclear metallohydrolases, these peaks were modeled as manganese ions. The orientation of the conserved active site residues, in particular those amino acids that participate in binding the metal ions and a pair of acidic residues (D153 and E274 in SPEB) that play a role in catalysis, are similar to other agmatinase and arginase enzymes and is consistent with a hydrolytic mechanism that proceeds via a metal-activated hydroxide ion.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Learning Latent Representations to Bridge Coarse-Grained and Atomistic Resolutions in Polymer Simulations

We present a machine-learning-based framework for learning reduced-order representations of polymer chain conformations across coarse-grained (CG) and united-atom (UA) fidelities. By employing linear singular value decomposition and nonlinear autoencoders, we compress high-dimensional polymer configurations into latent spaces with minimal loss of structural accuracy. Crucially, we demonstrate a near-perfect linear mapping between CG and UA latent spaces, enabling an efficient super-resolution back-mapping procedure that reconstructs high-fidelity UA configurations from CG simulations. While minor structural inaccuracies occur, they are effectively corrected through a brief molecular dynamics relaxation, forming a practical hybrid machine learning−physics scheme. This approach establishes the key structural prerequisites for accelerated polymer dynamics simulations: a compact and accurate latent encoding of polymer chain conformations and a validated multi-fidelity mapping that permits reconstruction of UA structures from CG configurations. The extension of this framework to explicit time evolution within the latent space, enabling dynamics to be propagated at CG fidelity and decoded to UA resolution only when required, represents a natural and well-motivated direction for future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Global rare earth element resources: A concise review

Deposits enriched in rare earth elements (REEs) are abundant and diverse in mineralogy, but those of current economic value have extremely limited geographic distribution. Due to rapidly increasing demand and concerns about supply chain security, new and improved methods of prospecting, beneficiation, separation, purification, and recycling are needed. By overviewing the types and geographic distribution of REE reserves globally, their petrogenesis and major mineralogic assemblages, this review aims to provide a foundation for posing new directions for research and development in these areas. In conclusion, our review also seeks to provide a concise summary of important background information that is accessible to researchers from a variety of disciplines who are seeking to engage in this rapidly expanding field.

58 GEOSCIENCES↗
DOE OSTI2021

Theoretical kinetics predictions for NH 2 + HO 2

Recent modeling studies of NH 3 oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies between existing literature mechanisms. In this study high level theoretical kinetics predictions have been obtained for the reaction of NH 2 with HO 2 , which has previously been highlighted as an important reaction with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations including large basis sets and high-level corrections to yield high accuracy (~0.2 kcal/mol) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature and pressure dependent kinetics. For the radical-radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constant as well as the branching to the NH 3 + O 2 , H 2 NO + OH, and HNO + H 2 O channels. Rate constants are also reported for the H 2 NO + OH reaction as they arise naturally from the analysis. The rate constant and branching fraction determined in this work for the NH 2 + HO 2 reaction deviate significantly from values used in most previous modeling studies. The fact that the main product channel is chain terminating, rather than propagating, has strong implications for modeling NH 3 ignition and oxidation, in particular at intermediate temperatures and elevated pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Bridging the gap between molecules and materials in quantum chemistry with localized active spaces

The number of materials that “bridge the gap” between single molecules and extended solids, such as metal-organic frameworks and organic semiconductors, has been increasing. Consequently, there is a growing need for modeling approaches that effectively integrate the real-space molecular perspective employed by computational chemists and the reciprocal-space dispersive perspective employed by computational physicists. Here, we propose the localized active space (LAS) approach as a promising method to successfully bridge this gap. The LAS approach extends the active space concept from multiconfigurational methods such as complete active space self-consistent field theory to multiple molecular fragments via a product-form wave function ansatz. Here, we apply this method to solid state phenomena by treating each unit cell as a fragment with different sets of local quantum numbers (e.g., charge and excitation number). State interaction between these LAS states (LASSI) thus provides a comprehensive basis for the study of charge and energy transfer, meeting and surpassing the capabilities of single-reference fragmentation approaches such as constrained density functional theory (cDFT). Most centrally, we show how combining this LASSI approach with multiconfigurational pair-density functional theory (MC-PDFT) provides an elegant and efficient method to compute band structures that capture multiconfigurational character. We apply the LASSI band structure approach to the computation of band gaps in stretched hydrogen chain, polyacetylene, and bulk nickel oxide (NiO), finding good or excellent quantitative agreement with reference values in all cases. Additionally, we use the LAS basis in one-dimensional model systems to demonstrate its ability to treat difficult solid-state phenomena such as exciton transfer and excitation at p-n junctions.

