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DOE OSTI2026

Hybrid Power Purchase Agreements for Flexible 24/7 Energy Delivery – A Comprehensive Review of Current Practices and Research Pathways

Power Purchase Agreements (PPAs) are becoming increasingly preferred among large energy consumers, such as data centers, to secure cost-effective energy and meet accelerating demand growth. Traditionally, variable renewable energy (VRE)-based PPAs operate on a pay-as-produced basis, balancing supply and demand for a relatively longer duration (e.g., annually). However, the focus is shifting toward matching supply and demand on an hourly basis to fully meet energy needs. This shift requires the integration of flexible energy resources, such as hydropower, thermal generation, and energy storage, to complement VRE sources like wind and solar, forming the foundation for 24/7 PPA. This work contributes by: (i) reviewing emerging market trends and current practices in PPA procurement, supported by data on PPA prices and technology portfolios; (ii) synthesizing the existing literature on modeling approaches for contract pricing, quantities, hybrid resource procurement, and risk management in 24/7 PPA design, while identifying key research gaps; and (iii) proposing an integrated 24/7 PPA design framework along with two contracting mechanisms from the perspectives of both PPA providers and consumers. The proposed framework highlights critical modeling challenges, risk-allocation issues, and future research opportunities for 24/7 PPA design.

24/7↗

NASA NTRS1984

Satellite Emission Range Inferred Earth Survey (SERIES) project

The Global Positioning System (GPS) was developed by the Department of Defense primarily for navigation use by the United States Armed Forces. The system will consist of a constellation of 18 operational Navigation Satellite Timing and Ranging (NAVSTAR) satellites by the late 1980's. During the last four years, the Satellite Emission Range Inferred Earth Surveying (SERIES) team at the Jet Propulsion Laboratory (JPL) has developed a novel receiver which is the heart of the SERIES geodetic system designed to use signals broadcast from the GPS. This receiver does not require knowledge of the exact code sequence being transmitted. In addition, when two SERIES receivers are used differentially to determine a baseline, few cm accuracies can be obtained. The initial engineering test phase has been completed for the SERIES Project. Baseline lengths, ranging from 150 meters to 171 kilometers, have been measured with 0.3 cm to 7 cm accuracies. This technology, which is sponsored by the NASA Geodynamics Program, has been developed at JPL to meet the challenge for high precision, cost-effective geodesy, and to complement the mobile Very Long Baseline Interferometry (VLBI) system for Earth surveying.

Buennagel, L. A.↗

NASA NTRS1999

Constraining the Global, Cloud-Free Reflected Solar Radiation Flux (RSRF) with Earth Observing System (EOS) Instruments

Variations in the top-of-atmosphere reflected solar radiation flux, and in the factors that determine its value, are among the most important diagnostic indicators of changes in Earth's energy balance. Data from the MISR (Multi-angle Imaging SpectroRadiometer), MODIS (Moderate-resolution Imaging Spectroradiometer), SAGE-3 (Stratospheric Aerosol and Gas Experiment), and CERES (Clouds and Earth's Radiant Energy System), all of which are spacecraft instruments scheduled for launch in 1999, will each constrain pieces of the RSRF budget. Prior to launch, we are performing studies to determine the sensitivity of these instruments to key factors that influence the cloud-free RSRF: aerosol optical depth, aerosol scattering properties, and surface visible bidirectional reflectance distribution function (BRDF). We are also assessing the ability of the aggregate of instruments to constrain the overall RSRF budget under natural conditions over the globe. Consider the MISR retrieval of aerosols: according to simulations over cloud-free, calm ocean, for pure particles with natural ranges of optical depth, particle size, and indices of refraction, MISR can retrieve column aerosol optical depth for all but the darkest particles, to an uncertainty of at most 0.05 or 20%, whichever is larger, even if the particle properties are poorly known. For one common particle type, soot, constraints on the optical depth over dark ocean are very poor. The simulated measurements also allow us to distinguish spherical from non-spherical particles, to separate two to four compositional groups based on indices of refraction, and to identify three to four distinct size groups between 0. 1 and 2.0 microns characteristic radius at most latitudes. Based on these results, we expect to distinguish air masses containing different aerosol types, routinely and globally, with multiangle remote sensing data. Such results far exceed current satellite aerosol retrieval capabilities, which provide only total optical depth for assumed particle properties; the new information will complement in situ data, which give details about aerosol size and composition locally. In addition, our team is using climatologies that reflect the constraints each instrument is expected to provide, along with ERBE (Earth Radiation Budget Experiment) data and a radiative transfer code, to study overall sensitivity to RSRF, helping us prepare for similar studies with new data from the EOS-era instruments.

