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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 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

FWP FEAA149: “Next Generation Environmental Barrier Coatings”

Environmental barrier coatings (EBCs) are required coatings for utilization of SiC/SiC ceramic matrix composite (CMC) components in gas turbines, where the EBC represents the life-limiting factor for such components. EBC/CMC systems have shown success in aero-engine applications with increased turbine inlet temperatures and improved efficiencies, which are achieved through higher temperature stability, lower density, and decreased reliance on cooling air compared to traditional superalloys. While industrial gas turbines (IGTs) do not currently utilize SiC/SiC CMCs, the current shift towards low-carbon or carbon-free fuel sources for power generation could result in a need for EBC/CMC components with higher temperature capabilities. In this work, three tasks were outlined to improve understanding of EBC lifetimes to encourage use in IGTs with carbon-free fuel such as hydrogen: 1. Define the bond coating oxidation kinetics and EBC failure criteria, 2. Measure thermal expansion coefficients of each layered material, and 3. Perform advanced characterization and modeling to assess EBC lifetimes. Cyclic steam oxidation tests were conducted on various EBC/Si/SiC chemistries and EBC/SiC architectures to define substrate oxidation kinetics and EBC failure modes. An open-source code was developed to quantify the undulating thermally grown oxide thickness with thousands of measurements from specimen cross-section images. Bond coating oxidation kinetics were determined and used to develop a kinetic and thermodynamic model for predicting EBC lifetimes. High-temperature Raman spectroscopy was utilized for determining the SiO 2 thermally grown oxide phase transformation as the life-limiting feature for EBCs. Model efforts supported the claim that the SiO 2 phase transformation causes elevated stress during thermal cycling with associated cracking that decreases the adhesion strength of the EBC, eventually resulting in coating spallation. The finite element model subroutine will be made publicly available upon internal review. Further development of an EBC lifetime model for IGTs involves definition of a critical SiO 2 thickness for EBC spallation and must also consider both environmental (gas velocity, pressure, etc.) and specimen (EBC dopants, layer architectures, etc.) effects into predicted bond coating oxidation kinetics for long-lifetime components.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Single Cobalt Sites Dispersed in Hierarchically Porous Nanofiber Networks for Durable and High-Power PGM-Free Cathodes in Fuel Cells

Increasing catalytic activity and durability of atomically dispersed metal–nitrogen–carbon (M–N–C) catalysts for the oxygen reduction reaction (ORR) cathode in proton-exchange-membrane fuel cells remains a grand challenge. In this study, a high-power and durable Co–N–C nanofiber catalyst synthesized through electrospinning cobalt-doped zeolitic imidazolate frameworks into selected polyacrylonitrile and poly(vinylpyrrolidone) polymers is reported. The distinct porous fibrous morphology and hierarchical structures play a vital role in boosting electrode performance by exposing more accessible active sites, providing facile electron conductivity, and facilitating the mass transport of reactant. The enhanced intrinsic activity is attributed to the extra graphitic N dopants surrounding the CoN 4 moieties. The highly graphitized carbon matrix in the catalyst is beneficial for enhancing the carbon corrosion resistance, thereby promoting catalyst stability. The unique nanoscale X-ray computed tomography verifies the well-distributed ionomer coverage throughout the fibrous carbon network in the catalyst. The membrane electrode assembly achieves a power density of 0.40 W cm –2 in a practical H 2 /air cell (1.0 bar) and demonstrates significantly enhanced durability under accelerated stability tests. The combination of the intrinsic activity and stability of single Co sites, along with unique catalyst architecture, provide new insight into designing efficient PGM-free electrodes with improved performance and durability.

