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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Transient fuel performance analysis for the preliminary fuel concept of general atomics fast modular reactor

This study investigates the transient fuel performance of General Atomics Fast Modular Reactor (GA-FMR) during accident scenarios, focusing on the behavior of its innovative fuel system that combines high-assay low enriched uranium dioxide (HALEUO2) fuel with SiGA® ceramic matrix composite silicon carbide cladding. The preliminary fuel design’s response was analyzed during reactivity-initiated accidents (RIA) and loss of coolant accidents (LOCA) using BISON fuel performance analysis code, which included both the diffusion enhanced and BISON-FASTGRASS coupled UO 2 models. The RIA analysis demonstrated that effective reactivity control reduced fuel temperature, though with transient fission gas release resulting in additional tensile stress state on the cladding. LOCA simulations revealed differing predictions between the two models: the BISON UO 2 model showed more transient fission gas release but minimal pellet expansion, while the BISON-FASTGRASS UO 2 model predicted less pronounced fission gas release but more fuel swelling and thermal expansion, potentially leading to pellet-cladding mechanical interaction. Here, these findings highlight critical areas for fuel design optimization and identify knowledge gaps requiring further experimental and computational investigation to advance GA-FMR fuel development.

Lee, Soon K. [Argonne National Laboratory (ANL), A↗
DOE OSTI2022

Remining and Restoring Abandoned US Mining Sites: The Case for Materials Needed for Zero-Carbon Transition

The electricity generation sector is responsible for 25% of the world’s greenhouse gas (GHG) emissions and thus has been the focus of efforts to transition to clean energy and sustainable development in many nations. In the past 20 years, renewable energy sources have been the fastest-growing energy source in the world, comprising almost 29% of the world’s electricity generation in 2020. Renewable energy sources are expected to comprise nearly 95% of the world’s power capacity growth through 2026, with a share of planned capacity expansion of up to 46% in 2026. The rapid development of renewable energy sources and technologies will require an enormous amount of raw materials to replace coal and gas plants and increase in the capacity to handle growing electricity demand because renewable energy sources have a low-power density and intermittent behavior. Accounting for the expected scale of rapidly deploying renewable energy sources that require rare earth elements (REEs), cement, and steel, the mining industry may face a supply problem for the materials critical for clean energy. And, as the exploration and development of new mining sites can be expensive and risky, the mining industry may require economic stimuli to grow supply. The increasing demand for renewable energy resources makes mining a threat to the environment unless proper regulations are established and calls for remining, cleanup, and circular economic development are made. Mining also contributes to environmental injustices related to the exploitation and pollution of lands near communities that are dependent on biodiversity in the area, while not always benefiting from technological advancements provided by the use of renewable energy and technologies. This study explored the opportunity of remining abandoned mining waste to extract metals and minerals essential for the production of renewable energy sources. The authors analyzed materials used in the production of these technologies, materials readily available in the United States, and which materials can be extracted locally in the United States from abandoned mine waste. The authors also studied environmental injustices that populations near mining sites experience and ways to mitigate these injustices, such as providing more control over extraction and cleanup activities, providing more job opportunities in those areas, and offsetting costs associated with cleanup and land restoration projects.

42 ENGINEERING↗
DOE OSTI2022

Short- vs . long-range elastic distortion: structural dynamics of a [2 × 2] tetrairon( II ) spin crossover grid complex observed by time-resolved X-Ray crystallography