Kahn, Ralph↗

NASA NTRS2006

The NASA Balloon Program: Implementing a New Flight Program for the Future

The U.S. National Aeronautics and Space Administration (NASA) Balloon Program continues to support the scientific community providing enhanced capabilities across a spectrum of balloon related disciplines. Long Duration Ballooning (LDB) continues to be a prominent element of the program with a mission model of a two flight campaign in each the Northern and Southern Hemispheres per year. A new LDB endurance record was achieved in Antarctica with the LDB/CREAM mission. Both polar and mid-latitude LDB capabilities continue to be on-going operational elements of the flight program. The Swedish Space Corporation/Esrange and the National Aeronautics and Space Administration (NASA) inaugurated a joint European/U.S. capability for LDB balloon flights from Sweden to Canada in June 2005. This will complement the NASA/U.S. National Science Foundation Office of Polar Programs achievement of more than a decade of successful long-duration flights around Antarctica. Most of Antarctic flights have flown one time around the South Pole in 8-20 days using conventional (zero differential pressure) balloons. One flight went twice around in 31 days and another went three times around in 42 days using conventional balloons. Balloon technology efforts have continued to broaden in scope and new plans for activities to provide advancements have been initiated. A new balloon volume record was established with the successful flight of a 1,700,000 m3 volume zero-pressure balloon. The capability to fly a 700 kg payload (200 kg science instrument) to 160,000 ft has also been demonstrated. A new super-pressure (constant volume) balloon is currently under development for future flights of 60 - 100 day at any latitude. The Ultra-Long Duration Balloon (ULDB) project for the development of a 100-day duration balloon capability has been progressing with additional ground and flight tests having been conducted. The Program has also continued to introduce new technology and improvements into flight systems, ground systems and operational techniques. An overview of the various aspects of the NASA Balloon Program will be presented as well as the outlook for the future.

Pierce, David L.↗

DOE OSTI2021

InteraChem: Virtual Reality Visualizer for Reactive Interactive Molecular Dynamics

Interactive molecular dynamics in virtual reality (IMD-VR) simulations provide a digital molecular playground for students as an alternative or complement to traditional molecular modeling kits or 2D illustrations. Previous IMD-VR studies have used molecular mechanics to enable simulations of macromolecules such as proteins and nanostructures for the classroom setting with considerable success. Here, we present the InteraChem molecular visualizer, intended for reactive IMD-VR simulation using semiempirical and ab initio methods. InteraChem visualizes not only the molecular geometry but also (1) isosurfaces such as molecular orbitals and electrostatic potentials and (2) two-dimensional graphs of time-varying simulation quantities such as kinetic/potential energy, internal coordinates, and user-applied force. Additionally, InteraChem employs speech recognition to facilitate user interaction and introduces a novel “atom happiness” visualization using emojis to indicate the energetic feasibility of a particular bonding arrangement. Furthermore, we include a set of accompanying exercises that we have used to teach chemical reactivity in small molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1975

Practical application of remote sensing in agriculture

Remote sensing program imagery from several types of platforms, from light aircraft to the LANDSAT (ERTS) satellites, have been utilized during the past few years, with preference for inexpensive imagery over expensive magnetic tapes. Emphasis has been on practical application of remote sensing data to increase crop yield by decreasing plant stress, disease, weeds and undesirable insects and by improving irrigation. Imagery obtained from low altitudes via aircraft provides the necessary resolution and complements but does not replace data from high altitude aircraft, Gemini and Apollo spacecraft, Skylab space station and LANDSAT satellites. Federal government centers are now able to supply imagery within about thirty days from data of order. Nevertheless, if the full potential of space imagery in practical agricultural operations is to be realized, the time span from date of imaging to user application needs to be shortened from the current several months to not more than two weeks.