25 ENERGY STORAGE↗
DOE OSTI2020

Microstructural stability of tantalum-alloyed ferritic-martensitic steel with neutron irradiation to 7.4 dpa at ~490 °C

Specimens of a reduced-activation ferritic-martensitic steel, called CNA1, were irradiated to 7.4 displacements per atom at ~490 °C in the High Flux Isotope Reactor. Vickers hardness and tensile properties revealed consistent softening that is attributed to some recovery during irradiation, with reduced laths and dislocation density. Detailed microstructural characterization by transmission electron microscopy and energy dispersive x-ray spectroscopy showed radiation-induced dislocation loops, few cavities, and slight dissolution of M 23 C 6 and MX precipitates. Partial amorphization was only observed in M 23 C 6 precipitated in matrix. Transmutation somewhat destabilized M 23 C 6 and MX, with a stronger effect on the later one by noticeable depletion of Ta with enriched W, which is consistent with the transmutation calculations. The microstructural evolution and associated strength changes were discussed with the assistance of computational thermodynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Machine learning Frenkel Hamiltonian parameters to accelerate simulations of exciton dynamics

In this manuscript, we develop multiple machine learning (ML) models to accelerate a scheme for parameterizing site-based models of exciton dynamics from all-atom configurations of condensed phase sexithiophene systems. This scheme encodes the details of a system’s specific molecular morphology in the correlated distributions of model parameters through the analysis of many single-molecule excited-state electronic-structure calculations. These calculations yield excitation energies for each molecule in the system and the network of pair-wise intermolecular electronic couplings. In this work, we demonstrate that the excitation energies can be accurately predicted using a kernel ridge regression (KRR) model with Coulomb matrix featurization. We present two ML models for predicting intermolecular couplings. The first one utilizes a deep neural network and bi-molecular featurization to predict the coupling directly, which we find to perform poorly. The second one utilizes a KRR model to predict unimolecular transition densities, which can subsequently be analyzed to compute the coupling. We find that the latter approach performs excellently, indicating that an effective, generalizable strategy for predicting simple bimolecular properties is through the indirect application of ML to predict higher-order unimolecular properties. Such an approach necessitates a much smaller feature space and can incorporate the insight of well-established molecular physics.

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

Constructing a Simulation Surrogate with Partially Observed Output

Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these surrogates. However, surrogate methods with dimension reduction generally rely on complete output training data. This article proposes a new Gaussian process surrogate method that permits the use of partially observed output while remaining computationally efficient. The new method involves the imputation of missing values and the adjustment of the covariance matrix used for Gaussian process inference. The resulting surrogate represents the available responses, disregards the missing responses, and provides meaningful uncertainty quantification. In conclusion, the proposed approach is shown to offer sharper inference than alternatives in a simulation study and a case study where an energy density functional model that frequently returns incomplete output is calibrated.

