Results for “Source term” — Page 26

DOE OSTI2025

Quantifying Sources of Voltage Decay in Long-Term Durability Testing for PEM Water Electrolysis

Meeting a competitive 1$/kg hydrogen cost target for polymer electrolyte membrane water electrolysis (PEMWE) will require advances to significantly reduce capital costs and precious metal catalyst usage, while simultaneously enabling 40,000–80,000 h stack lifetimes under dynamic use conditions. Minimizing cell voltage decay rates is therefore a key goal for PEMWE, although the fundamental processes governing voltage decay are not yet well understood. Here we present a quantitative approach to analyze the contributions to voltage decay in long-term PEMWE testing using polarization curves, impedance spectroscopy, and post-mortem electron microscopy. We apply this approach to analyze a 28 μV h −1 decay rate observed in a 4000 h durability test of a cell using 0.5 mg cm −2 total PGM catalyst loading (0.4 mg Ir cm −2 anode, 0.1 mg Pt cm −2 cathode) and 3 A cm −2 current density. We also analyze a comparative series of 1000 h tests under different conditions. These results provide valuable insights into anode catalyst degradation processes, as well as transferrable methodology for PEMWE durability research.

08 HYDROGEN↗

DOE OSTI2021

Readout rebalancing for near-term quantum computers

Readout errors are a significant source of noise for near-term intermediate-scale quantum computers. Mismeasuring a qubit as |1) when it should be |0) occurs much less often than mismeasuring a qubit as |0) when it should have been |1). We make the simple observation that one can improve the readout fidelity of quantum computers by applying targeted X gates prior to performing a measurement. These X gates are placed so that the expected number of qubits in the |1) state is minimized. Classical postprocessing can undo the effect of the X gates so that the expectation value of any observable is unchanged. This protocol is designed to have no effect when readout errors are symmetric. We show that the statistical uncertainty following readout error corrections is smaller when using readout rebalancing. The statistical advantage is circuit and computer dependent and is demonstrated for the W state, a Grover search, and for a Gaussian state. The benefit in statistical precision is most pronounced (and nearly a factor of 2 in some cases) when states with many qubits in the excited state have high probability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Validation of Interconnection and Interoperability of Grid-Forming Inverters Sourced by Hydrogen Technologies in View of 100% Renewable Microgrids

Grid-forming assets are required in microgrids to act as voltage-frequency masters. These grid-forming assets can operate in two modes of operation: grid-following mode and grid-forming mode. In grid-following mode of operation, these assets will follow real power and reactive power setpoints and in grid-forming mode of operation these assets will follow voltage and frequency setpoints. Traditionally, diesel generators or natural gas-based generators are widely used to act as a voltage-frequency master. However, many utilities are aiming to replace generators with grid forming-inverters supplied by solar photovoltaics (PV), batteries or fuel cells. Since grid-forming assets need a long-term reliable energy source, fuel cells are a reasonable and viable choice to supply the grid-forming inverters, but some of the challenges facing the wide deployment of grid-forming fuel cell inverters need to be addressed. Specifically, in our proposed work, we aim to focus on the interconnection and interoperability requirements of grid-forming fuel cell inverters. Currently, state-of-the-art fuel cell inverters follow the general interconnection requirements of distributed energy resources (DERs) and general interoperability requirements of DERs, but these requirements were built with PV and battery systems in mind. Fuel cells have different operational requirements, and therefore these requirements need to be appropriately modified for the grid operators to use. These additional steps add to the investment and operational cost to the grid operators. Through the ARIES platform, this proposed project aims to bridge this gap and use power hardware-in-the-loop (PHIL) and controller hardware-in-the-loop (CHIL) experiments to inform the creation of open-source interconnection and interoperability information that can aid in faster and cheaper installation and operation of grid-forming fuel cell inverters.

grid-forming↗

DOE OSTI2024

Validation of Interconnection and Interoperability of Grid-Forming Inverters Sourced by Hydrogen Technologies in View of 100% Renewable Microgrids