Phelps, R. A.↗

NASA NTRS1985

A zonal computational procedure adapted to the optimization of two-dimensional thrust augmentor inlets

A viscous-inviscid interaction methodology based on a zonal description of the flowfield is developed as a mean of predicting the performance of two-dimensional thrust augmenting ejectors. An inviscid zone comprising the irrotational flow about the device is patched together with a viscous zone containing the turbulent mixing flow. The inviscid region is computed by a higher order panel method, while an integral method is used for the description of the viscous part. A non-linear, constrained optimization study is undertaken for the design of the inlet region. In this study, the viscous-inviscid analysis is complemented with a boundary layer calculation to account for flow separation from the walls of the inlet region. The thrust-based Reynolds number as well as the free stream velocity are shown to be important parameters in the design of a thrust augmentor inlet.

Lund, T. S.↗

NASA NTRS1998

Design and Use of Microphone Directional Arrays for Aeroacoustic Measurements

An overview of the development of two microphone directional arrays for aeroacoustic testing is presented. These arrays were specifically developed to measure airframe noise in the NASA Langley Quiet Flow Facility. A large aperture directional array using 35 flush-mounted microphones was constructed to obtain high resolution noise localization maps around airframe models. This array possesses a maximum diagonal aperture size of 34 inches. A unique logarithmic spiral layout design was chosen for the targeted frequency range of 2-30 kHz. Complementing the large array is a small aperture directional array, constructed to obtain spectra and directivity information from regions on the model. This array, possessing 33 microphones with a maximum diagonal aperture size of 7.76 inches, is easily moved about the model in elevation and azimuth. Custom microphone shading algorithms have been developed to provide a frequency- and position-invariant sensing area from 10-40 kHz with an overall targeted frequency range for the array of 5-60 kHz. Both arrays are employed in acoustic measurements of a 6 percent of full scale airframe model consisting of a main element NACA 632-215 wing section with a 30 percent chord half-span flap. Representative data obtained from these measurements is presented, along with details of the array calibration and data post-processing procedures.

Humphreys, William M., Jr.↗

NASA NTRS1999

Precise Orbit Determination for the GEOSAT Follow-On Spacecraft

The US Navy's GEOSAT Follow-On spacecraft was launched on February 10, 1998 with its primary mission objective to map the oceans using a radar altimeter. The spacecraft tracking complement consists of GPS receivers, a laser retroreflector and Doppler beacons. Since the GPS receivers have not yet returned reliable data, the only means of providing high-quality precise orbits has been though satellite laser ranging (SLR). SLR has tracked the spacecraft since April 22, 1998, and an average of 7 passes per day have been obtained from US and foreign stations. Since the predicted radial orbit error due to the gravity field is only two to three cm, the largest contributor to the high SLR residuals (10 cm) is the mismodelling of the non-conservative forces. The SLR residuals show a clear correlation with beta prime (solar elevation) angle, peaking in mid-August 1998 when the beta prime angle reached -80 to -90 degrees. We report in this paper on the analysis of the GFO tracking data (SLR, Doppler, and if available GPS) using GEODYN, and on the tuning of the non-conservative force model and the gravity model using these data.

Lemoine, Frank G.↗

DOE OSTI2024

Comparing the interactions between particulate matter and cloud properties over two populated cities in Texas using WRF-Chem fine-resolution modeling