method development↗
DOE OSTI2022

First Application of Mass Measurements with the Rare-RI Ring Reveals the Solar r -Process Abundance Trend at A = 122 and A = 123

The Rare-RI Ring (R3) is a recently commissioned cyclotronlike storage ring mass spectrometer dedicated to mass measurements of exotic nuclei far from stability at Radioactive Isotope Beam Factory (RIBF) in RIKEN. The first application of mass measurement using the R3 mass spectrometer at RIBF is reported. Rare isotopes produced at RIBF— 127 Sn, 126 In, 125 Cd, 124 Ag, 123 Pd—were injected in R3. Masses of 126 In, 125 Cd, and 123 Pd were measured whereby the mass uncertainty of 123 Pd was improved. This is the first reported measurement with a new storage ring mass spectrometry technique realized at a heavy-ion cyclotron and employing individual injection of the preidentified rare nuclei. The latter is essential for the future mass measurements of the rarest isotopes produced at RIBF. The impact of the new 123 Pd result on the solar r-process abundances in a neutron star merger event is investigated by performing reaction network calculations of 20 trajectories with varying electron fraction Y e . It is found that the neutron capture cross section on 123 Pd increases by a factor of 2.2 and β-delayed neutron emission probability, P 1n , of 123 Rh increases by 14%. The neutron capture cross section on 122 Pd decreases by a factor of 2.6 leading to pileup of material at A = 122, thus reproducing the trend of the solar r-process abundances. The trend of the two-neutron separation energies (S 2n ) was investigated for the Pd isotopic chain. The new mass measurement with improved uncertainty excludes large changes of the S 2n value at N = 77. Finally, such large increase of the S 2n values before N = 82 was proposed as an alternative to the quenching of the N = 82 shell gap to reproduce r-process abundances in the mass region of A = 112 – 124.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1974

Management of natural resources through automatic cartographic inventory

The author has identified the following significant results. Significant correspondence codes relating ERTS imagery to ground truth from vegetation and geology maps have been established. The use of color equidensity and color composite methods for selecting zones of equal densitometric value on ERTS imagery was perfected. Primary interest of temporal color composite is stressed. A chain of transfer operations from ERTS imagery to the automatic mapping of natural resources was developed.

Rey, P. A.↗
DOE OSTI2022

ADAM: A web platform for graph-based modeling and optimization of supply chains

Modeling and optimization are essential tasks that arise in the analysis and design of supply chains (SCs). SC models are essential for understanding emergent behavior such as transactions between participants, inherent value of products exchanged, as well as impact of externalities (e.g., policy and climate) and of constraints. Unfortunately, most users of SC models have limited expertise in mathematical optimization, and this hinders the adoption of advanced decision-making tools. Here, in this work, we present ADAM, a web platform that enables the modeling and optimization of SCs. ADAM facilitates modeling by leveraging intuitive and compact graph-based abstractions that allow the user to express dependencies between locations, products, and participants. ADAM model objects serve as repositories of experimental, technology, and socio-economic data; moreover, the graph abstractions facilitate the organization and exchange of models and provides a natural framework for education and outreach. Here, we discuss the graph abstractions and software design principles behind ADAM, its key functional features and workflows, and application examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Glass transition temperature studies of planetary ball milled glasses: Accessing the rapidly cooled glassy state in Na 4 P 2 S 7-x O x , 0 ≤ x ≤ 7, Oxy-thio phosphate glasses

