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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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Spectroscopy-based isotopic (δ 13 C) analysis for high spatial resolution of carbon exchange in the rhizosphere

The rhizosphere is a highly dynamic zone bridging plant roots with needed nutrient resources in soil. While the rhizosphere may be small, it has a disproportionally large impact on plant success and biomass production. A suite of rhizosphere-hosted microbial and geochemical interactions facilitate nutrient acquisition by plant roots, and, in turn, the roots stimulate these processes by supplying organic carbon into the rhizosphere. The small physical dimensions of the rhizosphere, however, can constrain efforts to elucidate key carbon exchange processes and their spatial extent and localization. We present a method for spatially resolved δ 13 C analysis of rhizosphere samples by coupling laser ablation (LA) sampling with isotopic analysis using capillary absorption spectroscopy (CAS) which differs from conventional mass spectrometer (MS) approaches. The CAS system has high sensitivity (requires fewer nanomoles of CO 2 per analysis) than comparable MS systems, which enables reduced sample size requirements to thereby improve spatial resolution (from 25 μm to as low as a projected 5 μm spatial resolution). We demonstrate the utility of CAS using rhizosphere samples from switchgrass plants exposed to 13 CO 2 . As a result, this technique will provide a capability for tracking the extent and spatial distribution of root exudate into the rhizosphere at highly detailed spatial scales.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Scarcity of fixed carbon transfer in a model microbial phototroph–heterotroph interaction

Although the green alga Chlamydomonas reinhardtii has long served as a reference organism, few studies have interrogated its role as a primary producer in microbial interactions. Here, we quantitatively investigated C. reinhardtii’s capacity to support a heterotrophic microbe using the established coculture system with Mesorhizobium japonicum, a vitamin B 12 -producing α-proteobacterium. Using stable isotope probing and nanoscale secondary ion mass spectrometry (nanoSIMS), we tracked the flow of photosynthetic fixed carbon and consequent bacterial biomass synthesis under continuous and diurnal light with single-cell resolution. We found that more 13 C fixed by the alga was taken up by bacterial cells under continuous light, invalidating the hypothesis that the alga’s fermentative degradation of starch reserves during the night would boost M. japonicum heterotrophy. 15 NH 4 assimilation rates and changes in cell size revealed that M. japonicum cells reduced new biomass synthesis in coculture with the alga but continued to divide—a hallmark of nutrient limitation often referred to as reductive division. Despite this sign of starvation, the bacterium still synthesized vitamin B 12 and supported the growth of a B 12 -dependent C. reinhardtii mutant. Finally, we showed that bacterial proliferation could be supported solely by the algal lysis that occurred in coculture, highlighting the role of necromass in carbon cycling. Collectively, these results reveal the scarcity of fixed carbon in this microbial trophic relationship (particularly under environmentally relevant light regimes), demonstrate B 12 exchange even during bacterial starvation, and underscore the importance of quantitative approaches for assessing metabolic coupling in algal–bacterial interactions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Satellite Observations of the Tropical Terrestrial Carbon Balance and Interactions With the Water Cycle During the 21st Century

A constellation of satellites are now in orbit providing information about terrestrial carbon and water storage and fluxes. These combined observations show that the tropical biosphere has changed significantly in the last two decades from the combined effects of climate variability and land use. Large areas of forest have been cleared in both wet and dry forests, increasing the source of carbon to the atmosphere. Concomitantly, tropical fire emissions have declined, at least until 2016, from changes in land-use practices and rainfall, increasing the net carbon sink. Measurements of carbon stocks and fluxes from disturbance and recovery and of vegetation photosynthesis show significant regional variability of net biosphere exchange (NBE) and gross primary productivity (GPP) across the tropics and are tied to seasonal and interannual changes in water fluxes and storage. Comparison of satellite based estimates of evapotranspiration (ET), photosynthesis, and the deuterium content of water vapor with patterns of total water storage and rainfall demonstrate the presence of vegetation-atmosphere interactions and feedback mechanisms across tropical forests. However, these observations of stocks, fluxes and inferred interactions between them do not point unambiguously to either positive or negative feedbacks in carbon and water exchanges. These ambiguities highlight the need for assimilation of these new measurements with Earth System models for a consistent assessment of process interactions, along with focused field campaigns that integrate ground, aircraft and satellite measurements, to quantify the controlling carbon and water processes and their feedback mechanisms.

