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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Porous liquids: an integrated platform for gas storage and catalysis

Porous liquids (PLs) represent a new frontier in materials design, combining the unique features of fluidity in liquids and permanent porosity in solids. By engineering well-defined pores into liquids via designed structure modification techniques, the greatly improved free volume significantly enhances the gas transport and storage capability of PL sorbents. Triggered by the promising applications of PLs in gas separation, PLs are further explored in catalysis particularly to integrate the gas storage and catalytic transformation procedure. This emerging field has demonstrated promising progress to advance catalytic procedures using PLs as catalysts, with performance surpassing that of the pure liquid and porous host counterparts. In this perspective article, the recent discoveries and progress in the field of integrated gas storage and catalysis by leveraging the PL platforms will be summarized, particularly compared with the traditional homogeneous or heterogeneous catalytic procedures. The unique features of PLs endow them with combined merits from liquid and solid catalysts and beyond which will be illustrated first. This will be followed by the unique techniques being utilized to probe the porosity and active sites in PLs and the structural evolution during the catalytic procedures. The catalytic application of PLs will be divided by the reaction categories, including CO 2 -involving transformation, O 2 -involving reaction, H 2 S conversion, hydrogenation reaction, and non-gas involving cascade reactions. In each reaction type, the synthesis approaches and structure engineering techniques of PLs, structure characterization, catalytic performance evaluation, and reaction mechanism exploration will be discussed, highlighting the structure–performance relationship and the advancement benefiting from the unique features of PLs.

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

Assessing the impact of climate change on rainfall-triggered landslides: a case study in California

Landslides are widespread natural hazards which take a heavy toll on lives, property, and infrastructure each year. In January 2023 and 2024, widespread landslides occurred in California as a result of extreme winter precipitation. Estimating the regional evolution of landslide hazard in a changing climate is essential for adaptation planning and risk mitigation efforts. The complex effects of climate change on landslide hazard, however, are poorly understood. Here, we use climate and landslide observations to develop a novel data-driven approach for landslide susceptibility assessment under historical and future climate conditions. We apply this framework to investigate the evolution of landslide susceptibility in California and its impacts on the roadway system based on downscaled climate projections under moderate and high greenhouse gas emission scenarios. On average, the results indicate an increase in landslide susceptibility through 2100 in regions where historical susceptibility is moderate to very high. Although the spatio-temporal variations in landslide susceptibility are sensitive to climate model uncertainties in predicting extreme rainfall, the direst impacts are largely circumvented in lower emission scenarios.

Climate Change↗
DOE OSTI2026

Reactive CO 2 capture via controlled amine speciation in non-aqueous electrolytes

Current efforts to integrate CO 2 capture and electrochemical conversion (reactive capture) are often performed under aqueous conditions, resulting in undesired hydrogen evolution and reliance on precious metal catalysts and pure CO 2 streams. Here, in this study, we explore reactive capture in aprotic media. By shifting the amine–CO 2 adduct speciation to carbamic acid (instead of carbamate) in dimethyl sulfoxide, we increased CO 2 uptake threefold compared with an aqueous medium, suppressing hydrogen evolution and supporting a 78% Faradaic efficiency towards CO over an earth-abundant zinc catalyst. Under simulated high-oxygen-content flue gas (17% CO 2 , 17% O 2 , 66% N 2 ), we also obtained up to 43% CO Faradaic efficiency over multiple capture–conversion cycles. Our findings showcase the confluence of reactant speciation, electrolyte composition and electrocatalyst design in enabling selective and active electrochemical transformations.