Grid-forming assets are required in microgrids to act as voltage-frequency masters. These grid-forming assets can operate in two modes of operation: grid-following mode and grid-forming mode. In grid-following mode of operation, these assets will follow real power and reactive power setpoints and in grid-forming mode of operation these assets will follow voltage and frequency setpoints. Traditionally, diesel generators or natural gas-based generators are widely used to act as a voltage-frequency master. However, many utilities are aiming to replace generators with grid forming-inverters supplied by solar photovoltaics (PV), batteries or fuel cells. Since grid-forming assets need a long-term reliable energy source, fuel cells are a reasonable and viable choice to supply the grid-forming inverters, but some of the challenges facing the wide deployment of grid-forming fuel cell inverters need to be addressed. Specifically, in our proposed work, we aim to focus on the interconnection and interoperability requirements of grid-forming fuel cell inverters. Currently, state-of-the-art fuel cell inverters follow the general interconnection requirements of distributed energy resources (DERs) and general interoperability requirements of DERs, but these requirements were built with PV and battery systems in mind. Fuel cells have different operational requirements, and therefore these requirements need to be appropriately modified for the grid operators to use. These additional steps add to the investment and operational cost to the grid operators. Through the ARIES platform, this proposed project aims to bridge this gap and use power hardware-in-the-loop (PHIL) and controller hardware-in-the-loop (CHIL) experiments to inform the creation of open-source interconnection and interoperability information that can aid in faster and cheaper installation and operation of grid-forming fuel cell inverters.

controller hardware-in-the-loop↗

DOE OSTI2020

Robustness of energy performance of Zero-Net-Energy (ZNE) homes

Zero-net-energy (ZNE) homes produce an adequate amount of energy on-site to meet their energy demand based on source energy for an entire year. California building energy efficiency standards require new residential buildings started in 2020 to be ZNE. For various reasons, a home designed as ZNE may not achieve ZNE performance in real operation. Here we aimed to quantify the robustness of the energy performance of ZNE homes due to weather variability, climate change, and the uncertainty of occupant behavior. A single-family ZNE house, based on the optimal cost-effective design in three California climate zones, was used to develop the EnergyPlus simulation models. Weather variations were considered from a combination of the historical 30 years’ actual meteorological year (AMY) weather data, typical year weather data in TMY3, and future weather data based on Intergovernmental Panel on Climate Change scenarios. Three scenarios of occupant behavior from the energy perspective were defined to represent the uncertainty about occupants’ activities, comfort requirements, and their adaptive interactions with buildings and systems. In terms of annual source energy, the simulation results of the ZNE homes showed: (1) a decrease of 23–38 percent for occupants with energy austerity behavior and an increase of 120–130 percent for occupants with energy wasteful behavior, compared with the baseline assumption of normal occupants; (2) a variation range of –15 percent to +14 percent for the results using 30-year AMY weather data compared with the baseline results using TMY3 weather data; (3) an increase of 10–13 percent with future weather in Fresno and Riverside and a decrease of 15 percent with San Francisco; and (4) climate change can reduce the gap between the austerity and wasteful consumption. These findings provide insights into how ZNE homes may perform in reality and inform architects, engineers, occupants, and policymakers to pay more attention to occupant behavior on design, operation, and regulations of ZNE homes to ensure energy performance robustness.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

XMM–Newton study of the Sculptor dwarf spheroidal galaxy

ABSTRACT We analysed observations with XMM–Newton in the field of the Sculptor dwarf spheroidal galaxy (dSph). The aim of the study was the classification of X-ray binaries and accreting white dwarfs belonging to the Sculptor dSph. Using different methods of X-ray timing and spectral analyses, together with an extensive multiwavelength study of the optical and infrared counterparts of the X-ray sources, we classified the sources detected with XMM–Newton in the field of the Sculptor dSph. The long-term variability of the sources has been studied over two XMM–Newton observations. None of the members of the Sculptor dSph show significant long-term variability over these two observations. We also searched for periodicity and pulsation using the Lomb–Scargle and Rayleigh Z$^{2}_{n}$ techniques. No signals of pulsation or periodicity have been found for the X-ray sources. The results show the presence of a noticeable number of background X-ray sources in the field of this galaxy. We classified 43 sources as active galactic nuclei, galaxies, and galaxy candidates. Three Galactic foreground stars have been identified in the field of the Sculptor dSph, and one of them is an M-dwarf candidate. Moreover, we classified four symbiotic-star candidates and three quiescent low-mass X-ray binary candidates in the Sculptor dSph. The luminosity of these X-ray sources is ∼1033−35 erg s−1.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