Accurate modeling of aerosol-cloud interactions is essential for reliable weather and air quality simulations, given their significant impact on precipitation patterns, cloud dynamics, and aerosol distributions. This study employed the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) to examine the impact of enhanced meteorological simulations, achieved through advanced microphysics parameterization supported by data assimilation techniques, on air quality across Texas on August 19 and 20, 2022. We tested four distinct configurations: (1) the Morrison two-moment bulk microphysics scheme, (2) Morrison's with observation nudging, (3) the Spectral Bin Microphysics (SBM), and (4) SBM with observation nudging. While the SBM scheme is known for its detailed representation of aerosol-cloud interactions, our focus was on how improvements in meteorological accuracy translate to more precise air quality simulations. Our findings demonstrated a progressive improvement in simulation accuracy, starting with the Morrison's scheme and further enhanced by adopting the SBM scheme, complemented by incorporating observation nudging. Specifically, the combination of the SBM scheme and the nudging substantially enhanced the model's ability to capture convective precipitation events, as shown by better alignment with NEXRAD radar reflectivity, with R increasing from –0.21 to 0.82, IOA from 0.10 to 0.87, and NMB decreasing from 99% to 34% in Houston. The enhanced meteorology translated into more accurate PM 2.5 concentration simulations, particularly through the more accurate representation of aerosol washout during precipitation events. In Houston, the SBM scheme with nudging improved the model's PM 2.5 simulations significantly, with NMB decreasing from –20% to 5% and IOA improving from 0.43 to 0.61. In San Antonio, improvements were also notable, with NMB improved from –27% to –22%, R increased from 0.48 to 0.82, and IOA increased from 0.66 to 0.86. Furthermore, our results underscore the crucial role of accurate meteorological simulations in refining our understanding of aerosol behaviors in relation to precipitation patterns, directly enhancing the reliability and effectiveness of air quality modeling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Coastal-Urban-Rural Atmospheric Gradient Experiment (CoURAGE) Science Plan

Understanding the mechanisms governing the urban atmospheric environment is critical for informing urban populations regarding the impacts of climate change and associated mitigation and adaptation measures. Earth system (climate and weather) models have not yet been adapted to provide accurate predictions of climate and weather variability within cities, nor do they provide well-tested representations of the impacts of urban systems on the atmospheric environment. These limitations are largely due to limited field data available for testing and development of these models. We will deploy the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) user facility’s first Mobile Facility (AMF1) to the mid-Atlantic region surrounding the city of Baltimore for the Coast-Urban-Rural Atmospheric Gradient Experiment (CoURAGE). This deployment will create a four-node regional atmospheric observatory network including Baltimore and its three primary surrounding environments – rural, urban, and bay. CoURAGE investigators will study the interactions among the Earth’s surface, the atmospheric boundary layer, aerosols and atmospheric composition, clouds, radiation, and precipitation at each site, and examine how the spatial gradients across the region interact to create the climate conditions in Baltimore. This study will determine the degree to which Baltimore’s atmospheric environment depends on interactive feedbacks in the atmospheric system and the degree to which conditions in Baltimore depend on the surrounding environment. Some topics of interest include how urban land management exacerbates heat waves, the impact of regional mesoscale winds (nocturnal jet, bay breeze) on urban air pollution and cloud cover, and the impact of the urban heat island and aerosol production on heavy precipitation events. Understanding this integrated coast-urban-rural system quantitatively and with good accuracy and precision is critical to informing climate adaptation and mitigation efforts in the city of Baltimore. The understanding gained should be applicable to many similar coastal, mid-latitude urban centers. Another important objective of CoURAGE is to improve the representation of the climate of coastal cities in Earth systems models (ESMs). CoURAGE investigators will use the observations to test current ESMs, identify weaknesses and work towards improved simulations of this complex environment. The ARM core facility will be deployed in the city of Baltimore, complementing the Baltimore Social-Environmental Collaborative (BSEC), a DOE urban integrated field laboratory (UIFL). Ancillary sites will be deployed to rural Maryland northwest of Baltimore, and to the southern end of Kent Island within Chesapeake Bay. The fourth node will be a long-term atmospheric observatory operated in Beltsville, Maryland by Howard University and the Maryland Department of the Environment. Measurements will be conducted for one year, starting in December of 2024. There will be two intensive operational periods (IOPs), one in summer and one in winter, when the ancillary sites will be enhanced with additional balloon launches, tethered balloon system (TBS) operation, and added atmospheric composition measurements.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1972

STADAN and data relay satellite simulation (emphasis on the scheduler)