Gomes, Reginaldo J. [Univ. of Chicago, IL (United ↗
DOE OSTI2026

Mitigation of hydrogen crossover in liquid alkaline water electrolysers using gas recombination catalysts

The rising demand for hydrogen calls for improvements in the efficiency of liquid alkaline water electrolysers (LAWEs), which can be fulfilled by advanced electrodes or separators. Nevertheless, they also intensify hydrogen crossover and safety concerns, thus mandating efficient mitigation strategies. Here we studied the correlation between cathodes and hydrogen crossover behaviours and mitigated safety risks by designing a gas recombination catalyst (GRC). We attribute the elevated hydrogen crossover associated with platinum-based cathodes to their preferential utilization for the hydrogen evolution reaction that creates elevated hydrogen supersaturation, as evidenced by direct measurements of dissolved hydrogen concentration. Varying the placement of platinum layers relative to the cathode–separator interface also supports this conclusion. The implementation of a GRC reduces hydrogen crossover by 95% without affecting LAWE performance and functions for over 1,000 h at 1 A cm−2. This study provides insights into hydrogen supersaturation and the crossover mechanism, as well as offering a promising pathway to enhance the efficiency and reliability of alkaline water electrolysis.

Liu, Haotian↗
DOE OSTI2024

Machine learning-guided discovery of gas evolving electrode bubble inactivation

The adverse effects of electrochemical bubbles on the performance of gas-evolving electrodes are well known, but studies on the degree of adhered bubble-caused inactivation, and how inactivation changes during bubble evolution are limited. We study electrode inactivation caused by oxygen evolution while using surface engineering to control bubble formation. We find that the inactivation of the entire projected area, as is currently believed, is a poor approximation which leads to non-physical results. Using a machine learning-based image-based bubble detection method to analyze large quantities of experimental data, we show that bubble impacts are small for surface engineered electrodes which promote high bubble projected areas while maintaining low direct bubble contact. We thus propose a simple methodology for more accurately estimating the true extent of bubble inactivation, which is closer to the area which is directly in contact with the bubbles.

Lake, Jack R.↗
DOE OSTI2024

Influence of elevated temperature and oxygen on the capture of radioactive iodine by silver functionalized silica aerogel

Reprocessing is considered a competent strategy for spent nuclear fuel management, yet radioiodine ( 129 I) is emitted in reprocessing off-gas as a hazardous byproduct. Silver functionalized silica aerogel (Ag 0 -aerogel), a promising iodine capture material, experiences a reduction in its capacity after prolonged exposure to off-gas components at elevated temperatures, a phenomenon termed as aging. To fully understand this process, we isolated the contribution of each aging factor, exposing Ag 0 -aerogel samples to N 2 and dry air gas streams, respectively, at 150 °C for different time periods. Aged samples were loaded with I 2 to examine the capacity change and comprehensively characterized to investigate the evolution of their properties. Results show that temperature alone did not alter Ag 0 -aerogel's capacity but triggered Ag 0 nanoparticles sintering and generated organic sulfur species. The presence of O 2 reduced the capacity by ~20 %, causing (i) formation of silver sulfide (Ag 2 S) crystals and (ii) oxidation of Ag-thiolate (Ag-S-r) to Ag sulfonate (Ag-SO 3 -r). Given that Ag 2 S readily adsorbs I 2 , the formation of Ag-SO 3 -r is the major inhibitor for iodine adsorption. This hypothesis was supported by density functional theory (DFT) simulations. These findings unraveled key mechanisms of Ag 0 -aerogel aging, which are useful in the development of materials that withstand realistic spent-nuclear-fuel-reprocessing off-gas conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Achieving Unprecedented CO 2 Utilization InCO 2 Concrete™: System Design, Product Development and Process Demonstration

