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At least 109 records · Page 6

Experimental determination of the temperature-dependent Van Hove function in a Zr 80 Pt 20 liquid

Even though the viscosity is one of the most fundamental properties of liquids, the connection with the atomic structure of the liquid has proven elusive. By combining inelastic neutron scattering with the electrostatic levitation technique, the time-dependent pair-distribution function (i.e., the Van Hove function) has been determined for liquid Zr 80 Pt 20 . We show that the decay time of the first peak of the Van Hove function is directly related to the Maxwell relaxation time of the liquid, which is proportional to the shear viscosity. This result demonstrates that the local dynamics for increasing or decreasing the coordination number of local clusters by one determines the viscosity at high temperature, supporting earlier predictions from molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The High Energy X-ray Probe (HEX-P): supernova remnants, pulsar wind nebulae, and nuclear astrophysics

HEX-P is a probe-class mission concept that will combine high spatial resolution X-ray imaging (< 10" full width at half maximum) and broad spectral coverage (0.2–80 keV) with an effective area far superior to current facilities (including XMM-Newton and NuSTAR) to enable revolutionary new insights into a variety of important astrophysical problems. HEX-P is ideally suited to address important problems in the physics and astrophysics of supernova remnants (SNRs) and pulsar wind nebulae (PWNe). For shell SNRs, HEX-P can greatly improve our understanding via more accurate spectral characterization and localization of non-thermal X-ray emission from both non-thermal-dominated SNRs and those containing both thermal and non-thermal components, and can discover previously unknown non-thermal components in SNRs. Multi-epoch HEX-P observations of several young SNRs (e.g., Cas A and Tycho) are expected to detect year-scale variabilities of X-ray filaments and knots, thus enabling us to determine fundamental parameters related to diffusive shock acceleration, such as local magnetic field strengths and maximum electron energies. For PWNe, HEX-P will provide spatially-resolved, broadband X-ray spectral data separately from their pulsar emission, allowing us to study how particle acceleration, cooling, and propagation operate in different evolution stages of PWNe. HEX-P is also poised to make unique and significant contributions to nuclear astrophysics of Galactic radioactive sources by improving detections of, or limits on, 44Ti in the youngest SNRs and by potentially discovering rare nuclear lines as evidence of double neutron star mergers. Throughout the paper, we present simulations of each class of objects, demonstrating the power of both the imaging and spectral capabilities of HEX-P to advance our knowledge of SNRs, PWNe, and nuclear astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗

Density determination of the thermonuclear fuel region in inertial confinement fusion implosions

Understanding of the thermonuclear burn in an inertial confinement fusion implosion requires knowledge of the local deuterium–tritium (DT) fuel density. Neutron imaging of the core now provides this previously unavailable information. Two types of neutron images are required. The first is an image of the primary 14-MeV neutrons produced by the D +T fusion reaction. The second is an image of the 14-MeV neutrons that leave the implosion hot spot and are downscattered to lower energy by elastic and inelastic collisions in the fuel. These neutrons are measured by gating the detector to record the 6–12 MeV neutrons. Using the reconstructed primary image as a nonuniform source, a set of linear equations is derived that describes the contribution of each voxel of the DT fuel region to a pixel in the downscattered image. Using the measured intensity of the 14-MeV neutrons and downscattered images, the set of equations is solved for the density distribution in the fuel region. The method is validated against test problems and simulations of high-yield implosions. The calculated DT density distribution from one experiment is presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Heterogeneous fatigue damage in a nickel-based single-crystal superalloy unraveled using correlative 3D X-ray technology