A set of computer programs was developed which can be used to simulate the operation of NASA's Satellite Tracking and Data Acquisition Network (STADAN). The simulation consists of two major modules, a computerized algorithmic satellite scheduler (CASS) and a generalized evaluation model simulator (GEMS). CASS generates in-view time intervals of satellites over ground stations, and using these candidate passes, produces a schedule of service times for specific satellites to be serviced by specific ground stations in an attempt to fulfill certain inputted service requirements. GEMS than examines how well STADAN fulfills this schedule in terms of the availability and dependability of different (inputted) complements of equipment at the ground stations. The simulation was modified to allow for the introduction of one or more tracking and data relay satellites, which can serve as orbital receiving and command stations.

Kerne, B.↗

NASA NTRS1992

Virtual environment display for a 3D audio room simulation

The development of a virtual environment simulation system integrating a 3D acoustic audio model with an immersive 3D visual scene is discussed. The system complements the acoustic model and is specified to: allow the listener to freely move about the space, a room of manipulable size, shape, and audio character, while interactively relocating the sound sources; reinforce the listener's feeling of telepresence in the acoustical environment with visual and proprioceptive sensations; enhance the audio with the graphic and interactive components, rather than overwhelm or reduce it; and serve as a research testbed and technology transfer demonstration. The hardware/software design of two demonstration systems, one installed and one portable, are discussed through the development of four iterative configurations.

Chapin, William L.↗

NASA NTRS2019

Using Science Operations Tools and Methods from NASA for Remote Presence Ocean Exploration on Earth: E/V Nautilus Cruise NA108

NASA Ames' Exploration Ground Data Systems (xGDS) supports rapid scientific decision making by synchronizing information in time and space, including video and still images, scientific instrument data, and science and operations notes in geographic and temporal context. We have deployed xGDS at multiple NASA field analog missions over the past decade.In the last two years, we have participated in SUBSEA, a multi-institution collaborative project. SUBSEA used the research ship E/V Nautilus along with its two remotely operated vehicles (ROVs), Hercules and Argus, to explore deep ocean volcanic vents as an analog for ocean worlds (e.g. Enceladus). This work allowed us to compare the existing oceanographic operations methods and technologies used for ocean exploration with corresponding tools and approaches developed and used at NASA. In the first year of SUBSEA we observed existing remote science operations from the Inner Space Center (ISC). In the second year, we deployed xGDS at ISC to complement existing capabilities with xGDS tools designed to support remote Nautilus science operations from the ISC. During operations, video, ROV position and instrument telemetry were streamed from the ship to the ISC. As the science team watched dive operations, they could annotate the data with observations that were relevant to their work domain. Later, the team members could review the data at their own pace to collaboratively develop a dive plan for the next day, which had to be delivered on a fixed daily schedule.The opportunity to compare operations under different conditions enabled us to make several key observations about conducting remote science and planning operations efficiently: (i) Reviewing data collaboratively and interactively with temporal and spatial context was critical for the remote science team's ability to plan dive operations on the Nautilus. (ii) Science team members were actively engaged with the remote dive operations because they could interact with the collected data and visualize it as they desired. (iii) Being able to replay past events at accelerated speeds, and jump to points in time and spaced based on search results, provided efficient access to critical points of interest in a massive volume of data, so the remote science team could deliver plans on time. SUBSEA (Systematic Underwater Biogeochemical Science and Exploration Analog) is a multi-institution collaboration supported by NASA, NOAA's Office of Exploration Research (OER), the Ocean Exploration Trust (OET) and the University of Rhode Island's Graduate School of Oceanography (GSO). ISC is GSO's telepresence operations facility.