58 GEOSCIENCES↗
DOE OSTI2021

Noncollinear magnetic configurations and substrate-mediated interactions in Mn trimers on the GaN (000$\bar{1}$) surface

Collinear and noncollinear calculations based on density functional theory are carried out to elucidate the magnetic ordering of Mn trimers on a GaN ($000\bar{1}$) substrate. These trimers had previously been observed in $3a \times 3a$ surface reconstructions through Mn deposition onto the N-polar face of wurtzite GaN($000\bar{1}$). In this work, we start off by studying the effect of spin orbit coupling for the case of monomers and dimers of Mn atoms on top of a GaN surface. Based on an effective spin Hamiltonian, we estimate the magnetic anisotropy energy (MAE) for those cases and found that it is four orders of magnitude weaker than the exchange magnetic coupling between Mn adatoms. In the Mn trimer case, the magnetic ground state has the Mn spins in-plane with the GaN surface in which the relative spin orientation within each trimer is noncollinear due to the competition between the two antiferromagnetic interactions that affect each Mn spin in the trimer, which leads to the found energy minimum with 120 degree angles between the spins. By exploring the nature and fundamental mechanisms for the magnetic interaction among the Mn trimers, we find that the surface states of the substrate play a key role, involving a Ruderman-Kittel-Kasuya-Yosida (RKKY)-type interaction. We report on an electron-mediated long-distance exchange coupling between localized magnetic moments on a GaN($000\bar{1}$) surface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Formation of the skyrmionic polaron by Rashba and Dresselhaus spin-orbit coupling

Skyrmions in reduced dimensions such as thin layers and interfaces are of both fundamental and technological importance. In these systems, itinerant electrons are often present together with the Rashba and Dresselhaus spin-orbit coupling (SOC). Here, in this study, we show that an itinerant electron in the presence of these interactions can nucleate the skyrmion state, even when the standard Dzyaloshinskii-Moriya interaction (DMI) is absent, and the electron can become self-trapped in the skyrmion core, forming the “skyrmionic polaron” (SkP). The formation of the SkP is investigated from a continuum model of the electron, exchange coupled to the lattice spins, by solving the appropriate Euler-Lagrange equations. The skyrmion (antiskyrmion) texture is favored by the Rashba (Dresselhaus) SOC, with the binding energy increasing quadratically with the strength of the interaction. In contrast, if the skyrmion is already formed due to a nonzero DMI, the electron is delocalized and avoids the skyrmion core until the strength of the Rashba or Dresselhaus SOC exceeds a critical value. Below this critical value, the electron is not bound to the skyrmion core, the polaron does not form, and the electron has little effect on the skyrmion state. Our work envisions the possibility of manipulating the skyrmion state in device applications by altering the strength of the Rashba or Dresselhaus interactions, e.g., by an external electric field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Modeling Sorption of Water and Vanadium Cations by Ion-Exchange Membranes

We develop a macroscopic model for sorption of ions and solvent by ion-exchange membranes and use it to investigate how different membranes behave when exposed to electrolytes for vanadium flow batteries. The model combines a classical expression for the Gibbs free energy of a moderately concentrated electrolyte containing several ions with a term that describes elastic swelling of a polymer membrane. Parameters describing pairwise interactions between mobile ions and fixed membrane ions were fit to published experimental data and discussed in the context of the competition for sites in ion-exchange membranes. The model provides insights into why sorption of vanadium cations by Nafion is lower than predicted by Donnan theory and why switching to an anion-exchange membrane does not dramatically reduce vanadium sorption.

Electrochemistry↗
DOE OSTI2022

Phenyl‐Free Polynorbornenes for Potential Anion Exchange Ionomers for Fuel Cells and Electrolyzers

Abstract Ionomers in the catalyst layer play a critical role in the performance of fuel cells and electrolyzers. Phenyl adsorption on hydrogen oxidation catalysts and electrochemical oxidation of phenyl moieties on oxygen evolution catalysts are detrimental to the alkaline devices’ performance. Here the adsorption energy of phenyl‐containing ionomers is compared to provide the rationale for implementing phenyl‐free ionomers. Density functional theory calculations indicated that the norbornane fragment has minimal adsorption energy on Pt(111) due to the absence of aromatic π electrons. A soluble quaternized polynorbornene ionomer is prepared by vinyl addition polymerization, and it exhibits high performance in both fuel cells and electrolyzers, proving the advantage of the phenyl‐free structure. This study establishes the phenyl adsorption energy‐electrode performance relationship, highlighting the importance of material interactions between the catalysts and ionomers.

