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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Enhancement of disposal efficiency for deep geological repositories based on three design factors - Decay heat optimization, increased thermal limit of the buffer and double-layer concept

This study investigates the enhancement of disposal efficiency for deep geological repositories (DGRs) based on three design factors: decay heat optimization, increased thermal limit of the buffer, and double-layer concept using coupled thermo-hydro-mechanical (THM) numerical simulations. Decay heat optimization is achieved by iteratively emplacing spent nuclear fuels having the maximum and minimum decay heat in a canister. Disposal areas can be reduced by 20 % to 40 % compared to the current reference disposal system in Korea (KRS+) in accordance with the combinations of the three design factors, alleviating challenges in site selection for the DGR. This study additionally identifies an optimal layer spacing of 500 m for the double-layer concept in the viewpoint of the buffer temperature, where thermal interaction between the upper and lower layers nearly disappears. However, determining the ultimate disposal and layer spacing requires engineering judgement, considering not only the thermal performance of the DGR but also various factors such as cost and difficulties of the construction and rock mass stability. DGRs designed with an increased thermal limit of the buffer poses a greater probability of rock mass failure around disposal tunnels and deposition holes due to elevated thermal stresses. Densely arranged heat sources for the DGRs with enhanced disposal efficiency lead to larger temperature increase even at the far-field scale, raising a possibility of thermally driven fracture shear activation with associated hydraulic, mechanical, and seismic changes.

58 GEOSCIENCES↗
DOE OSTI2021

Wyoming CarbonSAFE: Advancing Commercialization of Low-Carbon Energy Technologies in Fossil-Rich Wyoming

Wyoming’s Powder River Basin (PRB) is the most prolific coal producer and exporter in the United States and the State of Wyoming’s largest oil-producing basin. In addition to being a leading energy producer, the PRB is the site of research programs whose aim is to develop and integrate low-carbon technologies into existing fossil fuel energy industries. Much of the PRB’s low-carbon research is focused around Dry Fork Station (DFS), which is the newest coal-fired power station in the western US. Currently, DFS hosts five carbon capture projects, including pilot-scale capture projects that utilize different capture technologies and a full front-end engineering and design (FEED) study, a commercial CO 2 pipeline for nearby CO 2 -enhanced oil recovery industry, and is also co-located with the Wyoming Integrated Test Center, which is a host facility for unconventional carbon utilization research (i.e. flue gas carbon-to-products innovations). DFS is also the host site for the Wyoming CarbonSAFE project. Wyoming CarbonSAFE, funded by the Department of Energy/National Energy Technology Laboratory, is a multi-phased program (currently in Phase II) whose core objective is developing and validating storage sites within a complex capable of storing 50 million metric tonnes of CO 2 over a 30 year project period using carbon capture, utilization and storage (CCUS). This paper will provide an overview of the project to-date, showing that CarbonSAFE goals are achievable with respect to geologic, environmental, regulatory, CO 2 source and economic conditions, and why the State of Wyoming offers one of the more favorable environments to advance the commercialization studies. In 2019, the project team designed and completed a ~10,000 foot stratigraphic test well just south of DFS. From this well, the team collected over 600 feet of core, fluid samples from target injection zones, and a full petrophysical log suite. In addition, legacy 2D seismic lines were acquired and a 3D seismic survey was acquired in the fall of 2020. The objective of these field activities has been to identify and characterize target storage reservoirs and associated caprock. This complex has several reservoirs that could meet commercial injection goals, and over 4000 feet of associated caprock. Simulations of site performance suggest that stacked injection provides the most effective storage strategy, and would necessitate several sites within the greater complex to meet final project injection goals. Other work within this project includes the development of a business-case around proximal fields with CO 2 -enhanced oil recovery potential and existing tax credits, assessment of regulatory conditions, including pore space ownership and Class VI injection well permitting requirements, implementation of a robust public outreach Electronic copy available at: https://ssrn.com/abstract=3821220 GHGT-15 McLaughlin 2 program, and surface site characterization activities that have focused on environmental factors. In the PRB and at DFS, the State of Wyoming and other entities have made carbon management a priority of its future energy industry by providing a regulatory and business framework that is favorable to advancing these technologies. These endeavors will become more realistic with the successful implementation of Wyoming CarbonSAFE, and its ability to secure and validate commercial-scale CCUS at the center of Wyoming’s premier low-carbon research efforts.