Anthropogenic sources of carbon dioxide are generated from a number of sources, but the key among these are ordinary Portland cement (OPC) production and combustion of fossil fuels. Cement production is the largest global CO 2 source from the mineral decomposition of carbonates. This is due to the clinkering process whereby limestone (mainly consisting of CaCO 3 ) is decomposed into CaO and CO 2 , and combined with silica rich clays at high temperatures to form clinkers (i.e. the four key minerals that comprise cement). The high temperature range of 1400 – 1550°C required for this process accounts for up to 60% of the generated CO 2 from cement production. Combination of the limestone decomposition and thermal requirements of the clinkering process causes cement production to contribute 8-9% of annual global CO 2 emissions. Combustion of fossil fuels (coal, oil and gas) was shown to contribute a much larger portion of global CO 2 emissions. As of 2018, combustion of fossil fuels accounted for 65% of global CO 2 , where 41% was derived from stationary sources for electricity and heat generation and the other 24% was related to transport. To reduce these contributions, key steps forward in CO 2 utilization technologies are required. Therefore, a CO 2 mineralization technology (CO 2 mineralization concrete) to reduce the OPC content in concrete, while utilizing flue gas emissions from fossil fuel combustion has been developed to address both areas simultaneously. This Reversa™ technology utilizes low-carbon cementation agents produced by in situ CO 2 mineralization (“mineral carbonation reactions”) to offer a promising alternative to OPC. CO 2 mineralization relies upon the reaction of dissolved CO 2 with inorganic alkaline reactants to precipitate mineral carbonates (e.g., CaCO 3 ), which bind proximate particles and achieve cementation. Herein, a concrete green body, which is composed of a mixture of binder, water, and mineral aggregates, is exposed to CO 2 borne in industrial flue gas streams. This manner of CO 2 mineralization allows the production of construction components that feature equivalent engineering attributes as their OPC-based counterparts while featuring a much smaller embodied carbon intensity (eCI). The purpose of this project is to demonstrate the feasibility of the Reversa process evolving from a TRL-3 technology at the bench-scale up to TRL-6 technology at the pilot-scale. The reliability of the Reversa technology was tested to prove the effective production of three standard industrial concrete products selected during the course of the project. The results detailed herein will demonstrate the evolution of this technology to the industrial scale. The culmination of this work resulted in 9 production runs completed at the National Carbon Capture Center (NCCC), Wilsonville, AL, using natural gas (NG) flue gas as the CO 2 source. Over the course of the production runs at NCCC, the CO 2 utilization as a function of time, 24-h CO 2 uptake, electricity usage, and 28-d net area compressive strength recorded for each run. Collection of this data will be used to determine the success of the demonstration goals: (1) achieving in excess of 0.2gCO 2 /g reactant , (2) achieving greater than 50% reduction in global warming potential compared to standard produced units, and (3) ensuring compliance of carbonated concrete with industry standard specifications.

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

High-Temperature Gas-Cooled Reactors Multiphysics Simulation Demonstration and Code Validation

This study presents a comprehensive benchmarking and verification effort of several thermal-hydraulic and multiphysics capabilities for high-temperature gas-cooled reactor applications. The first part of this effort focuses on the running-in verification of Griffin’s multiphysics capabilities, specifically for simulating the evolution of pebble-bed reactor cores from startup to equilibrium. Since Fiscal Year 2024, improvements and enhancements have been implemented in Griffin, including simplifying the process to specify streamlines and developing the online cross-section generation capability. In the absence of validation data, code-to-code comparisons are conducted with kugelpy, showing good agreement for integral quantities like k-eff predictions and predictions for maximum power density. However, accuracy issues are noted for more detailed quantities like the spatial distribution of fission rate densities which will require further work to address. The second part of this report presents an improved System Analysis Module (SAM) core channel model where the effects of cross flow are considered during the pressurized loss of forced cooling transient, resulting in an improved agreement of the predicted pebble temperature with respect to the predictions from the SAM 2D porous media model. Additionally, the wall channeling effect due to variable porosity at the near wall region of the core is also investigated. Furthermore, to demonstrate Griffin’s online cross-section generation capability, a Multiphysics simulation is performed by coupling Griffin to the SAM core channel model. In the third part of the report, as a part of the Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) thermal-hydraulic code validation benchmark activity for a high-temperature gas-cooled reactor, the High Temperature Test Facility (HTTF) is investigated first using the NekRS computational fluid dynamics (CFD) code to study the flow mixing phenomenon in the lower plenum of the facility. Then, code-to-code and code-to-data comparisons are performed for Test PG27, which is a pressurized conduction cooldown (PCC) test, using five different codes by six organizations from five countries. The different simulations show good agreements in terms of the general trend but there are differences in some results such as the peak temperatures of different regions and heat removal rate.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Lustre Unveiled: Evolution, Design, Advancements, and Current Trends