25 ENERGY STORAGE↗
DOE OSTI2023

Effect of Ligand Chemistry on the Electronic Properties and Reactivity of Cobalt Acetate Autoxidation Catalysts

Autoxidation chemistry catalyzed by cobalt(II) acetate is an industrial pathway for converting hydrocarbons into oxygenated compounds and has promising potential applications in plastic waste deconstruction. However, the chemical properties of the Co acetate-based catalysts and their roles in the reaction mechanism are poorly understood, and as a result, attempts to redesign the autoxidation chemical process for novel applications lack clear direction. In this work, we investigate the structure and electronic properties of a series of multinuclear Co(III) compounds that have been proposed as active participants in catalytic autoxidation. Through a combination of X-ray spectroscopic measurements [Co K-edge X-ray absorption spectroscopy (XAS), extended X-ray absorption fine structure (EXAFS), Kβ X-ray emission spectroscopy (XES), and high-energy resolution fluorescence detection (HERFD) XAS] and theoretical methods, we characterize the interactions of Co with acetate and hydroxyl ligands in these compounds. Here we show that the substitution of acetate ligands with hydroxyls in these compounds causes an increase in the electron density on Co, driven by the loss of a π back-bonding interaction between Co and acetate and an increase in electron donation to Co from the hydroxyl ligands. We further classify the bonding between Co and acetate based on the orbital overlap and show that the experimental absorption and emission spectra are well-described by the resulting molecular orbitals. Finally, we predict the impacts of acetate/hydroxyl ligand exchange on autoxidation catalytic properties, showing that the reaction free energies for key Co oxidation and reduction steps are extremely sensitive to metal-ligand bonding interactions and thus have meaningful impacts on overall reactivity. The results of this study constitute an important set of design criteria for developing novel homogeneous autoxidation catalysts.

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

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. In this paper, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Optimization of anionic conductivity through the coexistence of ionomer cluster and backbone-backbone morphologies in anion exchange membranes

Random copolymers of poly(4-vinylpyridine) and polyisoprene were synthesized, and subsequently quaternized with 1-alkylbromides. The number of carbons on the pendant side-chain of the resultant comb-shaped polymer, n, ranged from 2-8. The comb-shaped polymers were crosslinked employing thiol-ene chemistry to give mechanically robust ion conducting membranes. Analysis by wide and medium-angle X-ray scattering show three morphology regimes that are dependent on the number of carbons on the pendant side-chains. When n = 2, ionomer cluster morphology was dominant, when n = 8 backbone-backbone morphology was dominant, and when n = 3-6, the membrane showed a coexistence of both ionomer cluster and backbone-backbone morphologies. Evaluation of the water uptake of the membranes showed a maximum water uptake per cation of 9.5 when n = 5 at 95% relative humidity (RH) and 60 degrees C. Finally, conductivity of the samples characterized by electrochemical impedance spectroscopy showed bromide conductivity as high as 110 mS/cm when n = 3 at 95% RH and 90 degrees C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Solution and Interface Structure and Dynamics in Geochemistry: Gateway to Link Elementary Processes to Mineral Nucleation and Growth

Our understanding of the process of mineral nucleation is starting to evolve from the solely thermodynamical aspects in classical nucleation theory toward a mechanistic study of reactions influenced by solvation structures of ions and their dynamics. A knowledge of how these atomic and molecular interactions respond to changing solution composition and/or the nature of an interface will form a fundamental foundation to understand rate-limiting reactions and processes for nucleation and growth. Here, we review recent advances from multidisciplinary experimental and computational approaches of the structure and dynamics of aqueous solutions and mineral–liquid interfaces that will influence rates of nucleation (and growth behavior) both homogeneously in aqueous solutions and heterogeneously at mineral–liquid interfaces. Furthermore, these processes include structure (and extent) of solute clustering, solvent degrees of freedom, and the presence of noninnocent charge-balancing ions, all of which can drive the selectivity and exert control over nucleation mechanisms. Similar controlling reactions can also occur at interfaces with the added complexities of how solute ions interact with and assemble on surface sites and use different mechanisms from bulk solutes, such as lateral solvent exchanges between distinct surface sites. To gain a predictive understanding of nucleation chemistry, we emphasize several key knowledge gaps that will need to be addressed in this field and highlight the importance of combining computations and experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

River Dynamics Control Transit Time Distributions and Biogeochemical Reactions in a Dam-Regulated River Corridor