Spin crossover complexes (SCO) are among the most studied molecular switches due to their potential use in displays, sensors, actuators and memory components. A prerequisite to using these materials is the understanding of the structural changes following the spin transition at out-of-equilibrium conditions. So far, out-of-equilibrium studies in SCO solids have been focused on mononuclear complexes, though a growing number of oligonuclear SCO complexes showing cooperative effects are being reported. Here, we use time-resolved pink Laue crystallography to study the out-of-equilibrium dynamics of a [2 × 2] tetranuclear metallogrid of the form [Fe II 4 L Me 4 ](BF 4 ) 4 ·2MeCN ([L Me ] - = 4-methyl-3,5-bis{6-(2,2'-bipyridyl)}pyrazolate). The out-of-equilibrium spin state switching induced by a ps laser pulse demonstrates that the metallogrid exhibits a multi-step response similar to that reported for mononuclear complexes. Contrary to the mononuclear complexes, the metallogrid shows two types of elastic distortions at different time scales. The first is a short-range distortion that propagates over the entire Fe 4 grid complex during the ps time scale, and it is caused by the rearrangement of the coordination sphere of the photo-switching ion and the constant feedback between strongly linked metal ions. The second is a long-range distortion caused by the anisotropic expansion of the lattice during the ns time scale, observed in mononuclear materials. The structural analysis demonstrates that the long-range prevails over the short-range distortion, inducing the largest deformation of both the entire grid and the coordination sphere of each metal ion. The present study sheds light on the out-of -equilibrium dynamics of a non-cooperative oligonuclear complex.

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

Cyclic versus Linear Alkylammonium Cations: Preventing Phase Transitions at Operational Temperatures in 2D Perovskites

Two-dimensional lead halide perovskites offer numerous attractive features for optoelectronics owing to their soft, deformable lattices and high degree of chemical tunability. While alteration of the metal and halide ions gives rise to significant modification of the bandgap energy, the organic spacer cations offer in-roads to tuning phase behavior and more subtle functionalities in ways that remain to be understood. Here, we study six variations of 2D perovskites changing only the organic spacer cations and demonstrate that these components intrinsically impact material response in important ways such as altering crystallographic structure, temperature-induced phase transitions, and photoluminescence emission. Two-dimensional perovskites containing commonly utilized aliphatic linear spacers, such as butylammonium, undergo phase transitions near room temperature. These transitions and temperature changes induce spacer-dependent variations in the emission spectra. Conversely, 2D perovskites comprising cyclic aliphatic spacers, such as cyclobutylammonium, are found to lack first-order phase transitions. These cyclic molecules are more sterically hindered within the crystal lattice, leading to temperature-induced contraction or expansion along certain crystallographic planes but no other significant thermal effects; additionally, they undergo changes in their emission spectra that cannot be explained by simple thermal expansion. Finally, given the similarities in the dielectric and chemical makeup of this set of six alkylammonium molecules, these results are unexpected and suggest a large structural and thermal phase space via spacer manipulation that could lead to improved 2D perovskite functionalization.

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

Modeling Interfaces to Support Low-Level Waste Disposal System Performance Assessments - 20366

In low-level waste (LLW) disposal sites, interfaces between cementitious materials, used as waste forms and/or engineered barriers, and the surrounding soil or backfill material are often encountered. Reactions across these interfaces may lead to chemical and structural alteration of the cementitious and backfill materials that may ultimately affect long-term performance. For example, the ingress of carbon dioxide from soil gas into a waste tank concrete shell at the Hanford Site or Savannah River Site (SRS) or a low-level waste disposal vault at SRS leads to carbonation of cement hydration products (e.g. portlandite, calcium-silicate hydrate or C-S-H, and ettringite). The result of carbonation is a decrease in pH in the cement paste portion of the tank wall or vault concrete structure that could ultimately lead to de-passivation of the embedded structural steel and, eventually, to cracking. Cracking can lead to increased ingress of water into the structure, corresponding increased release of constituents of concern, and to subsequent increased transport of these constituents to the surrounding environment. The mobility of trace constituents (e.g., radionuclides of concern) in waste forms may increase in response to changes in pH, pore structure, and mineralogical gradients. Depletion of portlandite results in subsequent decalcification of C-S-H that leads to changes in the cement strength and may lead to structural failure. At the boundary between waste forms and concrete vaults, the migration of sulfate ions from the salt waste form (e.g., the saltstone waste form used for LLW disposal at the Savannah River Site in Saltstone Disposal Units, or SDUs) into the barrier or vault concrete has been predicted to result in expansive mineral phase formation (or 'sulfate attack'). Expansive mineral formation could result in cracking and potential loss of structural integrity in the vault concrete. In the performance assessment (PA) for the SRS SDUs, prediction of both the carbonation and sulfate attack fronts are critical to assessing the long-term performance of these LLW disposal vaults. A general purpose geochemical reactive transport model has been developed in LeachXS/ORCHESTRA to evaluate typical interfaces for LLW disposal environments, including SDUs at SRS. The model may be used to predict the long-term performance of interfaces between cementitious materials and saltstone or backfill materials with respect to primary phases by considering mass transport, cement chemistry, geochemical speciation, and multi-ionic diffusion over interfaces between different materials. The present study compares the performance and interactions between vault concrete and saltstone waste form for a representative SDU scenario. The materials were characterized using pH-dependence leaching test (EPA 1313) and semi-dynamic transport tests (EPA 1315) with test results used to parameterize the interface model. The development of a credible inter model provides an important basis for supporting future PAs where carbonation and sulfate attack are important aging and degradation mechanisms. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Reflections on Cyanobacterial Chromatic Acclimation: Exploring the Molecular Bases of Organismal Acclimation and Motivation for Rethinking the Promotion of Equity in STEM