McLaughlin, Fred↗
DOE OSTI2023

Energetic electron transport in magnetic fields with island chains and stochastic regions

This paper investigates energetic electron transport in magnetized toroidal plasmas with magnetic fields characterized by island chains and regions of stochastic field lines produced by coil perturbations. We report on experiments performed in the DIII-D tokamak, which utilize electron cyclotron heating and current drive pulses to ‘tag’ electron populations within different locations across the discharge. The cross-field transport of these populations is then inferred from electron cyclotron emission measurements and gamma emission signals from scintillator detectors. Two types of energetic particles are distinguished and discussed: non-relativistic suprathermal electrons and relativistic runaway electrons. The magnetic field topology in each discharge is reconstructed with field-line tracing codes, which are also used to determine the location and scale of magnetic islands and stochastic regions. Comparison of simulations and experiments suggests that suprathermal transport is suppressed when the tagging is performed at a smaller radial location than the location of the $q = 1$ island chain and enhanced otherwise. Here q is the safety factor. We further demonstrate that increasing the width of the stochastic region within the edge plasma yields enhancement of the suprathermal electron transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Enhancement of Photoemission on p-Type GaAs Using Surface Acoustic Waves

We demonstrate that photoemission properties of p-type GaAs can be altered by surface acoustic waves (SAWs) generated on the GaAs surface due to dynamical piezoelectric fields of SAWs. Multiphysics simulations indicate that charge-carrier recombination is greatly reduced, and electron effective lifetime in p-doped GaAs may increase by a factor of 10× to 20×. It implies a significant increase, by a factor of 2× to 3×, of quantum efficiency (QE) for GaAs photoemission applications, like GaAs photocathodes. Conditions of different SAW wavelengths, swept SAW intensities, and varied incident photon energies were investigated. Essential steps in SAW device fabrication on a GaAs substrate are demonstrated, including deposition of an additional layer of ZnO for piezoelectric effect enhancement, measurements of current–voltage (I–V) characteristics of the SAW device, and ability to survive high-temperature annealing. Results obtained and reported in this study provide the potential and basis for future studies on building SAW-enhanced photocathodes, as well as other GaAs photoelectric applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Utah FORGE 2-2446: Closing the Loop Between In-situ Stress Complexity and EGS Fracture Complexity - Workshop Presentation

This is a presentation on the Closing the Loop Between In-situ Stress Complexity and EGS Fracture Complexity project by Lawrence Livermore National Laboratory, presented by Dr. Matteo Cusini. The project's objective was to employ a combination of high-fidelity simulations and true-triaxial block fracturing tests at high temperature to explore the intricate relationship between in-situ stress and hydraulic fracture patterns and better characterize the in-situ stress at Utah FORGE. This presentation was featured in the Utah FORGE R&D Annual Workshop on September 7, 2023. The workshop provided a valuable opportunity to explore the progress made in each of the 17 Research and Development projects funded under Solicitation 2020-1 which aim to enhance our understanding of the crucial factors influencing the development of Enhanced Geothermal Systems (EGS) reservoirs and resources.

15 GEOTHERMAL ENERGY↗
DOE OSTI2026

Cosmic Axion Background detection using resonant cavity arrays

The axion is a well-motivated and generic extension of the Standard Model. If produced in the early universe, axions may still be relativistic today, forming a Cosmic Axion Background (CaB) potentially detectable in direct detection experiments. Although CaB is expected to be broadband, which makes it challenging to be detected, a high-quality-factor microwave cavity acts as a narrowband filter with response peaked at its resonant frequency. We propose a new strategy using multi-cavity arrays to distinguish signal from background noise by exploiting spatial correlations of the axion-induced electric field which are set by the cavity quality factor. We compute the two-point correlation function for electric fields in spatially separated cavities sourced by an isotropic CaB. Analyzing various cavity geometries, we find that stacked, wide-base cavity arrays offer coherent enhancement of the axion signal. We apply our formalism to prospective upgrades of the ADMX experiment, including configurations with four and eighteen coupled cavities. Although these arrays do not achieve a coherent enhancement, optimizing the geometry could potentially yield an $\mathcal{O}(1)$ improvement in the sensitivity to the CaB.