42 ENGINEERING↗
DOE OSTI2025

Laser Powder Directed Energy Deposition of Steels for Nuclear Applications

This comprehensive investigation examines the structure–property relationships in two nuclear alloy systems—Alloy 709 (A709) austenitic stainless steel and Grade 92 (G-92) ferritic/martensitic (F/M) steel—manufactured via directed energy deposition (DED) for sodium-cooled fast reactor applications. This study establishes the fundamental mechanisms for controlling microstructures for optimizing the mechanical performance of additively manufactured nuclear materials through systematic heat treatment optimization and multiscale characterization. As-deposited A709 steel develops a complex multiscale strengthening architecture consisting of a fine cellular solidification structure with diameter of 2-3 µm within10–50 µm grains, elevated dislocation densities from rapid thermal cycling, and grain boundary precipitates that activate concurrent Hall–Petch, dislocation, and precipitation hardening mechanisms to achieve exceptional properties [yield strength (YS): 603 MPa, ultimate tensile strength (UTS): 844 MPa, Vickers hardness: 220 HV] that achieve a 44% superior strength compared to that of the wrought material. Heat treatments produce different results. Solution annealing (SA) dissolves the cellular structure and reduces the hardness to 190 HV. Precipitation treatment (PT) keeps the cellular structure but adds carbides, allowing the hardness to reach 205 HV. The best approach combines both treatments (SA+PT) and creates uniform precipitate distributions with M 23 C 6 carbides at the grain boundaries and MX carbonitrides in the matrix, achieving a hardness of 195 HV. However, directional differences persist, with a 12%–15% strength variation between orientations due to the inherited layered microstructural architecture that survives aggressive heat treatment. While tensile testing at 550°C demonstrates 40%–50% thermal softening with dynamic strain aging, DED A709 steel still maintains a 71% higher YS than that of the wrought material. Ion irradiation studies (100–400 dpa) of DED A709 steel reveal progressive radiation damage with increasing void density and radiation-induced segregation causing nickel enrichment and chromium depletion, which will ultimately compromise mechanical properties. As-deposited G-92 exhibits exceptional strength (UTS: 1650–1700 MPa, 430 HV) through a complex microstructure containing both ferrite and martensite phases, a high geometrically necessary dislocation (GND) density (17.04×10 14 /m 2 ), and fine carbides. Heat treatments create distinct changes. Normalizing produces fresh martensite with the highest hardness (460 HV) and an increased GND density (20.23×10 14 /m 2 ). Tempering develops dual precipitation systems and reduces the hardness to 290 HV. The optimal approach uses sequential normalizing plus tempering, achieving balanced properties with the lowest hardness (250 HV) and a reduced GND density (11.01×10 14 /m 2 ). A processing-dependent anisotropy is observed: horizontal specimens achieve superior ductile behavior, while vertical specimens exhibit brittle failure. A tempering heat treatment successfully mitigates this anisotropic behavior by transforming the hard martensitic as-deposited structure into tempered martensite enabling both horizontal and vertical specimens to exhibit similar stress–strain characteristics with visible necking behavior. Remarkably, testing at 550°C reveals a reversal in the anisotropy, where as-deposited specimens achieve near isotropy with superior thermal stability (a 15%–20% strength reduction), while tempered specimens develop an orientation dependence with a 25%–30% strength reduction. Both alloy systems demonstrate that DED processing creates specimens with a superior strength through refined microstructural features, though with distinct strengthening mechanisms—austenitic through cellular structures and precipitates versus F/M through phase transformations and precipitates. Heat treatment optimization requires alloy-specific approaches, with A709 benefiting from controlled precipitation while G-92 requires careful phase transformation control. The results show that DED manufacturing can produce nuclear materials with exceptional performance, but directional effects and temperature-dependent behavior must be carefully considered for reactor component design and qualification.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

A novel fiber-fretting test for tribological characterization of the fiber/matrix interface

Ceramic matrix composites exhibit excellent high temperature properties and are candidate materials for structural applications from jet engines to nuclear fuel cladding. The strength and deformation behavior of these composites are intrinsically tied to the properties of the fiber/matrix interface. This research introduces a novel technique to evaluate the fundamental friction and wear characteristics of these interfaces. A case study on SiC f /PyC/SiC m composites applies in situ fiber fretting to investigate the kinetic friction coefficient and cyclic wear characteristics of the interphase. The experimental methodology is presented in explicit detail to encourage other researchers to explore the capabilities of this technique. Additionally, testing was carried out as a function of fiber roughness, PyC thickness (≈10, 500, 1200 nm), cycle count (10, 100, 1000), and frequency (1, 5, and 10 Hz). The friction coefficient and wear behavior changed with cycle length due to a transition from adhesive to abrasive mechanisms. SEM fractography provided insights to tribological evolution from adhesive sliding to three-body abrasive wear. The structural disorder at the tribo-surface relating to graphitic content and dangling bond density was investigated using Raman spectroscopy. Properties are contextualized with comparison to uniaxial tensile behavior of the parent composite.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A high‐order discontinuous Galerkin approach for physics‐based thermospheric modeling

Abstract The accurate prediction of aerodynamic drag on satellites orbiting in the upper atmosphere is critical to the operational success of modern space technologies, such as satellite‐based communication or navigation systems, which have become increasingly popular in the last few years due to the deployment of constellations of satellites in low‐Earth orbit. As a result, physics‐based models of the ionosphere and thermosphere have emerged as a necessary tool for the prediction of atmospheric outputs under highly variable space weather conditions. This paper proposes a high‐fidelity approach for physics‐based space weather modeling based on the solution of the Navier–Stokes equations using a high‐order discontinuous Galerkin method, combined with a matrix‐free strategy suitable for high‐performance computing on GPU architectures. The approach consists of a thermospheric model that describes a chemically frozen neutral atmosphere in nonhydrostatic equilibrium driven by the external excitation of the Sun. A novel set of variables is considered to treat the low densities present in the upper atmosphere and to accommodate the wide range of scales present in the problem. At the same time, and unlike most existing approaches, radial and angular directions are treated in a nonsegregated approach. The study presents a set of numerical examples that demonstrate the accuracy of the approximation and validate the current approach against observational data along a satellite orbit, including estimates of established empirical and physics‐based models of the ionosphere‐thermosphere system. Finally, a one‐dimensional radial derivation of the physics‐based model is presented and utilized for conducting a parametric study of the main thermal quantities under various solar conditions.