Cyanobacteria are photosynthetic organisms that exhibit characteristic acclimation and developmental responses to dynamic changes in the external light environment. Photomorphogenesis is the tuning of cellular physiology, development, morphology, and metabolism in response to external light cues. The tuning of photosynthetic pigmentation, carbon fixation capacity, and cellular and filament morphologies to changes in the prevalent wavelengths and abundance of light have been investigated to understand the regulation and fitness implications of different aspects of cyanobacterial photomorphogenesis. Chromatic acclimation (CA) is the most common form of photomorphogenesis that has been explored in cyanobacteria. Multiple types of CA in cyanobacteria have been reported, and insights gained into the regulatory pathways and networks controlling some of these CA types. I examine the recent expansion of CA types that occur in nature and provide an overview of known regulatory factors involved in distinct aspects of cyanobacterial photomorphogenesis. Additionally, I explore lessons for cultivating success in scientific communities that can be drawn from a reflection on existing knowledge of and approaches to studying CA.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Determination of Thermal Expansion, Defect Formation Energy, and Defect-Induced Strain of α-U Via ab Initio Molecular Dynamics

Uranium (U) is often alloyed with molybdenum (Mo) or zirconium (Zr) in order to stabilize its high-temperature body-centered cubic phase for use in nuclear reactors. However, in all metallic fuel forms, the α phase of U remains in some fraction. This phase decomposition due to temperature or compositional variance can play an outsized role on fuel performance and microstructural evolution. Relatively little is known about fundamental point defect properties in α -U at non-zero temperatures, from either computational or experimental studies. This work performs the first thorough evaluation of the α phase of U via ab initio molecular dynamics (AIMD). A number of thermophysical properties are calculated as a function of temperature, including equilibrium lattice parameters, thermal expansion, and heat capacity. These results indicate a two-region behavior, with the transition at 400 K. The thermal expansion/contraction in the a / b direction occurs rapidly from 100 up to 400 K, after which a more linear and gradual change in the lattice constant takes place. The volumetric expansion matches experiments quantitatively, but the individual lattice constant expansion only matches experiments qualitatively. Point defect formation energies and induced lattice strains are also determined as a function of temperature, providing insight on defect populations and the fundamentals of irradiation growth in α -U. Interstitials induce significantly more strain than vacancies, and the nature of that strain is highly dependent on the individual lattice directions. The direction of point defect-induced lattice strain is contrary to the irradiation growth behavior of α -U. This work shows that isolated point defects cannot be the primary driving force responsible for the significant irradiation-induced growth of α -U observed experimentally.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Transmission and Distribution Real-Time Analysis Software for Monitoring and Control: Design and Simulation Testing