Axions and ALPs↗
DOE OSTI2025

Kβ X-ray Emission Spectra Analysis Using Bayesian Optimization

The Kβ X-ray emission spectrum of 3 d transition metals is rich with electronic and structural information due to strong exchange interactions with the valence shell of the metal, and has become crucial for understanding their spin and oxidation states. The spectrum is commonly treated using crystal-field multiplet theory, a semi-empirical theory that uses tunable parameters to control the strength of the effects present in X-ray emission spectroscopy (XES). However, determining the experimental values of these parameters remains a challenge. We present a methodology that applies Bayesian optimization to crystal-field multiplet theory to determine parameter values. The algorithm is tested on the X-ray emission spectra of a collection of Mn, Co, and Ni oxides. We are able to find optimal values for the four most impactful parameters: Slater−Condon reduction factors F dd , F pd , and G pd , and crystal field splitting 10 Dq . The algorithm produces significantly improved accuracy compared to current analysis methods, and probes interparameter dependencies by modeling the error landscape. This advancement enhances XES analysis by offering an approach of obtaining quantitative electronic structural information on 3 d transition metal valence shells, facilitating applications across various scientific fields.

Bayesian optimization↗
DOE OSTI2022

Ab Initio Prediction of the 4 $\mathrm{H}$e($d, γ$) 6 $\mathrm{L}$i Big Bang Radiative Capture

We report the rate at which helium ( 4 He ) and deuterium (d) fuse together to produce lithium-6 ( 6 Li) and a γ ray, 4 $\mathrm{H}$e($d, γ$) 6 $\mathrm{L}$i, is a critical puzzle piece in resolving the discrepancy between big bang predictions and astronomical observations for the primordial abundance of 6 Li . The accurate determination of this radiative capture rate requires the quantitative and predictive description of the fusion probability across the big bang energy window (30 keV ≲ E ≲ 400 keV), where measurements are hindered by low counting rates. We present first-principle (or, ab initio) predictions of the 4 $\mathrm{H}$e($d, γ$) 6 $\mathrm{L}$i astrophysical S factor using validated nucleon-nucleon and three-nucleon interactions derived within the framework of chiral effective field theory. By employing the ab initio no-core shell model with continuum to describe 4 He-d scattering dynamics and bound 6 Li product on an equal footing, we accurately and consistently determine the contributions of the main electromagnetic transitions driving the radiative capture process. Our results reveal an enhancement of the capture probability below 100 keV owing to previously neglected magnetic dipole (M1) transitions and reduce by an average factor of 7 the uncertainty of the thermonuclear capture rate between 0.002 and 2 GK.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Hot Electron Driven Photocatalysis on Plasmon-Resonant Grating Nanostructures

Here, we demonstrate the hot electron injection of photoexcited carriers in an Ag-based plasmon resonant grating structure. By varying the incident angle of irradiation, sharp dips are observed in the reflectance with p-polarized light (electric field perpendicular to grating lines) when there is wavevector matching between the incident light and the plasmon resonant modes of the grating and no angle dependence is observed with s-polarized light. This configuration enables us to compare photoelectrochemical current produced by plasmon resonant excitation with that of bulk metal interband absorption simply by rotating the polarization of the incident light while keeping all other parameters of the measurement fixed. With 633 nm light, we observed a 12-fold enhancement in the photocurrent (i.e., reaction rate) between resonant and nonresonant polarizations at incident angles of ±7.6° from normal. At 785 nm irradiation, we observed similar resonant profiles to those obtained with 633 nm wavelength light but with a 44-fold enhancement factor. Using 532 nm light, we observed two resonant peaks (with approximately 10× enhancement) in the photocurrent at 19.4° and 28.0° incident angles, each corresponding to higher order modes in the grating with more nodes per period. The lower enhancement factors observed at shorter wavelengths are attributed to interband transitions, which provide a damping mechanism for the plasmon resonance. Finite difference time domain (FDTD) simulations of these grating structures confirm the resonant profiles observed in the angle-dependent spectra of these gratings and provide a detailed picture of the electric field profiles on and off resonance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Relaxor ferroelectric polymer exhibits ultrahigh electromechanical coupling at low electric field