Lees, David S.↗

NASA NTRS2020

Conducting Efficient Remote Science and Planning Operations for Ocean Exploration Using Exploration Ground Data Systems (xGDS)

NASA Ames’ Exploration Ground Data Systems (xGDS) supports rapid scientific decision making by synchronizing information in time and space, including video and still images, scientific instrument data, and science and operations notes in geographic and temporal context. We have deployed xGDS at multiple NASA field analog missions over the past decade. In the last two years, we have participated in SUBSEA, a multi-institution collaborative project*. SUBSEA used the research ship E/V Nautilus along with its two remotely operated vehicles (ROVs), Hercules and Argus, to explore deep ocean volcanic vents as an analog for ocean worlds (e.g. Enceladus). This work allowed us to compare the existing oceanographic operations methods and technologies used for ocean exploration with corresponding tools and approaches developed and used at NASA. In the first year of SUBSEA we observed existing remote science operations from the Inner Space Center (ISC)**. In the second year, we deployed xGDS at ISC to complement existing capabilities with xGDS tools designed to support remote Nautilus science operations from the ISC. During operations, video, ROV position and instrument telemetry were streamed from the ship to the ISC. As the science team watched dive operations, they could annotate the data with observations that were relevant to their work domain. Later, the team members could review the data at their own pace to collaboratively develop a dive plan for the next day, which had to be delivered on a fixed daily schedule. The opportunity to compare operations under different conditions enabled us to make several key observations about conducting remote science and planning operations efficiently: (i) Reviewing data collaboratively and interactively with temporal and spatial context was critical for the remote science team’s ability to plan dive operations on the Nautilus. (ii) Science team members were actively engaged with the remote dive operations because they could interact with the collected data and visualize it as they desired. (iii) Being able to replay past events at accelerated speeds, and jump to points in time and spaced based on search results, provided efficient access to critical points of interest in a massive volume of data, so the remote science team could deliver plans on time. * SUBSEA (Systematic Underwater Biogeochemical Science and Exploration Analog) is a multi-institution collaboration supported by NASA, NOAA’s Office of Exploration Research (OER), the Ocean Exploration Trust (OET) and the University of Rhode Island’s Graduate School of Oceanography (GSO).

Cohen, Tamar E.↗

DOE OSTI2024

Reduced-order condensed-phase kinetic models for polyethylene, polypropylene and polystyrene thermochemical recycling

Thermochemical recycling of plastic waste (PW) into chemicals and energy vectors requires coupling particle and reactor-scale simulations to accurate condensed phase pyrolysis mechanisms for each constituent. This work proposes a methodology to derive reduced-order condensed-phase kinetic models from validated semi-detailed kinetic mechanisms. Two types of kinetic models are obtained for polyethylene (PE), polypropylene (PP) and polystyrene (PS): reduced semi-detailed models and multi-step fully lumped ones. These families offer different compromises between accuracy and computational cost. The former employ 50–100 gas + liquid species and describe both the radical degradation and the detailed carbon distribution of the products. Conversely, the latter involves 5–10 species per polymer tracking only the main petroleum cuts. The kinetic mechanisms are complemented by the definition of thermochemical properties of gas, liquid, and solid-phase species, accounting for phase-transitions through pseudo-chemical reactions. Model validations are performed by comparison with experimental data and the original semi-detailed mechanisms in terms of mass loss, heat fluxes and product distribution profiles. The resulting CHEMKIN-like condensed-phase models are attached as Supplementary Material and as a GitHub repository. Extending the proposed approach to other polymers and coupling it with existing subsets in the CRECK kinetic framework (e.g., biomass, PVC, PET) offers a powerful tool to model thermochemical recycling of PW and biomass/PW mixtures.

kinetics↗

DOE OSTI2020

Electron- and light-induced stimulated Raman spectroscopy for nanoscale molecular mapping

We propose and theoretically analyze a new vibrational spectroscopy, termed electron- and light-induced stimulated Raman (ELISR) scattering, that combines the high spatial resolution of elec-tron microscopy with the molecular sensitivity of surface-enhanced Raman spectroscopy. WithELISR, electron-beam excitation of plasmonic nanoparticles is utilized as a spectrally-broadband butspatially-confined Stokes beam in the presence of a diffraction-limited pump laser. To characterizethis technique, we develop a numerical model and conduct full-field electromagnetic simulations toinvestigate two distinct nanoparticle geometries, nanorods and nanospheres, coated with a Raman-active material. Our results show the significant (10 6 -10 7 ) stimulated Raman enhancement that isachieved with dual electron and optical excitation of thesenanoparticle geometries. Importantly,the spatial resolution of this vibrational spectroscopy for electron microscopy is solely determinedby the nanoparticle geometry and the plasmon mode volume. Our results highlight the promiseof ELISR for simultaneous high-resolution electron microscopy with sub-diffraction-limited Ramanspectroscopy, complementing advances in superresolutionmicroscopy, correlated light and electronmicroscopy, and vibrational electron energy loss spectroscopy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Nuclear-level effective theory of 𝜇→𝑒 conversion: Formalism and applications