The US electric grid is facing operational, stability, and security challenges. Transmission system operators need some measure of visibility into distribution system renewable generation. Distribution system generation needs to support transmission system voltage. The grid is experiencing an expansion in measurement systems. How to take full advantage of this expansion and defend against attacks, both cyber and physical, poses additional challenges. This paper introduces software designed to meet these challenges. At the center of the software is an Integrated System Model (ISM) that spans from transmission to secondary distribution. The ISM is employed in real-time abnormality detection, voltage stability forecasting, and multi-mode control. The software architecture along with selected analysis modules is presented. Testing results are presented for: 1—attacks on utility infrastructure; 2—energy savings from optimal control; 3—distribution system control response during a low voltage transmission system event; 4—cyber-attacks on PV inverters, where physical inverters are used in hardware-in-the-simulation-loop studies. Contributions of this work include real-time analysis that spans from three-phase transmission through secondary distribution; an approach for detecting abnormalities that employs measurements from three independent measurement systems; and a multi-mode distribution system control that responds to cyber-attacks, physical attacks, equipment failures, and transmission system needs.

14 SOLAR ENERGY↗
DOE OSTI2023

Toward a Realistic Representation of Sucrose Transport in the Phloem of Plants

The significance of phloem hydrodynamics to plant mortality and survival, which impacts ecosystem-scale carbon and water cycling, is not in dispute. The phloem provides the conduits for products of photosynthesis to be transported to different parts of the plant for consumption or storage. The M$\ddot{u}$nch pressure flow hypothesis (PFH) is the leading framework to mathematically represent this transport. It assumes that osmosis provides the necessary pressure differences to drive water and sucrose within the phloem. Mathematical models utilizing the PFH approximate the phloem by a relatively rigid slender semi-permeable tube. However, the phloem consists of living cells that contract and expand in response to pressure fluctuations. The effect of membrane elasticity on osmotically driven sucrose front speed has rarely been considered and frames the scope here. Laboratory experiments were conducted to elucidate the elastic-to-plastic pressure-deformation relation in membranes and their effect on sucrose front speeds. It is demonstrated that membrane elasticity acts to retard the sucrose front speed. The retardation emerges because of two effects: (a) part of the osmotic pressure is diverted to perform mechanical work to expand the membrane instead of pressurizing water, and (b) expansion of the membrane reduces the sucrose concentration driving osmotic potential due to volume increases and concomitant dilution effects. Finally, these results offer a novel perspective about the much discussed presence of sieve plates throughout the phloem acting as structural expansion dampers.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Business Models for Scaling Demand Flexibility Volume IV – Program life cycle challenges and lessons learned from U.S. programs

Load growth at the grid edge is driving increased attention to the distribution system and its ability to enable customer technology adoption in an affordable and timely manner. Key industry stakeholders, including electric utilities and regulators, can benefit from strategies to manage and balance customer needs with infrastructure investments, such as demand flexibility. This report focuses on demand flexibility—the ability to reduce, shift, shed, generate, or modulate loads in response to building and grid needs—to reduce the need for costly grid upgrades by deferring investment needs and increase system reliability by shifting electricity usage during periods of high risk. Specifically, we focus on the emerging characteristics of business models for demand flexibility as a framework to understand how demand flexibility programs generate value. In this report, we focus on the life cycle of demand flexibility programs, which provides information on value creation and describes the various deployment phases program implementers navigate from initial program conceptualization through to program expansion and replication to new customer segments and regions. This report characterizes the key phases of the demand flexibility program life cycle, identifies existing challenges across the program deployment phases, and describes lessons learned. This report is part of a series that includes reports on customer relationship management strategies, stakeholder ecosystem management, and program life cycle.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Modeling detonation with CartaBlanca simulations

