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DOE OSTI2021

Independent normalization for γ -ray strength functions: The shape method

Here, the shape method, a novel approach to obtain the functional form of the γ-ray strength function (γSF), is introduced. In connection with the Oslo method the slope of the nuclear level density (NLD) and γSF can be obtained simultaneously even in the absence of neutron resonance spacing data. The foundation of the shape method lies in the primary γ-ray transitions which preserve information on the functional form of the γSF. The shape method has been applied to 56 Fe, 92 Zr, and 164 Dy, which are representative cases for the variety of situations encountered in typical NLD and γSF studies. The comparisons of results from the shape method to those from the Oslo method demonstrate that the functional form of the γSF is retained regardless of nuclear structure details or J π values of the states fed by the primary transitions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Shape of atomic nuclei in heavy ion collisions

In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flows v n are linearly related to the strengths of the multipole shape of the distribution of nucleons in the transverse plane, ε n : v n ∝ε n . The ε n , for n=1, 2, 3, 4, are sensitive to the shapes of the colliding ions, characterized by the quadrupole β 2 , octupole β 3 , and hexadecapole β 4 deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, $\langleε^{2}_{n}\rangle$ = $a^{'}_{n} + b^{'}_{n}β^{2}_{n}$, for events in a fixed centrality. The $\langleε^{2}_{1}\rangle$ has a contribution from β 3 and β 4 , and $\langleε^{2}_{3}\rangle$ from β 4 . In ultracentral collisions, there are little cross contributions between β 2 and ε 3 and between β 3 and ε 2 , but clear cross contributions are present in noncentral collisions. Additionally, $\langleε^{2}_{n}\rangle$ are insensitive to nonaxial shape parameters such as the triaxiality. This is good news because the measurements of v 2 , v 3 , and v 4 can be used to constrain simultaneously the β 2 , β 3 , and β 4 values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical $a^{'}_{n}$, to obtain a simple equation that relates the β n of the two species. Finally, this opens up the possibility to map the shape of the atomic nuclei at a timescale (<10 –24 s) much shorter than probed by low-energy nuclear structure physics (<10 –21 s), which ultimately may provide information complementary to that obtained in the nuclear structure experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Investigation of octupole collectivity near the A = 72 shape-transitional point

Enhanced octupole collectivity is expected in the neutron-deficient Ge, Se and Kr isotopes with neutron number N ≈ 40 and has indeed been observed for 70,72 Ge. Shape coexistence and configuration mixing are, however, a notorious challenge for theoretical models trying to reliably predict octupole collectivity in this mass region, which is known to feature rapid shape changes with changing nucleon number and spin of the system. To further investigate the microscopic configurations causing the prolate-oblate-triaxial shape transition at A ≈ 72 and their influence on octupole collectivity, the rare isotopes 72 Se and 74,76 Kr were studied via inelastic proton scattering in inverse kinematics. While significantly enhanced octupole strength of ≈32 Weisskopf units (W.u.) was observed for 72 Se, only strengths of ≈15 W.u. were observed for 74,76 Kr. In combination with existing data, the new data clearly question a simple origin of enhanced octupole strengths around N = 40. Furthermore, the present work establishes two regions of distinct octupole strengths with a sudden strength increase around the A = 72 shape transitional point.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Asymmetric jet shapes with two-dimensional jet tomography

Two-dimensional (2D) jet tomography is a promising tool to study jet medium modification in high-energy heavy-ion collisions. It combines gradient (transverse) and longitudinal jet tomography for selection of events with localized initial jet production positions. It exploits the transverse asymmetry and energy loss that depend, respectively, on the transverse gradient and jet path length inside the quark-gluon plasma (QGP). In this study, we employ 2D jet tomography to study medium modification of the jet shape of γ -triggered jets within the linear Boltzmann transport (LBT) model for jet propagation in heavy-ion collisions. Our results show that jets with small transverse asymmetry ( A N n ⃗ ) or small γ -jet asymmetry ( x J γ = p T jet / p T γ ) exhibit a broader jet shape than those with larger A N n ⃗ or x J γ , since the former are produced at the center and go through longer path lengths while the later are off center and close to the surface of the QGP fireball. In events with finite values of A N n ⃗ , jet shapes are asymmetric with respect to the event plane. Hard partons at the core of the jet are deflected away from the denser region while soft partons from the medium response at large angles flow toward the denser part of QGP. Future experimental measurements of these asymmetric features of the jet shape can be used to study the transport properties of jets and medium responses. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