Residence Time Distributions (RTDs) exert an important control on biogeochemical translation in the hydrological systems. Previous tracer studies have revealed that RTDs often followed time-invariant exponential, lognormal, or heavy-tailed RTDs that have power-law behavior for long tails in headwater or low-order streams. However, there is a recognition that RTDs can be more complicated and time-variable in response to dynamic hydrological forcing. Here, we use particle tracking to estimate RTDs along the Hanford Reach of the Columbia River and to quantify the influences of river stage fluctuations. Particle tracking is conducted using the velocity field from high-resolution 3D groundwater flow simulations. The effects of hydrological forcing on the residence time distribution were evaluated by varying river flow boundary conditions and releasing particles in different time windows. Our results revealed that dynamic stage fluctuations created rapidly changing losing-gaining conditions in the river and led to highly transient RTDs, which contributes to multiple modes of RTDs. Dam-induced high-frequency (sub-daily) flow variation contributes to the short-time (sub-daily) component of the RTDs. Deviation of the reactant consumption under the single-mode assumption compared to the multimodal RTDs is relatively small (~5%) and appears when the Damköhler number was close to one.More specifically, high-frequency (daily) dam-induced stage variations have higher impacts on biogeochemical reactions with faster reaction rate, and can potentially increase the reactant consumption by 26.68%. Based on these findings, we suggest that current river basin models could be improved by including bank storage and more complex RTDs influenced by both short and long term river stage fluctuations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Emergent facilitation and glassy dynamics in supercooled liquids

In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic–subdiffusive–diffusive crossover MSD behaviors commonly found in supercooled liquids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A New 1D Model for Thermal Mixing and Stratification in Advanced Reactor Transients

Thermal mixing and stratification in large pools and enclosures play a critical role in the safety and performance of pool-type nuclear reactors, particularly during transient scenarios involving significant temperature differences between incoming and bulk coolant. Accurate modeling of these phenomena is essential for predicting system behavior and supporting passive safety features such as natural circulation. Here, this paper presents a new 1D model for thermal mixing and stratification, developed and implemented in the SAM code. The model represents a large pool as 1D coolant jet channels and zero-dimensional bulk pool volumes, enabling the simulation of a wide range of flow configurations, including hot and cold jet interactions, stratified layers, and the influence of complex geometries such as ceilings, free surfaces, and internal obstacles. Heat exchange between jet and pool regions is governed by closure relations calibrated against 3D computational fluid dynamics (CFD) simulations. The model improves upon earlier approaches by incorporating time-dependent jet characteristics and capturing the associated delay effects more accurately. Code-to-code comparisons and validation against experimental data from the Thermal Stratification Test Facility demonstrate the model’s accuracy and flexibility. This work offers two key contributions: (1) an efficient and robust method for simulating thermal mixing and stratification at the system level, eliminating the need for external coupling between system analysis codes and CFD, and (2) a significant enhancement of SAM’s capabilities to analyze thermal stratification phenomena in advanced reactor systems.

SAM↗
DOE OSTI2020

Evaluation of Nuclear Spent Fuel Disposal in Clay-Bearing Rock - Process Model Development and Experimental Studies

The DOE R&D program under the Spent Fuel Waste Science Technology (SFWST) campaign has made key progress in modeling and experimental approaches towards the characterization of chemical and physical phenomena that could impact the long-term safety assessment of heat-generating nuclear waste disposition in deep clay/shale/argillaceous rock. International collaboration activities such as heater tests and postmortem analysis of samples recovered from these have elucidated key information regarding changes in the engineered barrier system (EBS) material exposed to years of thermal loads. Chemical and structural analyses of sampled bentonite material from such tests has as well as experiments conducted on these are key to the characterization of thermal effects affecting bentonite clay barrier performance and the extent of sacrificial zones in the EBS during the thermal period. Thermal, hydrologic, and chemical data collected from heater tests and laboratory experiments has been used in the development, validation, and calibration of THMC simulators to model near-field coupled processes. This information leads to the development of simulation approaches (e.g., continuum vs. discrete) to tackle issues related to flow and transport at various scales of the host-rock and EBS design concept. Consideration of direct disposal of large capacity dual-purpose canisters (DPCs) as part of the back-end SNF waste disposition strategy has generated interest in improving our understanding of the effects of elevated temperatures on the EBS design. This is particularly important for backfilled repository concepts where temperature plays a key role in the EBS behavior and long-term performance. This report describes multiple R&D efforts on disposal in argillaceous geologic media through development and application of coupled THMC process models, experimental studies on clay/metal/cement barrier and host-rock (argillite) material interactions, molecular dynamic (MD) simulations of water transport during (swelling) clay dehydration, first-principles studies of metaschoepite (UO 2 corrosion product) stability, and advances in thermodynamic plus surface complexation database development. Drift-scale URL experiments provides key data for testing hydrological-chemical (HC) model involving strong couplings of fluid mixing and barrier material chemical interactions. The THM modeling focuses on heater test experiments in argillite rock and gas migration in bentonite as part of international collaboration activities at underground research laboratories (URLs). In addition, field testing at an URL involves in situ analysis of fault slip behavior and fault permeability. Pore-scale modeling of gas bubble migration is also being investigated within the gas migration modeling effort. Interaction experiments on bentonite samples from heater test under ambient and elevated temperatures permit the evaluation of ion exchange, phase stability, and mineral transformation changes that could impact clay swelling. Advances in the development, testing, and implementation of a spent nuclear fuel (SNF) degradation model coupled with canister corrosion focus on the effects of hydrogen gas generation and its integration with Geologic Disposal Safety Assessment (GDSA). GDSA integration activities includes evaluation of groundwater chemistries in shale formations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Study of CC2p0$\pi$ Event Topologies in the MicroBooNE Detector