The neutron number probability distribution in coupled lumped assemblies

Here, the validity of the gamma distribution in describing the neutron number probability distribution function for both isolated and coupled multiplying assemblies when constrained to reproduce the true mean and variance is investigated in lumped geometry by numerical comparison with kinetic Monte Carlo simulations. The mean and variance are obtained from numerical solution of moment equations constructed from the relevant forward Master equation with assembly coupling coefficients obtained from a view factor method. Numerical results for a two-group, two coupled assemblies model, with static and dynamic reactivity insertion, show that except for subcritical assemblies, the gamma distribution well-approximates the number distribution. Differences in the fast and thermal neutron population shapes are explained in terms of effective source strengths due to downscatter and coupling.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

On the resolution of dual readout calorimeters

Dual readout calorimeters allow state-of-the-art resolutions for hadronic energy measurements. Their various incarnations are leading candidates for the calorimeter systems for future colliders. In this paper, we present a simple formula for the resolution of a dual readout calorimeter, which we verify with a toy simulation and with full simulation results. This formula can help those new to dual readout calorimetry understand its strengths and limitations. The paper also highlights that the dual readout correction works not just to compensate for binding energy loss, but also for energies escaping the calorimeter or clustering algorithm. Formulae are also presented for approximate resolutions and energy scales in terms of different sources of response.

Calorimeters↗

DOE OSTI2022

Drivers of Phytoplankton Variability in and Near the Pearl River Estuary, South China Sea During Typhoon Hato (2017): A Numerical Study

The Pearl River estuary-coastal system in the Northern South China Sea is frequently affected by tropical cyclones (TCs) every year. Previous in-situ and remote sensing studies have found typhoons can enhance phytoplankton biomass and induce blooms in this region. However, the mechanistic links between phytoplankton blooms and typhoons have not been well elucidated due to the interplay of multiple processes along the land-ocean-atmosphere interfaces. Unravelling these interactions will have to rely on an integrated modelling system. In this work, we constructed a realistic, 3-dimensional, land-ocean-atmosphere modelling system with the marine ecosystem and sediment components for the China Great Bay Area. By using the integrated modelling system, we quantitatively investigated phytoplankton response to hydrological conditions variations under Typhoon Hato (2017), a strong typhoon case. Passive tracer experiments showed that with high river discharge induced by heavy rainfall, the residence time of Lingding Bay is as short as 15-day, less than half of that under the climatological discharge. The increase in freshwater pulse washed out the phytoplankton biomass within Lingding Bay. While for the offshore region, the source and sink terms analysis showed that the increase of phytoplankton biomass in the first week was because of the uplift of nutrient-rich subsurface water, while in the second week was because of the seaward propagated nearshore high phytoplankton biomass water. While riverine nutrients support phytoplankton growth in the third week, a large part of phytoplankton biomass was lost to zooplankton grazing, showing the system shifted from the bottom-up control to the top-down control.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

ToF-SIMS evaluation of PEG-related mass peaks and applications in PEG detection in cosmetic products

Polyethylene glycols (PEGs) are used in industrial, medical, health care, and personal care applications. The cycling and disposal of synthetic polymers like PEGs pose significant environmental concerns. Detecting and monitoring PEGs in the real world calls for immediate attention. This study unveils the efficacy of time-of-flight secondary ion mass spectrometry (ToF-SIMS) as a reliable approach for precise analysis and identification of reference PEGs and PEGs used in cosmetic products. By comparing SIMS spectra, we show remarkable sensitivity in pinpointing distinctive ion peaks inherent to various PEG compounds. Moreover, the employment of principal component analysis effectively discriminates compositions among different samples. Notably, the application of SIMS two-dimensional image analysis visually portrays the spatial distribution of various PEGs as reference materials. The same is observed in authentic cosmetic products. The application of ToF-SIMS underscores its potential in distinguishing PEGs within intricate environmental context. ToF-SIMS provides an effective solution to studying emerging environmental challenges, offering straightforward sample preparation and superior detection of synthetic organics in mass spectral analysis. These features show that SIMS can serve as a promising alternative for evaluation and assessment of PEGs in terms of the source, emission, and transport of anthropogenic organics.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Polarization transmission in the Hadron Storage Ring of the Electron-Ion Collider