Electromechanical (EM) coupling—the conversion of energy between electric and mechanical forms—in ferroelectrics has been used for a broad range of applications. Ferroelectric polymers have weak EM coupling that severely limits their usefulness for applications. Here, we introduced a small amount of fluorinated alkyne (FA) monomers (<2 mol %) in relaxor ferroelectric poly(vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) (PVDF-TrFE-CFE) terpolymer that markedly enhances the polarization change with strong EM coupling while suppressing other polarization changes that do not contribute to it. Under a low–dc bias field of 40 megavolts per meter, the relaxor tetrapolymer has an EM coupling factor (k 33 ) of 88% and a piezoelectric coefficient (d 33 ) >1000 picometers per volt. These values make this solution-processed polymer competitive with ceramic oxide piezoelectrics, with the potential for use in distinct applications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Higher Ion Selectivity with Lower Energy Usage Promoted by Electro-osmotic Flow in the Transport through Conical Nanopores

The tradeoff between selectivity and throughput presents fundamental challenges to improve desalination and charge storage, salinity gradient-based energy harvesting, memory device/circuit development, and so forth. The well-known ion-current rectification and the recently resolved time-dependent transport hysteresis in conical nanopores or asymmetric nanointerfaces offer new opportunities for the selective transport of matter. This report shows that electro-osmotic flow (EOF) is an overlooked factor that increases ion selectivity while maintaining enhanced transport throughput in rectified nanoscale electrokinetic transport. The increased selectivity originates primarily from the suppression of anion flux by the fluid flow in the opposite direction under the applied electrical field. By solving the Poisson and Nernst–Planck (PNP) equations without and with coupled Navier–Stokes (PNP–NS) equations, the EOF effects on cation and anion transport are unequivocally revealed in asymmetric nanopipettes. The flux of cations and anions as well as the transference number and flow velocity are elucidated using the models and boundary conditions validated by previous experiments. A dimensionless parameter, radius over the Debye length, reveals optimal ion selectivity and energy cost at intermediate ion concentrations and nanopore sizes, up to hundreds of millimolars and tens of nanometers under time-dependent potential stimulus. Furthermore, the fundamental insights into EOF at nanointerfaces suggest new routes/strategies for better separation, analysis, and energy applications.

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

Plasmonic Core–Shell–Satellites with Abundant Electromagnetic Hotspots for Highly Sensitive and Reproducible SERS Detection

In this work, we develop a Ag@Al2O3@Ag plasmonic core–shell–satellite (PCSS) to achieve highly sensitive and reproducible surface-enhanced Raman spectroscopy (SERS) detection of probe molecules. To fabricate PCSS nanostructures, we employ a simple hierarchical dewetting process of Ag films coupled with an atomic layer deposition (ALD) method for the Al2O3 shell. Compared to bare Ag nanoparticles, several advantages of fabricating PCSS nanostructures are discovered, including high surface roughness, high density of nanogaps between Ag core and Ag satellites, and nanogaps between adjacent Ag satellites. Finite-difference time-domain (FDTD) simulations of the PCSS nanostructure confirm an enhancement in the electromagnetic field intensity (hotspots) in the nanogap between the Ag core and the satellite generated by the Al2O3 shell, due to the strong core–satellite plasmonic coupling. The as-prepared PCSS-based SERS substrate demonstrates an enhancement factor (EF) of 1.7 × 107 and relative standard deviation (RSD) of ~7%, endowing our SERS platform with highly sensitive and reproducible detection of R6G molecules. We think that this method provides a simple approach for the fabrication of PCSS by a solid-state technique and a basis for developing a highly SERS-active substrate for practical applications.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Simulations of divertor heat flux width using transport code with cross-field drifts under the BOUT++ framework