The Lustre filesystem serves as a vital element in high-performance parallel storage, meeting the rising demands of scientific, research, and enterprise environments. Widely deployed across HPC environments, ranging from small-scale applications in AI/ML, to domains like oil and gas, drug discovery, and meteorology, and manufacturing, Lustre addresses the universal challenge of efficiently accessing vast and ever-increasing volumes of data. Lustre is the filesystem of choice on six out of the top 10 fastest supercomputers in the world today, over 65% of the top 100, and also for over 60% of the top 500. Despite its widespread popularity, there is a lack of a complete and up-to-date reference, covering Lustre’s evolution, design, and various advancements made over the years. In this journal, we aim to fill this gap by providing a comprehensive journey of Lustre, including its history with significant contributions to HPC, detailed architecture and design elements, exploration of advancements added through its evolution, and future directions. Additionally, we present a comparison of Lustre with other prominent storage technologies of the era. To illustrate the current state of Lustre, we analyze several filesystem trends, including utilization, performance, and usage patterns on Orion, the Lustre filesystem on the first exascale supercomputer Frontier. We hope that this journal serves as a comprehensive educational reference for the current and future generations interested in HPC filesystem storage aspects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The impact of environment on size: Galaxies are 50% smaller in the Fornax Cluster compared to the field

Size is a fundamental parameter for measuring the growth of galaxies and the role of the environment on their evolution. However, the conventional size definitions used for this purpose are often biased and miss the diffuse, outermost signatures of galaxy growth, including star formation and gas accretion. We address this issue by examining low surface brightness truncations or galaxy ‘edges’ as a physically motivated tracer of size based on star formation thresholds. Our total sample consists of ∼900 galaxies with stellar masses ranging from 10 5 M ⊙ < M ⋆ < 10 11 M ⊙ . This sample of nearby cluster, group satellite, and nearly isolated field galaxies was compiled using multi-band imaging from the Fornax Deep Survey, deep IAC Stripe 82, and Dark Energy Camera Legacy Surveys. We find that the edge radii scale as R edge ∝ M ⋆ 0.42 , with a very small intrinsic scatter (∼0.07 dex). The scatter is driven by the morphology and environment of galaxies. In both the cluster and field, early-type dwarfs are systematically smaller by approximately 20% compared to late-type dwarfs. However, galaxies in the Fornax cluster are the most impacted. At a fixed stellar mass, edges in the cluster can be found at about 50% smaller radii, and the average stellar surface density at the edges is a factor of two higher, ∼1 M ⊙ /pc 2 . Our findings support the rapid removal of loosely bound neutral hydrogen (H I ) in hot, crowded environments, which truncates galaxies outside-in earlier, preventing the formation of more extended sizes and lower density edges. Our results highlight the importance of deep imaging surveys to the study of low surface brightness imprints of the large-scale structure and environment on galaxy evolution.

Astronomy & Astrophysics↗
DOE OSTI2025

Fractal Scaling of Explosively Driven Product Gases

ABSTRACT Characterization of the interface between explosive product gases and ambient air in an explosion is a complicated task due to the turbulent mixing and inherently three‐dimensional expansion of the interface. This study aims to quantify the evolution of the interface as a temporally varying Hausdorff dimension. Two test series were conducted with Composition C‐4 charges with masses of 105 and 880 g. Imaging data were collected from the time of detonation until shock wave detachment using ultra‐high‐speed cameras. Gas cloud profiles were extracted using automated image processing algorithms, and the Hausdorff dimension of these two‐dimensional slices of the gas cloud was then estimated using boxcounting algorithms. When scaled with standard gas dynamic nondimensional scalings, the Hausdorff dimension of all explosive events appears to collapse towards a single curve. The fireball was initially nonfractal and began to develop fractal properties as the shock wave separated from the detonation products. Artificial perturbation of the charged surface had no detectable impact on the evolution of the Hausdorff dimension in the early development of the fireball outside of error, despite visible phenomenological differences in the early development of mixing on the fireball surface.