Nickel-based single-crystal (Ni-SX) superalloys under cyclic stress are susceptible to cracking at stress-concentration sites, eventually leading to low-cycle fatigue (LCF) failure. LCF cracks typically originate from intrinsic defects (e.g., voids and carbides) within solidified dendrites. However, systematic quantitative experimental analyses of defect-mediated local damage remain limited. To thoroughly understand the microscopic origins and evolution of LCF damage, correlated 3D mapping of dendrites across various regions is essential. Here, in this study, macroscale micro-computed tomography (μ-CT) was initially used to capture internal interdendritic secondary cracks within bulk DD413 superalloy after LCF testing at 760 °C. Subsequently, a multimodal methodology combining synchrotron 3D microdiffraction (3D-μXRD), high-resolution μ-CT, and electron microscopy was established. This approach allowed precise localization of internal damage zones near interdendritic secondary cracks and detailed mapping of the 3D correlated distributions of dendrites, defects, and residual stress/strain fields within these zones at submicron spatial resolution. Finally, the same approach was applied to specimens subjected to interrupted loading at approximately 40 % of the fatigue life to uncover the early damage states of dendrites. The dendrite cores (DCs) and interdendritic regions (IDs) exhibit microscale heterogeneous mechanical responses: nearly defect-free DCs accumulate local irreversible slip along specific slip systems to generate slip bands, while the IDs containing various defects accommodate local microplasticity through the activation of multiple slip systems around these defects. The local tensile stress near defects in the IDs exceeds that in the DC slip band regions by more than threefold, leading to the generation of local damage zones within the IDs. Chain-like defect distributions facilitate the interconnection of these local zones into a continuous damage region, further elevating the overall tensile stress in the IDs. Additionally, geometrically necessary dislocations alone are insufficient as indicators of LCF damage; both the internal stress state and its magnitude must be considered. These experimental results provide critical data and insights for the development of multi-physics fatigue models.

Localized deformation↗

Atmospheric Ionizing Radiation and Human Exposure

Atmospheric ionizing radiation is of interest, apart from its main concern of aircraft exposures, because it is a principal source of human exposure to radiations with high linear energy transfer (LET). The ionizing radiations of the lower atmosphere near the Earth s surface tend to be dominated by the terrestrial radioisotopes especially along the coastal plain and interior low lands and have only minor contributions from neutrons (11 percent). The world average is substantially larger but the high altitude cities especially have substantial contributions from neutrons (25 to 45 percent). Understanding the world distribution of neutron exposures requires an improved understanding of the latitudinal, longitudinal, altitude and spectral distribution that depends on local terrain and time. These issues are being investigated in a combined experimental and theoretical program. This paper will give an overview of human exposures and describe the development of improved environmental models.

Wilson, J. W.↗

Atmospheric Ionizing Radiation and Human Exposure

Atmospheric ionizing radiation is of interest, apart from its main concern of aircraft exposures, because it is a principal source of human exposure to radiations with high linear energy transfer (LET). The ionizing radiations of the lower atmosphere near the Earth s surface tend to be dominated by the terrestrial radioisotopes. especially along the coastal plain and interior low lands, and have only minor contributions from neutrons (11 percent). The world average is substantially larger but the high altitude cities especially have substantial contributions from neutrons (25 to 45 percent). Understanding the world distribution of neutron exposures requires an improved understanding of the latitudinal, longitudinal, altitude and spectral distribution that depends on local terrain and time. These issues are being investigated in a combined experimental and theoretical program. This paper will give an overview of human exposures and describe the development of improved environmental models.

Wilson, John W.↗

Cosmic diffuse gamma rays from 2 to 25 MeV

Results are reported for measurements of cosmic diffuse gamma rays performed with a double Compton scatter gamma-ray telescope flows aboard a balloon at 3.5-g/sq cm residual atmosphere. The operation and calibration of the telescope are briefly reviewed, unwanted backgrounds are identified, and the only significant background for the telescope used is shown to arise from the interaction of albedo neutrons with hydrogen and carbon in one of the liquid scintillators. The fluxes of cosmic diffuse gamma rays with energies of 2 to 3, 3 to 5, 5 to 7, 7.5 to 10 MeV are listed, and upper limits are provided for energies of 10 to 15 and 15 to 25 MeV. These data are compared with numerous previous measurements, and no indication is found that the diffuse radiation is statistically different from isotropic. Upper limits are placed on the gamma-ray fluxes (mainly 3 to 25 MeV) from various localized sources.

White, R. S.↗

Processing and Archiving Camera Data Effectively for Operando Neutron Measurement of Metal Additive Manufacturing

As the name suggests, The Operando Neutron Measurement of Metal Additive Manufacturing project conducted by ORNL’s Manufacturing Demonstration Facility (MDF) is experimenting with advanced additive metal manufacturing techniques while analyzing the process using the Spallation Neutron Source’s (SNS) beamline. As part of this experiment, the MDF is seeking to employ 2 XIMEA visible light cameras and a single infrared camera to analyze and correct manufacturing in real-time. The MDF requires a solution for capturing the high-resolution data feed from the cameras with compression while preserving enough detail for their software to detect and correct errors in real time. Our solution was to develop a Robot Operating System (ROS) driver to feed the camera data into ROS. From ROS, the feed is compressed and temporarily stored locally to a stripped 4 NVMe SSD RAID array. Post-experiment, the data is transitioned to long-term storage for archival purposes.