The successful operation of the future Electron-Ion Collider is contingent on maintaining high hadron beam polarization up to 275 GeV. The Hadron Storage Ring lattice, however, features a symmetry-breaking interaction region that excites strong, nonsystematic spin resonances, posing a significant threat to polarization preservation. This paper systematically investigates two complementary strategies to ensure high polarization transmission. The first method involves optimizing the vertical betatron phase advance between Siberian snakes to orchestrate a cancellation of depolarizing kicks across the ring. We demonstrate through simulations that both dynamic and fixed-optics solutions based on this principle can successfully preserve polarization through the strongest resonances. The second, more powerful approach involves optimizing the snake rotation axes to suppress resonance driving terms at their source. We revisit established symmetric configurations, such as the Lee-Courant schemes, and introduce a novel, highly symmetric “Doubly Lee-Courant” (DLC) scheme, which enforces a local 𝜋 spin phase advance across every consecutive pair of snakes. Our analysis reveals a clear performance hierarchy, with the DLC configuration providing an exceptionally robust and energy-insensitive baseline for polarization preservation. We conclude that a hybrid strategy, using a DLC snake scheme as a symmetric foundation and betatron phase tuning for fine corrections, offers the most effective path forward for the EIC and future high-energy polarized-beam facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Wasatch Fault Structure from Machine Learning Arrival Times and High-Precision Earthquake Locations

Abstract On 18 March 2020, a magnitude 5.7 earthquake hit the Salt Lake valley in the state of Utah, United States. Using a dense geophone deployment and machine learning (ML), an additional several thousand events were detected and located. Currently, both the mainshock and the majority of the aftershocks are suspected to have occurred on or near a deeper portion of the Salt Lake segment of the Wasatch fault—part of a large range-bounding fault system thought to be capable of generating an Mw 7.2 earthquake. However, a small subset of aftershocks may have occurred on a portion of the more steeply, eastward dipping, and poorly understood West Valley fault. Unfortunately, the catalog locations and lack of focal mechanisms for this subset of aftershocks provide only a crude constraint on the true fault structure. To better illuminate fault structure, we relocate the ML-generated catalog with a range of magnitudes from −2 to 4.6, using: (1) NonLinLoc, a nonlinear location algorithm, (2) source-specific station terms, and (3) waveform coherence. We further compute first-motion focal mechanisms for 68 events. Results of the relocation suggest a simpler, minimally listric Wasatch fault geometry, contrary to what has been previously proposed. We also find that analysis of the focal mechanisms and waveform similarity indicates minimal event similarity throughout the Magna sequence, suggesting a highly complex and heterogeneous rupture zone, as opposed to rupture on a single plane. These findings suggest an increased seismic hazard due to the overall shallowness of the earthquake sequence and highly varied rupture mechanisms.

Geochemistry & Geophysics↗

DOE OSTI2021

The ERL Facility PERLE at Orsay

The realisation of the LHeC and the FCC-eh at CERN require the development of the energy recovering technique in multipass mode and for large currents O(10) mA in the SRF cavities. For this purpose, a technology development facility, PERLE, is under design to be built at IJCLab Orsay, which has the key LHeC ERL parameters, in terms of configuration, source, current, frequency and technical solutions, cryomodule, stacked magnets. In this talk we review the design and comment on the status of PERLE.