42 ENGINEERING↗
DOE OSTI2024

Femtosecond Core-Level Spectroscopy Reveals Involvement of Triplet States in the Gas-Phase Photodissociation of Fe(CO) 5

Excitation of iron pentacarbonyl [Fe(CO) 5 ], a prototypical photocatalyst, at 266 nm causes the sequential loss of two CO ligands in the gas phase, creating catalytically active, unsaturated iron carbonyls. Despite numerous studies, major aspects of its ultrafast photochemistry remain unresolved because the early excited-state dynamics have so far eluded spectroscopic observation. This has led to the long-held assumption that ultrafast dissociation of gas-phase Fe(CO) 5 proceeds exclusively on the singlet manifold. Herein, we present a combined experimental–theoretical study employing ultrafast extreme ultraviolet transient absorption spectroscopy near the Fe M 2,3 -edge, which features spectral evolution on 100 fs and 3 ps time scales, alongside high-level electronic structure theory, which enables characterization of the molecular geometries and electronic states involved in the ultrafast photodissociation of Fe(CO) 5 . We assign the 100 fs evolution to spectroscopic signatures associated with intertwined structural and electronic dynamics on the singlet metal-centered states during the first CO loss and the 3 ps evolution to the competing dissociation of Fe(CO) 4 along the lowest singlet and triplet surfaces to form Fe(CO) 3 . Calculations of transient spectra in both singlet and triplet states as well as spin–orbit coupling constants along key structural pathways provide evidence for intersystem crossing to the triplet ground state of Fe(CO) 4 . Finally, our work presents the first spectroscopic detection of transient excited states during ultrafast photodissociation of gas-phase Fe(CO) 5 and challenges the long-standing assumption that triplet states do not play a role in the ultrafast dynamics.

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

The aluminium-26 distribution in a cosmological simulation of a Milky Way-type Galaxy

Context . The 1.8 MeV γ -rays corresponding to the decay of the radioactive isotope 26 Al (with a half-life of 0.72 Myr ) have been observed by the SPI detector on the INTEGRAL spacecraft and extensively used as a tracer of star formation and current nucleosynthetic activity in the Milky Way Galaxy. Further information is encoded in the observation related to the higher 26 Al content found in regions of the Galaxy with the highest line-of-sight (LoS) velocity relative to an observer located in the Solar System. However, this feature remains unexplained. Aims . We ran a cosmological “zoom-in” chemodynamical simulation of a Milky Way-type galaxy, including the production and decays of radioactive nuclei in a fully self-consistent way. We then analyzed the results to follow the evolution of 26 Al throughout the lifetime of the simulated galaxy to provide a new method for interpreting the 26 Al observations. Methods . We included the massive star sources of 26 Al in the Galaxy and its radioactive decay into a state-of-the-art galactic chemical evolution model, coupled with cosmological growth and hydrodynamics. This approach allowed us to follow the spatial and temporal evolution of the 26 Al content in the simulated galaxy. Results . Our results are in agreement with the observations with respect to the fact that gas particles in the simulation with relatively higher 26 Al content also have the highest LoS velocities. On the other hand, gas particles with relatively lower 26 Al content (i.e., not bright enough to be observed) generally display the lowest LoS velocities. However, this result is not conclusive because the overall rotational velocity of our simulated galaxy is higher than that observed for cold CO gas in the Milky Way Galaxy. Furthermore, we found no significant correlation between gas temperature, rotational velocity, and 26 Al content at any given radius. We also found the presence of transient 26 Al-rich spots at low LoS velocities and we show that one such spot had been captured by the INTEGRAL/SPI data. Based on our model, we present a prediction for the detection of 1.8 MeV γ -rays by the future COSI mission. We find that according to our model, the new instrument will be able to observe similar 26 Al-emission patterns to those seen by INTEGRAL/SPI.