This paper details the very first in-depth study of the glass transition temperature (T g ) for planetary balled milled (PBM) Na 4 P 2 S 7-x O x (NaPSO), where 0 ≤ x ≤ 7, glasses. For 0 ≤ x ≤ 5, fully amorphous, homogeneous, and chemically reacted compositions can be prepared. For samples with 5 < x ≤ 7, partially amorphous but fully chemically reacted glass-ceramics can be produced. The reproducible, thermally cyclable onset T g and the onset crystallization temperature, T c , were investigated as a function of the composition and of the short-range order (SRO) structures of the glasses. Additionally, we examined the extreme sub-T g exothermic relaxations present due to the high energy milling processing and correspondingly high effective quenching rate. Using a differential scanning calorimeter (DSC) and scanning from well below the onset T g , the glasses are observed to relax exothermally below T g . The integrated relaxation enthalpy, ΔH rel , is ~ 0 for the x = 2 glass, but is significantly exothermic for lower and higher values of x. Once the high fictive state of these glasses has been erased by scanning to above the T g , but below the T c of the glass, the DSC scans of the glasses recover normal behavior for a normally cooled glass without any relaxation exotherm. The T g s of these glasses remain relatively constant for 0 ≤ x ≤ 3, but for glasses with 3 < x ≤ 5, T g increases sharply following the combined effects of the phosphate chain length increasing caused by the formation of bridging oxygens and the increasing concentration of more charge dense non-bridging oxygens (NBOs). For x > 5, both T g and Tc decrease sharply, becoming nearly identical at x = 7 where glass formation essentially ceases. For smaller values of x, T c increases with both chain length and the structural complexity of the composition but decreases sharply for glass-ceramics of x > 5.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Commuter preferences for a first-mile/last-mile microtransit service in the United States

Transportation system models rely heavily upon value of time (VOT) estimates to predict customer behavior. Accurate VOT estimates are particularly vital for planning new services such as on-demand ride hailing or microtransit because customers’ sensitivity to wait time, walk time, and route detour time affects their likelihood of selecting these modes. If an incorrect VOT is assumed during service planning, then ridership will be depressed because of a mismatch between their preferences and how the system is designed. In this paper, we report on the measurement of VOT for microtransit, a shared first-mile/last-mile mobility service, obtained using stated preference microdata from four U.S. cities. Here, we found a median in-vehicle VOT for microtransit of $\$$18.63 (95% CI: $\$$13.39–$\$$24.46) and an access VOT of $\$$75.38 (95% CI: $\$$59.22–$\$$94.96). The former is practically equal to the VOT we found for respondents’ current modes ($\$$20.24, 95% CI: $\$$13.71–$\$$26.94). We also found that men, younger riders, the highly educated, and transit riders are more likely to be interested in microtransit. Since the disutility of time spent on microtransit is not higher than that of other modes, we believe this new service has the potential to attract riders, and particularly if the system is designed with low waiting and walking times.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1976

Comparison of chain sampling plans with single and double sampling plans

The efficiency of chain sampling is examined through matching of operating characteristics (OC) curves of chain sampling plans (ChSP) with single and double sampling plans. In particular, the operating characteristics of some ChSP-0, 3 and 1, 3 as well as ChSP-0, 4 and 1, 4 are presented, where the number pairs represent the first and the second cumulative acceptance numbers. The fact that the ChSP procedure uses cumulative results from two or more samples and that the parameters can be varied to produce a wide variety of operating characteristics raises the question whether it may be possible for such plans to provide a given protection with less inspection than with single or double sampling plans. The operating ratio values reported illustrate the possibilities of matching single and double sampling plans with ChSP. It is shown that chain sampling plans provide improved efficiency over single and double sampling plans having substantially the same operating characteristics.