Over the next decade new 𝜇→𝑒 conversion searches at Fermilab (Mu2e) and J-PARC (COMET, DeeMe) are expected to advance limits on charged lepton flavor violation (CLFV) by more than four orders of magnitude. Here, by considering the consequence of 𝑃 and 𝐶⁢𝑃 on elastic 𝜇→𝑒 conversion and the structure of possible charge and current densities, we show that rates are governed by six nuclear responses and a single scale, 𝑞/𝑚 𝑁 , where 𝑞 ≈ 𝑚 𝜇 is the momentum transferred from the leptons to the nucleus. To relate this result to microscopic formulations of CLFV, we construct in nonrelativistic effective theory (NRET) the CLFV nucleon-level interaction, pointing out the relevance of the dimensionless scales 𝑦=($^{𝑞⁢𝑏}_2$) 2 ⁢ > |$\overrightarrow{𝑣}_N$⁢|>|$\overrightarrow{𝑣}_μ$⁢|>|$\overrightarrow{𝑣}_T$| , where 𝑏 is the nuclear size, $\overrightarrow{𝑣}_N$ and $\overrightarrow{𝑣}_μ$ are the nucleon and muon intrinsic velocities, and $\overrightarrow{𝑣}_T$ is the target recoil velocity. We discuss previous work, noting the lack of a systematic treatment of the various small parameters. Because the parameter 𝑦 is not small, a proper calculation of 𝜇→𝑒 conversion requires a full multipole expansion of the nuclear response functions, an apparently daunting task with Coulomb-distorted electron partial waves. We demonstrate that the multipole expansion can be carried out to high precision by introducing a simplifying local momentum 𝑞 eff for the electron. Previous work has been limited to simple charge or spin interactions, thereby treating the nucleus effectively as a point particle. We show that such formulations are not compatible with the general form of the 𝜇→𝑒 conversion rate, failing to generate three of the six allowed nuclear response functions. The inclusion of the nucleon velocity $\overrightarrow{𝑣}_N$ yields an NRET with 16 operators and a rate of the general form. Consequently, in the current discovery era for CLFV, it provides the most sensible starting point for experimental analysis, defining what can and cannot be determined about CLFV from the highly exclusive process of 𝜇→𝑒 conversion. Finally, we expand the NRET operator basis to account for the effects of $\overrightarrow{𝑣}_μ$, associated with the muon's lower component, generating corrections to the CLFV coefficients of the point-nucleus response functions. Using advanced shell-model methods, we compute 𝜇→𝑒 conversion rates for a series of experimental targets, deriving bounds on the coefficients of the CLFV operators. These calculations are the first to include a general basis of CLFV operators, full evaluation of the associated nuclear response functions, and an accurate treatment of electron and muon Coulomb effects. We discuss target selection as an experimental “knob” that can be turned to probe the microscopic origins of CLFV. We describe two types of coherence that enhance certain CLFV operators and selection rules that blind elastic 𝜇→𝑒 conversion to others. We discuss the matching of the NRET onto higher level effective field theories, such as those constructed at the light quark level, noting opportunities to build on existing work in direct detection of dark matter. We discuss the relation of 𝜇→𝑒 conversion to 𝜇→𝑒+𝛾 and 𝜇→3⁢𝑒, showing how MEG II and Mu3e results will complement those of Mu2e and COMET. Finally we describe a accompanying script—in Mathematica and Python versions—that can be used to compute 𝜇→𝑒 conversion rates in various nuclear targets for the full set of NRET operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