The accurate modeling of high explosive (HE) detonation and the con- sequent large solid deformation, failure, plastic flow, porosity growth, and shock wave propagation is important because simulations can capture spatial and temporal features that experimental diagnostics cannot capture. However, the simulation of the explosive event poses challenges to a computational scientist. These include the accurate modeling of ductile damage, crack formation, plastic deformation, as well as physical and nu- merical instabilities. The material response can be history-dependent and subject to large material deformation. Our research simulates the impact of a high explosive (Detasheet) onto a tantulum metal plate. We performed the simulations using CartaBlanca at different mesh resolutions. We decided the study would be impactful if we perform the simulations with the Material Point Method. Differences were observed at the different mesh resolutions in velocity and nodal stress magnitude, so increased mesh resolutions may be required. In addition, the Discontinuous Galerkin method would be needed to account for the large gas expansion.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The anomalous magnetic moment of the muon in the Standard Model

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant α and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including O(α 5 ) with negligible numerical uncertainty. The electroweak contribution is suppressed by (m μ / M W ) 2 and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at O(α 2 ) and is due to hadronic vacuum polarization, whereas at O(α 3 ) the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first- principle, lattice-QCD approach. The final result reads $a$$^{SM}_{μ}$ = 116 591 810(43) × 10 −11 and is smaller than the Brookhaven measurement by 3.7σ. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. Furthermore, this and the prospects to further reduce the theoretical uncertainty in the near future – which are also discussed here – make this quantity one of the most promising places to look for evidence of new physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Vegetation Type and Decomposition Priming Mediate Brackish Marsh Carbon Accumulation Under Interacting Facets of Global Change

Coastal wetland carbon pools are globally important, but their response to interacting facets of global change remain unclear. Numerical models neglect species-specific vegetation responses to sea level rise (SLR) and elevated CO 2 (eCO 2 ) that are observed in field experiments, while field experiments cannot address the long-term feedbacks between flooding and soil growth that models show are important. Here, we present a novel numerical model of marsh carbon accumulation parameterized with empirical observations from a long-running eCO 2 experiment in an organic rich, brackish marsh. Model results indicate that eCO 2 and SLR interact synergistically to increase soil carbon burial, driven by shifts in plant community composition and soil volume expansion. Furthermore, newly parameterized interactions between plant biomass and decomposition (i.e. soil priming) reduce the impact of eCO 2 on marsh survival, and by inference, the impact of eCO 2 on soil carbon accumulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Accounting for linkages between wildfire-driven shifts in plant-microbial interactions and soil carbon dynamics in Arctic tundra

Increasing wildfire regimes in the rapidly changing Arctic tundra are altering the soil carbon budget through increased permafrost degradation, shrubs expansion, and shifts in microbial activities. Whether future arctic wildfires will result in net C losses or gains in the future will depend on complex biotic and abiotic interactions that regulate belowground C biogeochemical processes, including linkages among biotic communities. One important linkage is plant-microbe interactions. While these interactions are likely shaped or altered by wildfires, they remain little explored in the context of successional trajectories. Yet, incorporating plant-microbe interactions in frameworks for defining and understanding post-fire soil C trajectories is critical to predict belowground C responses to future tundra wildfires. Here, we provide examples of and discuss how fire-mediated changes in plant-soil-microbe (PSM) interactions can impact soil C dynamics in the Arctic tundra. We consider different impacts of wildfires on PSM interactions and their implications to soil C dynamics, as well as the nuances associated with particular wildfire regimes (severity and intensity) and successional timescales. We suggest that accounting for plant-microbial linkages in future wildfire-succession interactions frameworks can inform future experimental designs and reduce uncertainties in our ability to predict the net effect of Arctic wildfires on ecosystem C.

fungi, bacteria↗
DOE OSTI2023

Final-state interactions and spin structure in E 1 breakup of Li 11 in halo effective field theory