Stephens, K. S.↗
DOE OSTI2025

Exploring Microphase Separation in Semi-Fluorinated Diblock Copolymers: A Combined Experimental and Modeling Investigation

We report the combined experimental and theoretical study of the bulk self-assembly behavior of polystyrene-blockpoly( 2,3,4,5,6-pentafluorostyrene) diblock copolymers. These block copolymers were designed to create highly antagonistic blocks (with a high Flory−Huggins interaction parameter, χ) with minimum disruption to the molecular construct (i.e., only replacing five hydrogen atoms with five fluorine atoms). A large library of diblock copolymers (41 samples) was synthesized by reversible addition− fragmentation chain transfer (RAFT) polymerization to map out a major portion of the phase space. All block copolymers exhibited narrow molecular weight distributions with dispersity (D) values between 1.07 and 1.32, and subsequent thermal annealing revealed phase separation into well-defined nanoscale morphologies depending on their molecular composition, as determined from small-angle X-ray scattering and transmission electron microscopy analyses, with an experimental phase diagram being constructed. The χ value at 25 °C for this block copolymer was estimated to be 0.2 using strong segregation theory, based on trends in phase-separated domain spacing and interfacial width. When applying theoretical approaches, the majority of the domain spacing data trends were captured by a coil−coil diblock copolymer model; however, a better fit to the data for samples with shorter fluorinated blocks was obtained with a rod−coil model, indicating that the chains in these fluorinated blocks likely have a higher inherent stiffness and were thus rod-like. This observation demonstrates that, due to the very high value of χ, a transition from coil−coil to rod−coil behavior can be obtained purely by reducing the length of the stiffer of the two blocks and without varying temperature or the chemical composition of the polymers. Here, this work showcases the presence of strong microphase separation within AB diblock copolymers despite the relatively similar chemical composition of the constituent “A” and “B” units, with a clear transition from rod−coil to coil−coil segregation behavior.

RAFT polymerization↗
DOE OSTI2022

Unconventional Highly Active and Stable Oxygen Reduction Catalysts Informed by Computational Design Strategies

Abstract Discovering and engineering new materials with fast oxygen surface exchange kinetics and robust long‐term stability is essential for the large‐scale, economically viable commercialization of solid oxide fuel cell (SOFC) technology. The perovskite catalyst material BaFe 0.125 Co 0.125 Zr 0.75 O 3 (BFCZ75), predicted to be promising from recent density functional theory (DFT) calculations and unconventional due to its extremely high Zr content and low electronic conductivity, exhibits oxygen reduction reaction surface exchange rates on par with Ba 0.5 Sr 0.5 Co 0.8 Fe 0.2 O 3 (BSCF) and excellent stability at typical operating temperatures. New composite electrodes are engineered by integrating BFCZ75 with commercial electrode materials La 1– x Sr x MnO 3 (LSM) and La 1– x Sr x Co y Fe 1– y O 3 (LSCF) and achieve high performance as measured by low area specific resistance (ASR) values, with the LSCF/BFCZ75 ASR values comparable to top performing noncomposite electrode materials such as SrCo 0.8 Sc 0.2 O 3– δ , BaNb 0.05 Fe 0.95 O 3– δ and BaCo 0.7 Fe 0.22 Y 0.08 O 3– δ . The use of BFCZ75 as a composite with LSCF achieving low ASR values shows that BFCZ75 is highly active and can easily integrate into existing SOFC material supply chains, lowering the barrier for potential commercial application of new electrode materials. Finally, these findings point to a broader unexplored class of perovskite materials with high fractions of redox inactive species (e.g., Zr, Nb, and Ta) that may unlock new pathways to realizing improved commercial SOFCs.