Bogacz, Alex↗

DOE OSTI2026

Use of Hardware-in-the-Loop to De-Risk Field Deployment of Hydrogen Assets

Grid-forming assets are required in microgrids to act as voltage-frequency masters. These grid-forming assets can operate in two modes of operation: grid-following mode and grid-forming mode. In grid-following mode of operation, these assets will follow real power and reactive power setpoints and in grid-forming mode of operation these assets will follow voltage and frequency setpoints. Traditionally, diesel generators or natural gas-based generators are widely used to act as a voltage-frequency master. However, many utilities are aiming to replace generators with grid forming-inverters supplied by solar photovoltaics (PV), batteries or fuel cells. Since grid-forming assets need a long-term reliable energy source, fuel cells are a reasonable and viable choice to supply the grid-forming inverters, but some of the challenges facing the wide deployment of grid-forming fuel cell inverters need to be addressed. Specifically, in our proposed work, we aim to focus on the interconnection and interoperability requirements of grid-forming fuel cell inverters. Currently, state-of-the-art fuel cell inverters follow the general interconnection requirements of distributed energy resources (DERs) and general interoperability requirements of DERs, but these requirements were built with PV and battery systems in mind. Fuel cells have different operational requirements, and therefore these requirements need to be appropriately modified for the grid operators to use. These additional steps add to the investment and operational cost to the grid operators. Through the ARIES platform, this proposed project aims to bridge this gap and use power hardware-in-the-loop (PHIL) and controller hardware-in-the-loop (CHIL) experiments to inform the creation of open-source interconnection and interoperability information that can aid in faster and cheaper installation and operation of grid-forming fuel cell inverters.

08 HYDROGEN↗

DOE OSTI2020

EXPRES. I. HD 3651 as an Ideal RV Benchmark

The next generation of exoplanet-hunting spectrographs should deliver up to an order of magnitude improvement in radial velocity (RV) precision over the standard 1 m s{sup −1} state-of-the-art spectrographs. This advance is critical for enabling the detection of Earth-mass planets around Sun-like stars. New calibration techniques such as laser frequency combs and stabilized etalons ensure that the instrumental stability is well characterized. However, additional sources of error include stellar noise, undetected short-period planets, and telluric contamination. To understand and ultimately mitigate error sources, the contributing terms in the error budget must be isolated to the greatest extent possible. Here, we introduce a new high-cadence RV program, the Extreme Precision Spectrograph (EXPRES) 100 Earths Survey, which aims to identify rocky planets around bright, nearby G and K dwarfs. We also present a benchmark case: the 62 day orbit of a Saturn-mass planet orbiting the chromospherically quiet star, HD 3651. The combination of high eccentricity (0.6) and a moderately long orbital period ensures significant dynamical clearing of any inner planets. Our Keplerian model for this planetary orbit has a residual rms of 58 cm s{sup −1} over a ∼6 month time baseline. By eliminating significant contributors to the RV error budget, HD 3651 serves as a standard for evaluating the long-term precision of extreme precision RV programs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Integrated Mid-Continent Stacked Carbon Storage Hub Project Phase II (Final Summary Report)