The fluid transport code [trans-electric field (Er) module] under the BOUT++ framework has been used to simulatedivertor heat flux width and boundary Er with all drifts and the sheath potential in the scrape-off layer. The calculated steady state radial Er in the pedestal region has been compared with that of experimental measurements from the Alcator C-Mod tokamak. The magnitude and shape of Er are similar to those of the experimental data. In order to understand the relative role of cross-field drifts vs turbulent transport in setting the heat flux width, four C-Mod enhanced Dα H-mode discharges with a lower single null divertor configuration should be simulated. BOUT++ transport simulations with cross-field drifts included yield similar heat flux width λq to that of experimental measurements (within a factor of 2) from both the probe and the surface thermocouple diagnostics and show a similar trend with plasma current to that of the Eich experimental scaling. The simulations show that both drifts and turbulent transport compete to determine the heat flux width. The magnetic drifts play a dominant role in setting the divertor heat-flux width, while the E × B drift decreases the heat flux width by 10%–25%, leading to improved agreement with the experiment relative to Goldston’s model. A turbulence diffusivity scan (χ) identifies two distinct regimes: a drift dominant regime when χ is small and a turbulence dominant regime when χ is large. The Goldston heuristic drift model yields a lower limit of the width λq.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Electron emission from bromouracil and uracil induced by protons and radiosensitization

Absolute double differential cross sections (DDCS) of electrons emitted from uracil and 5-bromouracil (BrU) in collisions with protons of energy 200 keV have been measured for various forward and backward emission angles over wide range of electron energies. The measured DDCS are compared with the continuum distorted wave-eikonal initial state (CDW-EIS) calculations. The optimized structure of the BrU was estimated along with the population analysis of all the occupied orbitals using a self-consistent field density. A comparison between the measured DDCS data for the two molecules show that the cross section of low energy electrons emitted from BrU is substantially larger than that for uracil. The BrU-to-uracil DDCS ratios obtained from the present measurements indicate an enhancement of the electron emission by a factor which is as large as 2.0 to 2.5. These electrons being the major agent for damaging the DNA/RNA of the malignant tissues, the present results are expected to provide an important input for the radiosensitization effect in hadron therapy. It is noteworthy to mention that the CDW-EIS calculations for Coulomb ionization cannot predict such enhancement. A large angular asymmetry is observed for uracil with a broad structure, which is absent in case of BrU.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Look Up: Probing the Vertical Profile of New Particle Formation and Growth in the Planetary Boundary Layer With Models and Observations

Abstract The processes of new particle formation (NPF) and growth are important contributors to cloud condensation nuclei (CCN) concentrations, and CCN are important for climate from their impact on planetary radiative forcing. While the general ubiquity and importance of NPF is understood, the vertical extent and governing mechanisms of NPF and growth in the lower troposphere are uncertain. We present an analysis of four NPF events and two non‐NPF events during the HI‐SCALE field campaign at the Southern Great Plains observatory in Oklahoma, USA. First, we analyzed airborne and ground‐based observations of aerosol and gas‐phase properties. Second, we used a column aerosol chemistry and microphysics model to probe factors that influence the vertical profile of NPF. During HI‐SCALE, we found several instances of enhanced NPF occurring several hundred meters above the surface; however, the spatio‐temporal characteristics of the observed NPF made comparisons between airborne‐ and ground‐based observations difficult. The model represented the observed NPF (or lack of NPF) and particle growth at the surface to final diameters within 10 nm. The model predicted enhanced NPF rates in the upper mixed layer, and this enhancement is primarily due to the temperature dependence in the NPF schemes, but this was also dependent on the vertical profile of gas‐phase precursors measured during HI‐SCALE. We found vertical mixing in the model either enhanced or suppressed NPF rates, aerosol number concentrations, and particle growth rates at the surface. Finally, our analysis provides insights for future field campaigns and modeling efforts investigating the vertical profile of NPF.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Synergistic Use of Pyridine and Selenophene in a Diketopyrrolopyrrole‐Based Conjugated Polymer Enhances the Electron Mobility in Organic Transistors