36 MATERIALS SCIENCE↗

Constraints on the Electromagnetic Counterpart of the Neutron-star–Black-hole Merger GW200115

We report the results of our follow-up campaign for the neutron-star—black-hole (NSBH) merger GW200115 detected during the O3 run of the Advanced LIGO and Advanced Virgo detectors. We obtained wide-field observations with the Deca-Degree Optical Transient Imager covering ~20% of the total probability area down to a limiting magnitude of w = 20.5 AB at ~23 hr after the merger. Our search for counterparts returns a single candidate (AT2020aeo), likely not associated with the merger. In total, only 25 sources of interest were identified by the community and later discarded as unrelated to the GW event. We compare our upper limits with the emission predicted by state-of-the-art kilonova simulations and disfavor high-mass ejecta (>0.1 M⊙), indicating that the spin of the system is not particularly high. By combining our optical limits with gamma-ray constraints from Swift and Fermi, we disfavor the presence of a standard short-duration burst for viewing angles ≲15° from the jet axis. Our conclusions are, however, limited by the large localization region of this GW event, and accurate prompt positions remain crucial to improving the efficiency of follow-up efforts.

79 ASTRONOMY AND ASTROPHYSICS↗

U.S. Department of Energy: National Virtual Biotechnology Laboratory (Technical Report)

With funding from the CARES Act, the U.S Department of Energy (DOE) established the National Virtual Biotechnology Laboratory (NVBL) in March 2020 to address key challenges associated with the COVID-19 crisis. The NVBL brought together the broad scientific and technical expertise and resources of DOE’s 17 national laboratories to help tackle medical supply shortages, discover potential drugs to fight the virus, develop and validate COVID-19 testing methods, model disease spread and impact across the nation, and understand virus transport in buildings and the environment. National laboratory resources leveraged for this effort include a suite of world-leading user facilities broadly available to the research community, such as light and neutron sources, nanoscale science research centers, sequencing and biocharacterization facilities, and high-performance computing facilities. As part of the NVBL framework, DOE rapidly assembled five project teams to (1) identify new targets for medical therapeutics; (2) develop innovations in testing capabilities; (3) provide epidemiological and logistical support; (4) understand viral fate and transport in the environment; and (5) address supply chain bottlenecks by harnessing extensive additive manufacturing capabilities. Each research team was charged with defining high-impact projects that could be completed in a 6-month sprint while coordinating their developments with academia, other government agencies, and the private sector. Within months, NVBL teams used DOE’s high-performance computers and light and neutron sources to identify promising candidates for antibodies and antivirals that universities and drug companies are now evaluating. NVBL researchers also developed new diagnostic targets and sample collection approaches, and supported efforts by the U.S. Food and Drug Administration, Centers for Disease Control and Prevention, and U.S. Department of Defense to establish national guidelines used in administering millions of tests. Researchers used artificial intelligence and high-performance computing to produce near-real-time data analysis to forecast disease transmission, stress on public health infrastructure, and economic impact, which supported decision-makers at the local, state, and national levels. To minimize virus uptake and protect human health, NVBL teams studied how to control indoor virus movement. Researchers also produced innovations in materials and advanced manufacturing that mitigated shortages in test kits and personal protective equipment, creating nearly 1,000 new jobs. Through its NVBL framework, DOE has contributed significantly to the nation’s COVID response, demonstrating in only a few months the critical impact of its national laboratories. NVBL’s accomplishments demonstrate not only the powerful resource represented by DOE’s national laboratories working together to meet national needs, but also the effectiveness of the integrated NVBL framework for rapidly responding to emergencies with research and development solutions. Going forward, the NVBL is poised to apply the unique capabilities and expertise of the national laboratory complex to future national and international emergencies, both natural and engineered. Through this framework, DOE will continue to be an integral component of agency-wide efforts to prepare for and respond to biorisks and other crises. This technical report describes the goals, progress, and results of NVBL’s five project teams—Molecular Design for COVID-19 Therapeutics, COVID-19 Testing, Epidemiological Modeling, Viral Fate and Transport, and Materials and Manufacturing of Critical Supplies—and lists each team’s publications and research output.