The precise measurement of neutrino oscillation parameters is a critical component of understanding neutrino oscillations. As future accelerator neutrino experiments will utilize 40 Ar as the target nucleus it is important to understand the influence that nuclear effects have on neutrino-nucleon cross-sections. Processes that lead to 2 particle-2 hole (2p2h) states are of particular interest, such as Meson Exchange Currents (MEC) and Short Range Nucleon-Nucleon Correlations. In the MicroBooNE detector, a charged-current interaction that produced a 2p2h state would create a 3 track topology with 1 muon and 2 protons connected to a single interaction vertex (CC2p0$\pi$). We present here a study of MicroBooNE’s potential sensitivity to a variety of MEC models as well as CC2p0$\pi$ events selected from a combination of data collected from the first 3 years of running of the MicroBooNE experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Improved Predictive Tools for Structural Properties of Metal–Organic Frameworks

The accurate determination of structural parameters is necessary to understand the electronic and magnetic properties of metal–organic frameworks (MOFs) and is a first step toward accurate calculations of electronic structure and function for separations and catalysis. Theoretical structural determination of metal-organic frameworks is particularly challenging because they involve ionic, covalent, and noncovalent interactions, which must be treated in a balanced fashion. Here, we apply a diverse group of local exchange-correlation functionals (PBE, PBEsol, PBE-D2, PBE-D3, vdW-DF2, SOGGA, MN15-L, revM06-L, SCAN, and revTPSS) to a broad test set of MOFs to seek the most accurate functionals to study various structural aspects of porous solids, in particular to study lattice constants, unit cell volume, two types of pore size characteristics, bond lengths, bond angles, and torsional angles). The recently developed meta functionals revM06-L and SCAN, without adding any molecular mechanics terms, are able to predict more accurate structures than previously recommended functionals, both those without molecular mechanics terms (PBE, PBEsol, vdW-DF2, and revTPSS) and those with them (PBE-D2 and PBE-D3). To provide a broader test, these two functionals are also tested for lattice constants and band gaps of unary, binary, and ternary semiconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A study of the 2H(e, e ' p)X reaction at large 4-momentum transfers and high missing momenta

The short-range region (r < 1 fm) of the nucleon-nucleon potential may be studied via deuteron electro-disintegration. Such an experiment was done at Hall C of Jefferson Lab at 4-momentum transfers of Q^2 = 4.07 (GeV/c)^2 and reaching missing momenta up to 900 MeV/c. At such settings, complications arising from Meson Exchange Currents (MEC) and Isobar Currents are expected to be signifi cantly minimized, as well as Final State Interactions (FSI) at recoiling angles of ¿_Xq ~ 40 deg. This makes comparisons of experimental and theoretical cross sections less model dependent. A luminosity study was done to determine the reduction of liquid deuterium targets with increasing beam current. A 2.8% in the charge yield was found between 0 to 70 µA. Electron scattering from the walls of the target chamber was determined to be negligible, but caution was taken by considering scattering events away from the walls. A neutron was found to be contained in the missing mass spectrum for each missing momentum setting. Extraction of the deuteron total cross section is still on going.

Love, Shawn [California State Univ. (CalState), Lo↗