Engineering↗
DOE OSTI2020

Microstructural development in DED stainless steels: applying welding models to elucidate the impact of processing and alloy composition

Austenitic stainless steel microstructures produced by directed energy deposition (DED)are analogous to those developed during welding, particularly high energy density welding. To better understand microstructural development during DED, theories of microstructural evolution,which have been established to contextualize weld microstructures, are applied in this study to microstructural development in DED austenitic stainless steels. Phenomenological welding models that describe the development of oxide inclusions, compositional microsegregation, ferrite,matrix austenite grains, and dislocation substructures are utilized to clarify microstructural evolution during deposition of austenitic stainless steels. Two different alloys, 304L and 316L, arecompared to demonstrate the broad applicability of this framework for understanding microstmctural development during the DED process. Despite differences in grain morphology and solidification mode for these two alloys (which can be attributed to compositional differences),similar tensile properties are achieved. It is the fine-scale compositional segregation and dislocation structures that ultimately determine the strength of these materials. The evolution of microsegregation and dislocation structures is shown to be dependent on the rapid solidification and thermomechanical history of the DED processing method and not the composition of the starting material.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Chemical compatibility of hollow ceramic cenospheres as thermal insulation for high-temperature thermal energy storage applications with molten nitrate salt

An effective insulation material that is both thermally and chemically stable in molten salts could transform the design of molten-salt-based thermal energy storage (TES) tanks. Most current molten salt TES tanks hold the metallic tank structure in direct contact with hot salt inventory, a design which leads to thermal expansion of the tank and triggers stresses that can lead to thermomechanical failures. With an internal insulation to lower the temperature at the tank structure, the extent of thermal expansion can be reduced, thereby reducing expansion-induced stresses and allowing for consideration of lower-cost tank structure materials. Conventional insulation materials are either 1) too porous and allow molten salts to permeate into the matrix, which significantly increases the thermal conductivity or 2) too dense and have a thermal conductivity that cannot provide sufficient thermal insulation. This paper presents an alternative thermal insulation concept using cenospheres which have an alumino-silicate structure. The cost analysis suggests that the low-density cenospheres can be one of the cheapest materials to provide cost-effective thermal insulation. The chemical compatibility of cenospheres is investigated in molten 60 wt% NaNO3/40 wt% KNO3 salt which is close to industrial-grade Solar Salt. This paper shows that diffusion of the sodium and potassium cations from the salt into the cenospheres occurs based on weight analysis, energy dispersive spectroscopy (EDS), X-ray diffraction (XRD) and Fourier-transform infrared (FTIR) spectroscopy. The cation diffusion breaks the bridging oxygen bonds and causes volume expansion of the microstructure which is responsible for the failure of the cenosphere particles. The chemical composition of the cenospheres is found to affect their compatibility with molten nitrate salt. A cenosphere product with low iron content showed the best compatibility with an average survival rate of 77.9% +/- 9.8% after 7 days of immersion in the molten nitrate salt. While even the low-iron cenospheres appear to require protection from direct molten salt contact, their slow degradation rate, closed-cell porosity, and low cost hold potential for effective use as internal tank insulation.