42 ENGINEERING↗

Proposal from the NA61/SHINE Collaboration for update of European Strategy for Particle Physics

Building on the current program's success and driven by new physics challenges, the NA61/SHINE Collaboration proposes to continue measuring hadron production properties in reactions induced by hadron and ion beams after CERN Long Shutdown 3. These measurements are of significant interest to the heavy-ion, cosmic-ray, and neutrino physics communities and will focus on: - Investigating hadron production in the light-ion systems to explore the diagram of high-energy nuclear collisions, and to obtain new insight into the unexpected violation of isospin (flavor) symmetry recently observed by the experiment; - Measuring charm-anticharm correlations to gain unique insights into the production locality of charm and anticharm quark pairs; - Examining strangeness and multi-strangeness production to improve our understanding of the early Universe's evolution and neutron star formation; - Measuring cross sections relevant for cosmic-ray measurements, significantly boosting searches for new physics in our Galaxy; - Conducting hadron production measurements with proton, pion, and kaon beams for neutrino physics, enhancing the precision of hadron production data needed for initial neutrino flux predictions in neutrino oscillation experiments; - Measuring hadron production processes relevant for understanding the flux of atmospheric neutrinos, as well as neutrinos and muons from spallation sources. To achieve these objectives, a detector upgrade and a beam upgrade are required, with data-taking planned for the period 2029-2032 and beyond.

Adhikary, H. [Jan Kochanowski U.] (ORCID:000000025↗

Unexpected Hydride: Ce 4 B 2 C 2 H 2.42 , a Stuffed Variant of the Nd 2 BC Structure Type

Ce 4 B 2 C 2 H 2.42 was grown as large crystals from a cerium/copper eutectic flux. The structure was characterized by single-crystal X-ray and neutron diffraction and was found to be a stuffed variant of Nd 2 BC with the addition of two interstitial hydrogen positions. The tetrahedral hydrogen position is fully occupied, while the octahedral position has an occupancy of 42(3)%. Initial synthesis was due to hydrogen contamination of the cerium metal but has been successfully repeated using anthracene as a carbon and hydrogen source. Density of states calculations suggest that the incorporation of hydrogen stabilizes the compound with respect to the nonhydrided model. Magnetic susceptibility data show a complex magnetic ordering at 7.7 K that originates from the localized electron on the Ce 3+ in the structure. The trivalent state is also supported by X-ray photoelectron spectroscopy measurements. Heat capacity and electrical resistivity data show that the phase transition is broad in temperature, which may be due to structural disorder. Furthermore, the large low temperature value of C/T also indicates possible heavy fermion behavior.

36 MATERIALS SCIENCE↗

National Virtual Biotechnology Laboratory: Report on Rapid R&D Solutions to the COVID-19 Crisis