Wehmeyer, B. (ORCID:0009000254149292)↗
DOE OSTI2024

Guided Mode Evolution and Ionization Injection in Meter-Scale Multi-GeV Laser Wakefield Accelerators

Here, we show that multi-GeV laser wakefield electron accelerators in meter-scale, low density hydrodynamic plasma waveguides operate in a new nonlinear propagation regime dominated by sustained beating of lowest order modes of the ponderomotively modified channel; this occurs whether or not the injected pulse is linearly matched to the guide. For a continuously doped gas jet, this emergent mode beating effect leads to axially modulated enhancement of ionization injection and a multi-GeV energy spectrum of multiple quasimonoenergetic peaks; the same process in a locally doped jet produces single multi-GeV peaks with <10% energy spread. A three-stage model of drive laser pulse evolution and ionization injection characterizes the beating effect and explains our experimental results.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Chemical Differences between Phenolic Secondary Organic Aerosol Formed through Gas-Phase and Aqueous-Phase Reactions

Phenolic compounds, which are significant emissions from biomass burning (BB), undergo rapid photochemical reactions in both gas and aqueous phases to form secondary organic aerosol, namely, gasSOA and aqSOA, respectively. The formation of gasSOA and aqSOA involves different reaction mechanisms, leading to different product distributions. In this study, we investigate the gaseous and aqueous reactions of guaiacol a representative BB phenol to elucidate the compositional differences between phenolic aqSOA and gasSOA. Aqueous-phase reactions of guaiacol produce higher SOA yields than gas-phase reactions (e.g., roughly 60 vs 30% at one half-life of guaiacol). These aqueous reactions involve more complex reaction mechanisms and exhibit a more gradual SOA evolution than their gaseous counterparts. Initially, gasSOA forms with high oxidation levels (O/C > 0.82), while aqSOA starts with lower O/C (0.55–0.75). However, prolonged aqueous-phase reactions substantially increase the oxidation state of aqSOA, making its bulk chemical composition closer to that of gasSOA. Additionally, aqueous reactions form a greater abundance of oligomers and high-molecular-weight compounds, alongside a more sustained production of carboxylic acids. AMS spectral signatures representative of phenolic gasSOA have been identified, which, together with tracer ions of aqSOA, can aid in the interpretation of field observation data on aerosol aging within BB smoke. The notable chemical differences between phenolic gasSOA and aqSOA highlighted in this study also underscore the importance of accurately representing both pathways in atmospheric models to better predict the aerosol properties and their environmental impacts.

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

New proxies for second-order cumulants of conserved charges in heavy-ion collisions within the EPOS4 framework

Proxies for cumulants of baryon number 𝐵, electric charge 𝑄, and strangeness 𝑆 are usually measured in heavy-ion collisions via moments of net-number distribution of given hadronic species. Since these cumulants of conserved charges are expected to be sensitive to the existence of a critical point in the phase diagram of nuclear matter, it is crucial to ensure that the proxies used as substitutes are as close to them as possible. Hence, we use the EPOS 4 framework to generate Au + Au collisions at several collision energies of the BNL Relativistic Heavy Ion Collider beam energy scan. We compute second-order net cumulants of 𝜋, 𝐾, and 𝑝, for which experimental data have been published as well as the corresponding conserved charge cumulants. We then compare them with proxies, defined in previous lattice QCD and hadron resonance gas model studies, which are shown to reproduce more accurately their associated conserved charge cumulants. We investigate the impact of hadronic rescatterings occurring in the late evolution of the system on these quantities, as well as the amount of signal actually originating from the bulk medium which endures a phase transition.

Physics↗
DOE OSTI2025

Measurement of the free neutron lifetime in a magneto-gravitational trap with in situ detection

Here, in this study, we publish three years of data from the UCNτ experiment performed at the Los Alamos Ultracold Neutron Facility at the Los Alamos Neutron Science Center. These data are in addition to our previously published data. Our goals in this paper are to better understand and quantify systematic uncertainties and to improve the lifetime statistical precision. We previously reported a value from our 2017–2018 data for the neutron lifetime of 877.75 ± 0.28 (statistical) +0.22–0.16 (systematic) s. We have collected an additional three years of data reported here for the first time. When all the data from UCNτ are averaged for 2017, 2018, 2020, 2021, and 2022, we report an updated value for the lifetime of 877.83 ± 0.22 (statistical)+0.20–0.17 (systematic) s. We utilized improved monitor detectors, reduced our correction due to UCN upscattering on residual gas, and employed four different UCN detector geometries both to reduce the correction required for rate dependence and to explore potential contributions due to phase space evolution.

Cabibbo-Kobayashi-Maskawa matrix↗