14 SOLAR ENERGY↗
DOE OSTI2021

Multi-energy reconstructions, central electron temperature measurements, and early detection of the birth and growth of runaway electrons using a versatile soft x-ray pinhole camera at MST

A multi-energy soft x-ray pinhole camera has been designed, built, and deployed at the Madison Symmetric Torus to aid the study of particle and thermal transport, as well as MHD stability physics. This novel imaging diagnostic technique employs a pixelated x-ray detector in which the lower energy threshold for photon detection can be adjusted independently on each pixel. The detector of choice is a PILATUS3 100 K with a 450 μm thick silicon sensor and nearly 100 000 pixels sensitive to photon energies between 1.6 and 30 keV. An ensemble of cubic spline smoothing functions has been applied to the line-integrated data for each time-frame and energy-range, obtaining a reduced standard-deviation when compared to that dominated by photon-noise. The multi-energy local emissivity profiles are obtained from a 1D matrix-based Abel-inversion procedure. Central values of Te can be obtained by modeling the slope of the continuum radiation from ratios of the inverted radial emissivity profiles over multiple energy ranges with no a priori assumptions of plasma profiles, magnetic field reconstruction constraints, high-density limitations, or need of shot-to-shot reproducibility. In tokamak plasmas, a novel application has recently been tested for early detection, 1D imaging, and study of the birth, exponential growth, and saturation of runaway electrons at energies comparable to 100 × Te,0; thus, early results are also presented.

Delgado-Aparicio, L. F. (ORCID:0000000167394380)↗
DOE OSTI2022

Properties and microstructure evolution of silicon nitride and zirconium nitride following Ni ion irradiation

We report that silicon nitride and zirconium nitride have been proposed as potential materials for multiple nuclear applications (inert matrix fuels, accident tolerant fuels, space nuclear power, fusion reactor design), yet knowledge on their behavior under irradiation remains limited. Ion irradiations were performed using 15 MeV Ni 5+ ions on Si 3 N 4 and ZrN samples, with midrange doses (around 3 µm) from 1 to 50 dpa and temperatures from 300 to 700°C. Volumetric lattice swelling was determined by grazing incidence X-ray diffraction, defect production and evolution were tracked using Transmission Electron Microscopy, and nanoindentation was performed to quantify the ceramics’ mechanical properties evolution. The results from these irradiation studies on nitride ceramics help fill the current gap present in the literature. Behavior consistent with past work on irradiated Si 3 N 4 was observed with respect to mechanical properties and defect formation up to 15 dpa and 500°C. Failure of the grain boundary sintering aid in Si 3 N 4 was observed above these conditions. Different behavior was observed in both nitrides at 50 dpa and 700°C, where lattice swelling increased past potential saturation values. Unreported cavity formation was witnessed in both materials under all irradiation conditions, with stable number density and slight size increase above 15 dpa. The mechanism for the cavity formation remains to be determined.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Solving the electronic structure problem for over 100000 atoms in real space

Using a real-space high-order finite-difference approach, we investigate the electronic structure of large spherical silicon nanoclusters. Within Kohn-Sham density functional theory and using pseudopotentials, we report the self-consistent field convergence of a system with over 100000 atoms: a Si 107,641 ⁢H 9,084 nanocluster with a diameter of 16 nm. Our approach uses Chebyshev-filtered subspace iteration to speed up the convergence of the eigenspace, and blockwise Hilbert space-filling curves to speed up sparse matrix-vector multiplications, all of which are implemented in the parsec code. For the largest system, we utilized 2048 nodes (114 688 cores) on the Frontera machine in the Texas Advanced Computing Center. Our quantitative analysis of the electronic structure shows how it gradually approaches its bulk counterpart as a function of nanocluster size. The band gap is enlarged due to quantum confinement in nanoclusters, but decreases as the system size increases, as expected. In conclusion, our work serves as a proof of concept for the capacity of the real-space approach in efficiently parallelizing very large calculations using high-performance computer platforms, which can straightforwardly be replicated in other systems with more than 10 5 atoms.