With funding from the CARES Act, the U.S Department of Energy (DOE) established the National Virtual Biotechnology Laboratory (NVBL) in March 2020 to address key challenges associated with the COVID-19 crisis. NVBL brought together the broad scientific and technical expertise and resources of DOE’s 17 national laboratories to help tackle medical supply short ages, discover potential drugs to fight the virus, develop and validate COVID-19 testing methods, model disease spread and impact across the nation, and understand virus transport in buildings and the environment. National laboratory resources leveraged for this effort include a suite of world-leading user facilities broadly available to the research community, such as light and neutron sources, nanoscale science research centers, sequencing and biocharacterization facilities, and high-performance computing facilities. Within months, NVBL teams produced innovations in materials and advanced manufacturing that mitigated shortages in test kits and personal protective equipment (PPE), creating nearly 1,000 new jobs. They used DOE’s high-performance computers and light and neutron sources to identify promising candidates for antibodies and antivirals that universities and drug companies are now evaluating. NVBL researchers also developed new diagnostic targets and sample collection approaches, and supported U.S. Food and Drug Administration (FDA), Centers for Disease Control and Prevention (CDC), and U.S. Department of Defense (DoD) efforts to establish national guidelines used in administering millions of tests. Researchers used artificial intelligence and high-performance computing to produce near-real-time data analysis to forecast disease transmission, stress on public health infrastructure, and economic impact, which supported decision-makers at the local, state, and national levels. NVBL teams also studied how to control indoor virus movement to minimize uptake and protect human health. NVBL’s accomplishments demonstrate not only the powerful resource represented by DOE’s national laboratories working together to meet national needs, but also the effectiveness of the integrated NVBL framework for rapidly responding to emergencies with research and development (R&D) solutions. As the fight against COVID continues, sustained efforts are needed to confront this pandemic as well as future threats. Examples include: 1) Establishing “supply chains on demand” to meet emergency production needs by leveraging the materials and manufacturing expertise of DOE national laboratories and developing advances in electronics, sensing, robotics, and automation capabilities; 2) Improving the speed and robustness of drug discovery by integrating experimental platforms with DOE’s computational and experimental user facilities, which provide unique resources to support the discovery of high-potential therapeutic agents; 3) Protecting public, environmental, and animal health by developing new testing protocols and instrumentation adaptable to diverse sample types (both physiological and environmental) to quickly detect a wide range of pathogens and monitor other biorisks; 4) Supporting near-real-time data needs of decision-makers at the local, regional, state, and national levels by advancing data curation, analysis, and modeling using artificial intelligence and new data science tools for managing and evaluating large diverse datasets; 5) Harnessing DOE’s expertise in environmental modeling to design rooms and air handling for offices, classrooms, restaurants, and other structures to minimize biorisk transmissions. Going forward, NVBL is poised to apply the unique capabilities and expertise of the national laboratory complex to future national and international emergencies, both natural and engineered. Through this framework, the Office of Science will continue to be an integral component of agency wide efforts to prepare for and respond to biorisks and other crises.

42 ENGINEERING↗

NICER Discovers the Ultracompact Orbit of the Accreting Millisecond Pulsar IGR J17062-6143

We present results of recent Neutron Star Interior Composition Explorer (NICER) observations of the accreting millisecond X-ray pulsar (AMXP) IGR J17062-6143 that show that it resides in a circular, ultracompact binary with a 38-minute orbital period. NICER observed the source for 26 kiloseconds over a 5.3-day span in 2017 August, and again for 14 and 11 kiloseconds in 2017 October and November, respectively. A power spectral analysis of the August exposure confirms the previous detection of pulsations at 163.656 Hertz in Rossi X-ray Timing Explorer (RXTE) data, and reveals phase modulation due to orbital motion of the neutron star. A coherent search for the orbital solution using the Z squared method finds a best-fitting circular orbit with a period of 2278.21 seconds (37.97 minutes), a projected semimajor axis of 0.00390 lt-s (Localization Test Statistic), and a barycentric pulsar frequency of 163.6561105 Hertz. This is currently the shortest known orbital period for an AMXP. The mass function is 9.12 times 10 (sup minus 8) solar mass, presently the smallest known for a stellar binary. The minimum donor mass ranges from approximately 0.005 to 0.007 times the solar mass for a neutron star mass from 1.2 to 2 times the solar mass. Assuming mass transfer is driven by gravitational radiation, we find donor mass and binary inclination bounds of 0.0175-0.0155 times the solar mass and 19 degrees less than i less than 27.5 degrees, where the lower and upper bounds correspond to 1.4 and 2 times the solar mass neutron stars, respectively. Folding the data accounting for the orbital modulation reveals a sinusoidal profile with fractional amplitude 2.04 plus or minus 0.11 percent (0.3-3.2 kiloelectronvolts).

Strohmayer, T. E.↗

VERDI: VERsatile DIffractometer with wide-angle polarization analysis for magnetic structure studies in powders and single crystals

The VERsatile DIffractometer will set a new standard for a world-class magnetic diffractometer with versatility for both powder and single crystal samples and capability for wide-angle polarization analysis. The instrument will utilize a large single-frame bandwidth and will offer high-resolution at low momentum transfers and excellent signal-to-noise ratio. A horizontal elliptical mirror concept with interchangeable guide pieces will provide high flexibility in beam divergence to allow for a high-resolution powder mode, a high-intensity single crystal mode, and a polarized beam option. A major science focus will be quantum materials that exhibit emergent properties arising from collective effects in condensed matter. The unique use of polarized neutrons to isolate the magnetic signature will provide optimal experimental input to state-of-the-art modeling approaches to access detailed insight into local magnetic ordering.