The Phase II Integrated Midcontinent Stacked Carbon Storage Hub (IMSCS-HUB) is part of the Carbon Storage Assurance Facility Enterprise (CarbonSAFE) established by the United States Department of Energy (DOE) National Energy Technology Laboratory (NETL). CarbonSAFE is phased to support the development of commercial-scale (50 million metric tonnes [Mt] over a 30-year period) carbon capture, utilization, and storage (CCUS) in the United States. The IMSCS-HUB study area comprises carbon dioxide (CO 2 ) sources in Iowa, Kansas, and Nebraska (the source corridor), and CO 2 sinks in Kansas and Nebraska (the storage corridor), representing the first large-scale project for the Midcontinent region. The stacked storage corridor is characterized by alternating sequences of deep saline formations, oil-bearing reservoirs, shale, and evaporite units that are conducive to vertically stacked CO 2 injection for geologic storage and enhanced oil recovery (EOR). Three sites within the IMSCS-HUB stacked storage corridor were evaluated in Phase II for commercial CCUS feasibility: one in southwest-central Nebraska, Sleepy Hollow Field (SHF), a second in southwestern Nebraska near Madrid (Madrid), and a third in southwestern Kansas, the Patterson Site (composed of the Patterson, Heinitz, Hartland, and Oslo fields). In Phase II, the team assessed the feasibility of storage complexes at the potential storage sites in Nebraska and Kansas to support a commercial-scale storage hub that integrates proven CO 2 capture technology and transport from nearby ethanol sources. Building on lessons learned from the DOE-NETL Regional Carbon Sequestration Partnerships (RCSPs), the Project Team has identified a clear strategy to meet DOE’s 2025 objective of commercial carbon capture and storage (CCS) implementation by developing a CO 2 market and infrastructure that relies on multiple ethanol-based CO 2 sources in the short term and the incorporation of multiple coal-fired power plant CO 2 sources when commercial capture is economically viable. The team also leveraged the updated 45Q tax credit to develop capture and transport infrastructure. Commercial-scale CCUS is feasible at two candidate storage sites studied, the Madrid, Nebraska Site and the Patterson Site in Kearny County, Kansas. The Sleepy Hollow Field in Nebraska was found to be an attractive candidate for stacked storage with CO 2 -EOR (Battelle 2020e). Outreach efforts facilitated engagement from industry, government, and research sectors (Battelle and GPI, 2020) and an outreach plan for future phases of the project was developed to address issues that are of concern in the IMSCS-HUB project area (Battelle, 2020f). All components of a CCUS project were determined to be feasible in the IMSCS-HUB region and Risk Mitigation Plan was developed and includes strategies to mitigate risks associated with each project component (Battelle, 2020j). A roadmap was developed to obtain the required UIC permits for an integrated CCUS project (Battelle, 2020k). The regional storage resource characterization demonstrated significant opportunity for commercial-scale projects in the IMSCS-HUB storage corridor with 577.4 Mt of stacked CO 2 storage capacity and the potential to produce 181.9 MMbbls of oil via EOR across 17 individual storage areas (Battelle and ARI, 2020). The pipeline assessment study found viable pipeline routes that connected 45Q-eligible ethanol plants, coal fired power plants, and other sources in the IMSCS-HUB corridor. The comprehensive results of subsurface characterization, modeling efforts, outreach assessment, and regulatory analysis from were integrated to develop a Detailed Commercial Development Plan for the IMSCS-HUB (Battelle, 2020n). Commercialization efforts will involve obtaining Class VI UIC permits, establishing and finalizing the pipeline route, and evaluating capture projects at participating CO 2 sources. Phases I and II of the IMSCS-HUB CarbonSAFE provide a strong foundation for safely, efficiently, and cost-effectively characterizing and permitting commercial-scale project sites in the region. The plan for implementation of commercial-scale CCUS projects in the IMSCS-HUB is aligned with the objectives of CarbonSAFE Phase III: Site Characterization and CO 2 Capture Assessment.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2022

The status and prospects of materials for carbon capture technologies

In order to combat climate change, carbon dioxide (CO 2 ) emissions from industry, transportation, buildings, and other sources need to be captured and long-term stored. Decarbonization of these sources requires special types of materials that have high affinities for CO 2 . Potassium hydroxide is a benchmark aqueous sorbent that reacts with CO 2 to convert it into K 2 CO 3 and subsequently precipitated as CaCO 3 . Another class of carbon capture materials is solid sorbents that are usually functionalized with amines or have natural affinities for CO 2 . The next wave of materials for carbon capture under investigation includes activated carbon, metal–organic frameworks, zeolites, carbon nanotubes, and ionic liquids. In this issue of MRS Bulletin, some of these materials are highlighted, including solvents and sorbents, membranes, ionic liquids, and hydrides. Other materials that can capture CO2 from low concentrations of gas streams, such as air (direct air capture) are also discussed. Also covered in this issue are machine learning-based computer algorithms developed with the goal to speed up the progress of carbon capture materials development, and to design advanced materials with high CO 2 capacity, improved capture and release kinetics, and improved cyclic durability.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Determining the leading-order contact term in neutrinoless double β decay

We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe - e - amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n ( p 1 ) n ( p 2 ) W + ( k ) → $ p\left({p}_1^{\prime}\right)p\left({p}_2^{\prime}\right){W}^{-}(k) $ , in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon ( NN ) scattering in the 1 S 0 channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog I = 2 NN contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the 1 S 0 NN scattering lengths. While our analysis is performed in the $ \overline{\mathrm{MS}} $ scheme, we express our final result in terms of the scheme-independent renormalized amplitude $ {\mathcal{A}}_{\nu}\left(\left|\mathbf{p}\right|,\left|\mathbf{p}^{\prime}\right|\right) $ at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for $ {\mathcal{A}}_{\nu } $ , one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