0-dimensional systems↗
DOE OSTI2020

Effect of heat treatment on the tensile behavior of selective laser melted Ti-6Al-4V by in situ X-ray characterization

Selective Laser Melted Ti-6Al-4V (as-SLMed) exhibits decreased yield strength, increased work hardening, and increased ductility after heat treatment at 730 degrees C (HT-730) or 900 degrees C (HT-900) for 2 h. To understand the change of mechanical properties, in situ high energy X-ray diffraction (HEXRD) is used to examine the phase composition, load partitioning, slip system activity, and dislocation density evolution in all three specimens. The as-SLMed specimen is dominated by martensitic α'. After heat treatment, α' partly or fully decomposes into α+β, reducing the yield strength. In HT-730, beta precipitates with confined size show much higher lattice strain than the α'/α matrix during deformation; in HT-900, the lattice strain difference is mostly eliminated. This is a key reason for the increased ductility in HT-900. From the anisotropic lattice strain development, basal slip is identified as the easiest slip system in α'/α. Using an elasto-plastic self-consistent (EPSC) model, the critical resolved shear stress ratio between prismatic slip and basal slip (CRSS prism /CRSS basal ) is estimated to be 1.31 and 1.16 in the as -SLMed and the HT-900 specimens, respectively. Further, the alpha phase in HT-900 is able to activate multiple slip systems and accumulate more dislocations during plastic deformation. This explains why HT-900 has better ductility and higher work hardening rate than the other two specimens.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Exploring the speciation of actinide salts in the presence of contaminants related to molten salt reactors

Molten salt reactors (MSR) are up-and-coming Generation IV nuclear reactors with either coolant and/or radioactive fuel in molten salt form. Due to their improved safety, efficiency, affordability and convenient waste processing system, these reactors are considered a superior alternative to conventional ones. However, prior to commercial implementation, it is necessary to have an extensive understanding of the reactions occurring in the MSR. The safety parameters of the MSR are determined by the rheological properties such as density and viscosity of the molten salt and these properties are governed by the local structure of the molten salts. Due to the high operational temperatures of MSR's, corrosion plays an important role. Because of their influence, the container corrosion products become part of the fuel salt matrix. In this work, we are investigating how these corrosion products, e.g., Mo, Ni, Cr, would impact the speciation of the actinide metal centers. For the initial studies, lanthanides are used as a surrogate for actinides. Lanthanide chloride salts (LnCl3) are mixed with transition metals and excess of alkali or alkali earth metal salts or salt mixtures (LiCl, NaCl, KCl). These are added to an alumina crucible, placed in a quartz tube, and sealed under a vacuum. This is heated up to around 1000 °C and slowly cooled to a temperature above the melting point of the salt and at that temperature, the reaction is taken out of the furnace. The excess salt is removed, and the resulting product is analyzed using X-ray diffraction techniques, scanning electron microscopy, and spectroscopic methods such as Raman, UV-Visible, and FTIR spectroscopy.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗
DOE OSTI2024

Coupled Gel/Seeded Growth of Cs2AgBiBr6 Single Crystals for Radiation Detection

Abstract— The all-inorganic lead free Cs2AgBiBr6 perovskite represents a highly promising environment-friendly radiation detector material. The first attempt to grow Cs2AgBiBr6 single crystals using the unique gel growth method is reported in this study. This technique enables controlled reagent diffusion in a gel medium at room temperature, fostering the growth of visible single crystals. It offers advantages over conventional methods, leading to fewer equilibrium and non-equilibrium defects and simplified execution. Interestingly, the as-grown crystals exhibited variations in size and colors within the gel matrix, indicating the influence of Bi solutes in Bi-poor and Bi-rich Cs2AgBiBr6 crystals. Once the crystals were confirmed by powder xray diffraction, a series of comprehensive material characterizations was performed. The resistivity of Cs2AgBiBr6 single crystals was measured at 1.12x107 Ω•cm. Trap density analysis yielded a value of 2.82 x1010 cm-3. The charge carrier mobility was determined to be 32.9 cm2V-1S-1, suggesting the suitability for radiation detector applications. Additional growth optimization is going on and further characterization will be reported during the presentation. Our work helps accelerate the development of lead-free perovskite materials toward radiation detector applications.

James, Ralph B.↗
DOE OSTI2022

Diabatic Hamiltonian matrix elements made simple

With a view to applying the generator coordinate method to large configuration spaces, we propose a simple approximate formula to compute diabatic many-body matrix elements without having to evaluate two-body interaction matrix elements. Here, the method is illustrated with two analytically solvable Hamiltonians based on the harmonic oscillator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