36 MATERIALS SCIENCE↗

Propagation of nuclear burning fronts on accreting neutron stars: X-ray bursts and sub-hertz noise

We identify a new regime of time dependent helium burning for high accretion rate neutron stars and suggest that this burning is the origin of the low-level luminosity variations (on timescales of 10-10(exp 4) s, designated the 'very low-frequency noise'(VLFN) by van der Klis and collaborators) always detected in the brightest accreting X-ray sources. Only two nuclear burning regimes were previously recognized. At accretion rates in excess of the Eddington limit (dot-M approximately greater than (1-3) x 10(exp -8) solar mass/yr), the accreted matter fuses steadily. At very low dot-M, the star's entire surface is rapidly (approximately less than 10 s) burned by a fast propagating convective burning front at regular intervals, giving quasi-periodic Type I X-ray bursts. We show that for the observationally interesting range of 5 x 10(exp -10) solar mass/yr approximately less than dot-M approximately less than 10(exp -8) solar mass/yr, parts of the stellar surface burn slowly. At these accretion rates, a local thermonuclear instability starts a fire which propagates horizontally at v approximately 300 cm/s. The fire propagates around the flammable surface in roughly the same time it takes to accrete enough fuel for the next instability (approximately 10(exp 3)-10(exp 4), so that only a few fires are burning at once, giving rise to large luminosity flares. Nuclear burning is always time dependent for sub-Eddington local accretion rates: a local patch undergoes a recurrent cycle, accumulation fuel for hours until it becomes thermally unstable or is 'ignited' by a nearby burning region. The global pattern of burning and the resulting luminosity are thus very dependent on how fast nuclear fires spread around the star. The nuclear burning luminosity is not uniform over the stellar surface and so may provide a handle on measuring, or constraining, the spin periods of these neutron stars.

Bildsten, Lars↗

The rate of neutron star binary mergers in the universe - Minimal predictions for gravity wave detectors

Of the many sources which gravitational wave observatories might see, merging neutron star binaries are the most predictable. Their waveforms at the observable frequencies are easy to calculate. And three systems which will merge in less than a Hubble time have already been observed as binary pulsars: two in the disk of the Galaxy, and one in a globular cluster. From the lifetimes and positions of these, a lower limit to the merger rate in the Galaxy and globular cluster system are inferred with confidence. Taking the merger rate in other galaxies to scale with the star formation rate, the merger rate expected in the local universe is computed. An ultraconservative lower limit to the rate gives three per year within 1 Gpc. The best estimate, still conservative in that it considers only systems like those already observed, gives three per year within 200 Mpc. An upper limit of three mergers per year within 23/h Mpc is set by the rate of Type Ib supernovae. The rates of black hole binary mergers and black hole-neutron star binary mergers are model-dependent, but could be comparable to the given rate of neutron-star binary mergers.

Phinney, E. S.↗

Super-Eddington radiation transfer in soft gamma repeaters

Bursts from soft gamma repeaters (SGRs) have been shown to be super-Eddington by a factor of 1000 and have been persuasively associated with compact objects. Super-Eddington radiation transfer on the surface of a strongly magnetic (greater than or equal to 10(exp 13) G) neutron star is studied and related to the observational constraints on SGRs. In strong magnetic fields, Thompson scattering is suppressed in one polarization state, so super-Eddington fluxes can be radiated while the plasma remains in hydrostatic equilibrium. We discuss a model which offers a somewhat natural explanation for the observation that the energy spectra of bursts with varying intensity are similar. The radiation produced is found to be linearly polarized to one part in 1000 in a direction determined by the local magnetic field, and intensity variations between bursts are understood as a change in the radiating area on the source. The net polarization is inversely correlated with burst intensity. Further, it is shown that for radiation transfer calculations in limit of superstrong magnetic fields, it is sufficient to solve the radiation transfer for the low opacity state rather than the coupled equations for both. With this approximation, standard stellar atmosphere techniques are utilized to calculate the model energy spectrum.

Ulmer, Andrew↗