Jacobs, Ryan↗
DOE OSTI2023

Assessing the economic viability of unconventional rare earth element feedstocks

Sourcing rare earth elements (REEs) from unconventional feedstocks has substantial environmental and societal-economic benefits, but its economic viability remains unclear. Here, we propose a framework for assessing the economic viability of unconventional REE feedstocks. Here, we first develop a database of capital and operating expenses for REE recovery and establish consistent process unit costs for common stages in the conventional supply chain. We then use market prices to develop well-defined methods for determining diverse product values. Finally, we report the effects of economies of scale and feedstock purity on capital and operating costs. These tools can reduce the uncertainty in the assessment of the economic viability of producing REE from unconventional feedstocks, determine the value of innovative pathways for REE production from diverse sources, and inform research priorities across a wide range of REE product development stages, contributing to a sustainable REE supply.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2019

Criticality Accident Alarm System Shielding Benchmark: Integral Experiment Request 498, Critical Engineering Decision 1 Report

This report supports Critical/Subcritical Experiment Decision 1 (CED-1) for Integral Experiment Request (IER) 498, a shielding benchmark produced using the Godiva IV critical assembly at the National Critical Experiments Research Center (NCERC). Shielding benchmarks are datasets collected to provide a comparison for computer models that simulate the effect of shielding on radiation transmission from a source to a detector. The purpose of a CED-1 report is to produce a conceptual design for an integral experiment and to identify the long lead-time items. The design presented in this report favors certain detailed design options such as material selections. However, alternative options can be selected as the project evolves. Dimensions are specified only as needed to evaluate feasibility and performance. Development of Criticality Accident Alarm System (CAAS) shielding benchmarks supports two main programmatic needs. The first need is to improve confidence in models of facilities that house nuclear material handling operations. Better models can support effective CAAS detector placement when criticality may result in dose, and it enables more accurate analysis of criticality accident impacts at various locations in a facility. A key quantity that can be verified is the secondary gamma production caused by neutron interactions with various materials. The second programmatic need supported by shielding benchmarks is the ongoing development of methods being integrated into nuclear simulation codes such as the Monte Carlo N-Particle (MCNP) transport code and the SCALE code system used in efforts funded by the Nuclear Criticality Safety Program (NCSP). Previous work performed under the International Criticality Safety Benchmark Experimental Program (ICSBEP) to produce shielding benchmark data is primarily limited to a set of measurements at the SILENE critical assembly at the Valduc facility in France. The experiment used an open configuration and a burst mode operation, which limited detector options to thermoluminescent dosimeters (TLDs) and activation foils. Because TLDs do not record gamma spectra, it was difficult to verify the gamma energy spectrum from the experiment. In this work, the Godiva IV assembly will be used because it is a fast system capable of producing a wide range of source strengths, including super-prompt critical bursts. The room return for the facility is expected to be substantial and challenging to characterize, so a more closed, shielded experimental configuration is considered. Furthermore, because the physics of radiation transport outside the assembly does not change between the burst mode and the delayed critical mode, it is anticipated that most measurements will be made with the Godiva IV assembly in delayed critical mode, operating within a range that will allow electronic counters to collect accurate data. Scoping calculations concluded that a workable room return shield is comprised of 40 cm of 5% borated polyethylene backed by 7 cm of lead. This configuration was shown to produce a ratio of signal–to–room return of over 100 for up to 2 mean free paths of shield sample material, and over 10 for up to 4 mean free paths of shield sample material, ensuring that useful results can be obtained. With no shielding sample in the room return shield, it was shown that the neutron and gamma spectra do not appreciably change with a change in room size. This scoping calculation does not preclude the use of tungsten powder in a binder, some other effective gamma shielding material, or a hybrid design. Dose rates for various source intensities at an unshielded detector are listed herein to inform detector selection during CED-2, and calibration chains are identified. Preliminary estimates of costs and schedules are outlined but remain to be verified. Values could double or triple as estimates become more accurate and are principally included here to demonstrate feasibility. Preliminary estimates indicate that the apparatus can be installed within a feasible schedule and budget. Two measurements per day are assumed. Producing a shielding benchmark at NCERC using the Godiva IV assembly has been shown to be feasible, with manageable uncertainties and risks. A clear, continuing need for shielding benchmark data remains present, and this report identifies and evaluates a method for creating integrated shielding benchmark datasets.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