Abstract To achieve semiconducting materials with high electron mobility in organic field‐effect transistors (OFETs), low‐lying energy levels (the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO)) and favorable molecular packing and ordering are two crucial factors. Here, it is reported that the incorporation of pyridine and selenophene into the backbone of a diketopyrrolopyrrole (DPP)‐based copolymer produces a high‐electron‐mobility semiconductor, PDPPy‐Se. Compared with analogous polymers based on other DPP derivatives and selenophene, PDPPy‐Se features a lower LUMO that can decrease the electron transfer barrier for more effective electron injection, and simultaneously a lower HOMO that, however, can increase the hole transfer barrier to suppress the hole injection. Combined with thermal annealing at 240 °C for thin film morphology optimization to achieve large‐scale crystallite domains with tight molecular packing for effective charge transport along the conducting channel, OFET devices fabricated with PDPPy‐Se exhibit an n‐type‐dominant performance with an electron mobility (μ e ) as high as 2.22 cm 2 V −1 s −1 and a hole/electron mobility ratio (μ h /μ e ) of 0.26. Overall, this study demonstrates a simple yet effective approach to boost the electron mobility in organic transistors by synergistic use of pyridine and selenophene in the backbone of a DPP‐based copolymer.

Liu, Qian↗
DOE OSTI2025

Slow Electron Spin Relaxation at Ambient Temperatures with Copper Coordinated by a Rigid Macrocyclic Ligand

Paramagnetic transition metal complexes can serve as quantum bits, storing phase information through unpaired electrons. Despite their promise, these systems often require low temperatures and tend to rapidly decohere. Recent efforts have sought to improve longitudinal relaxation (T 1 ), which provides an upper limit for phase coherence (T m ), by investigating existing literature compounds with reduced vibrational coupling and orbital angular momentum. However, synthetic strategies for improving T 1 through novel ligand design have remained scant. Here, we disclose the synthesis of a new modular macrocyclic ligand framework with four nitrogen donors (N 4 ) derived from phenanthroline that supports room-temperature coherent Cu(II) spin centers. The optimized complex more than doubles the T 1 over the next best Cu(II)-N 4 compound and exhibits a room temperature coherence time (T m ) of 0.28 μs, close to previously reported values. This performance enhancement arises from a tight binding site with short Cu–N distances, resulting in a stronger ligand field and reduced thermal accessibility of symmetric vibrational modes. This work demonstrates a practical approach to enabling spin coherence at room temperature, a factor critical to accessing relevant quantum bits and biological sensors, through a designer macrocyclic ligand platform.

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

Neutron-neutron scattering length from the 6 He(p,pα)nn reaction

We propose a novel method to measure the neutron-neutron scattering length using the 6 He(p,pα)nn reaction in inverse kinematics at high energies. The method is based on the final-state interaction (FSI) between the neutrons after the sudden knockout of the α particle. We show that the details of the neutron-neutron relative-energy distribution allow for a precise extraction of the s-wave scattering length. Here, we present the state of the art in regard to the theory of this distribution. The distribution is calculated in two steps. First, we calculate the ground-state wave function of 6 He as a αnn three-body system. For this purpose we use Halo effective field theory, which also provides uncertainty estimates for the results. We compare our results at this stage to model calculations done with the computer code face. In a second step we determine the effects of the nn FSI using the nn t-matrix. We compare these FSI results to approximate FSI approaches based on standard FSI enhancement factors. While the final distribution is sensitive to the nn scattering length, it depends only weakly on the effective range. Throughout we emphasize the impact of theoretical uncertainties on the neutron-neutron relative-energy distribution, and discuss the extent to which those uncertainties limit the extraction of the neutron-neutron scattering length from the reaction 6 He(p,pα)nn.

6 ≤ A ≤ 19↗