In this work, we calculate the E1 breakup of the 2n halo nucleus 11 Li in halo effective field theory (Halo EFT) at leading order. In Halo EFT, 11 Li is treated as a three-body system of a 9 Li core and two neutrons. We present a detailed investigation of final-state interactions (FSIs) in the neutron-neutron (nn) and neutron-core (nc) channels. We employ Møller operators to formulate an expansion scheme that satisfies the non-energy-weighted cluster sum rule and successively includes higher-order terms in the multiple-scattering series for the FSI. Computing the E1 strength up to third order in this scheme, we observe apparent convergence and good agreement with experiment. The neutron-neutron FSI is by far the most important contribution and largely determines the maximum value of the E1 distribution. However, inclusion of nc FSI does shift the peak position to slightly lower energies. Moreover, we investigate the sensitivity of the E1 response to the spin structure of the neutron- 9 Li interaction. We contrast results for an interaction that is the same in the spin-1 and spin-2 channels with one that is only operative in the spin-2 channel, and find that good agreement with experimental data is only obtained if the interaction is present in both spin channels. The latter case is shown to be equivalent to a calculation in which the spin of 9 Li is neglected.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Cosmological preference for a negative neutrino mass

The most precise determination of the sum of neutrino masses from cosmological data, derived from analysis of the cosmic microwave background (CMB) and baryon acoustic acoustic oscillations (BAO) from the Dark Energy Spectroscopic Instrument (DESI), favors a value below the minimum inferred from neutrino flavor oscillation experiments. We explore which data is most responsible of this puzzling aspect of the current constraints on neutrino mass and whether it is related to other anomalies in cosmology. We demonstrate conclusively that the preference for negative neutrino masses is a consequence of larger than expected lensing of the CMB in both the two- and four-point lensing statistics. Furthermore, we show that this preference is robust to changes in likelihoods of the BAO and CMB optical depth analyses given the available data. We then show that this excess clustering is not easily explained by changes to the expansion history and is likely distinct from the preference for for dynamical dark energy in DESI BAO data. Finally, we discuss how future data may impact these results, including an analysis of Planck CMB with mock DESI 5-year data. Here, we conclude that the negative neutrino mass preference is likely to persist even as more cosmological data is collected in the near future.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Real-time estimation and control of divertor surface heat flux on the DⅢ-D tokamak

We report Future tokamaks will require robust technologies for the mitigation of heat exhaust onto the plasma-facing components. As a first step towards this development, a system has been developed at DIII-D that estimates and controls in real-time the heat flux to the PFCs. Real-time estimation of the peak power flux from this model-based approach is validated with off-line infra-red measurements for various DIII-D plasma discharges. A nonlinear free-boundary simulation code (GSevolve) is used for simulating the closed loop response and for the off-line determination of the control parameters. The implementation and first experimental results of the application during the DIII-D plasma campaign are reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Leptodermic corrections to the TOV equations and nuclear astrophysics within the effective surface approximation

The macroscopic model for a neutron star (NS) as a liquid drop at the equilibrium is used to extend the Tolman-Oppenheimer-Volkoff (TOV) equations taking into account the gradient terms responsible for the system surface. The parameters of the Schwarzschild metric in the spherical case are found with these surface corrections to the known leading (zero) order of the leptodermic approximation a/R << 1, where a is the NS effective-surface (ES) thickness, and R is the effective NS radius. The energy density $\mathscr{E}$ is considered in a general form including the functions of the particle number density and of its gradient terms. The macroscopic gravitational component $Φ$(ρ) of the energy density is taken into account in the simplest form as expansion in powers of $ρ$ – $\overline{ρ}$, where $\overline{ρ}$ is the saturation density, up to second order, in terms of its contributions to the separation particle energy and incompressibility. Density distributions ρ across the NS ES in the normal direction to the ES, which are derived in the simple analytical form at the same leading approximation, was used for the derivation of the modified TOV (MTOV) equations by accounting for their NS surface corrections. As a result, the MTOV equations are analytically solved at first order and the results are compared with the standard TOV approach of the zero order.

Magner, A. G. [Institute for Nuclear Research, Kyi↗