Theoretical study of triaxial shapes of neutron-rich Mo and Ru nuclei

Here, whether atomic nuclei can possess triaxial shapes at their ground states is still a subject of ongoing debate. According to theory, good prospects for low-spin triaxiality are in the neutron-rich Mo-Ru region. Recently, transition quadrupole moments in rotational bands of even-mass neutron-rich isotopes of molybdenum and ruthenium nuclei have been measured. The new data have provided a challenge for theoretical descriptions invoking stable triaxial deformations. The purpose of this study is to understand experimental data on rotational bands in the neutron-rich Mo-Ru region, we carried out theoretical analysis of moments of inertia, shapes, and transition quadrupole moments of neutron-rich even-even nuclei around 110 Ru using self-consistent mean-field and shell model techniques. Methods: To describe yrast structures in Mo and Ru isotopes, we use nuclear density functional theory (DFT) with the optimized energy density functional UNEDF0. We also apply triaxial projected shell model (TPSM) to describe yrast and positive-parity, near-yrast band structures. As a result, our self-consistent DFT calculations predict triaxial ground-state deformations in 106,108 Mo and 108,110,112 Ru and reproduce the observed low-frequency behavior of moments of inertia. As the rotational frequency increases, a negative-gamma structure, associated with the aligned ν(h 11/2 ) 2 pair, becomes energetically favored. The computed transition quadrupole moments vary with angular momentum, which reflects deformation changes with rotation; those variations are consistent with experiment. The TPSM calculations explain the observed band structures assuming stable triaxial shapes. Lastly, the structure of neutron-rich even-even nuclei around Ru-110 is consistent with triaxial shape deformations. Our DFT and TPSM frameworks provide a consistent and complementary description of experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Shape Changes in the N = 28 Island of Inversion: Collective Structures Built on Configuration-Coexisting States in 43 S

The neutron-rich nuclei in the N = 28 island of inversion have attracted considerable experimental and theoretical attention, providing great insight into the evolution of shell structure and nuclear shape in exotic nuclei. In this study, for the first time, quadrupole collectivity is assessed simultaneously on top of the 3/2 - ground state and the 7/2 - shape-coexisting isomer of 43 S, putting the unique interpretation of shape and configuration coexistence at N = 27 and 28 in the sulfur isotopic chain to the test. From an analysis of the electromagnetic transition strengths and quadrupole moments predicted within the shell model, it is shown that the onset of shape coexistence and the emergence of a simple collective structure appear suddenly in 43 S with no indication of such patterns in the N = 27 isotone 45 Ar.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Spectrotemporal Shaping of Attosecond X-Ray Pulses with a Fresh-Slice Free-Electron Laser

We propose a scheme allowing coherent shaping, i.e., controlling both the amplitude and phase, of attosecond x-ray pulses at free-electron lasers. Here, we show that by seeding an FEL with a short coherent seed that overfills the amplification bandwidth, one can shape the Wigner function of the pulse by controlling the undulator taper profile. The examples of controllable pulse pairs and trains, as well as isolated spectrotemporally shaped pulses with very broad bandwidths are examined in detail. Existing attosecond XFELs can achieve these experimental conditions in a two-stage cascade, in which the seed is generated by a short current spike in an electron bunch and shaped in an unspoiled region within the same bunch. We experimentally demonstrate the production and control of phase-stable pulse trains using this method at the Linac Coherent Light Source II.

47 OTHER INSTRUMENTATION↗

DOE OSTI2018

Direct observations of shape fluctuation in long-time atomistic simulations of metallic nanoclusters

Metallic nanoclusters are functional materials whose unique physical and chemical properties are sensitively controlled by their shapes and structures. An in-depth understanding of their morphological stability is therefore of crucial importance. It has been well documented by transmission electron microscopy (TEM) studies that metallic nanoclusters can interconvert between different isomers. However, the relevant mechanisms remain elusive because the timescales of such shape fluctuations are too short to be resolved experimentally and yet too long for conventional atomistic simulations. By employing massively parallel accelerated molecular dynamics (AMD) simulations reaching timescales of milliseconds, here we provide a clear description of the dynamical processes leading to shape fluctuation in metallic nanoclusters of platinum, silver, copper, and gold at different sizes and temperatures. In all these materials, direct transformations between face-centered-cubic and fivefold symmetric structures (decahedron or icosahedron) are observed away from the melting point. These transitions occur following either a slip-mediated twinning mechanism or a surface-reconstruction driven process. The identified pathways are shown to be reversible, allowing for genuine shape fluctuation processes that do not involve melting or other external factors.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Characterization of the shape and line-edge roughness of polymer gratings with grazing incidence small-angle X-ray scattering and atomic force microscopy

Grazing-incidence small-angle X-ray scattering (GISAXS) is increasingly used for the metrology of substrate-supported nanoscale features and nanostructured films. In the case of line gratings, where long objects are arranged with a nanoscale periodicity perpendicular to the beam, a series of characteristic spots of high-intensity (grating truncation rods, GTRs) are recorded on a two-dimensional detector. The intensity of the GTRs is modulated by the three-dimensional shape and arrangement of the lines. Previous studies aimed to extract an average cross-sectional profile of the gratings, attributing intensity loss at GTRs to sample imperfections. Such imperfections are just as important as the average shape when employing soft polymer gratings which display significant line-edge roughness. Herein are reported a series of GISAXS measurements of polymer line gratings over a range of incident angles. Both an average shape and fluctuations contributing to the intensity in between the GTRs are extracted. Lastly, the results are critically compared with atomic force microscopy (AFM) measurements, and it is found that the two methods are in good agreement if appropriate corrections for scattering from the substrate (GISAXS) and contributions from the probe shape (AFM) are accounted for.

36 MATERIALS SCIENCE↗

DOE OSTI2015

A new gamma-ray detector, 3-dimension, fast scanning table for pulse-shape analysis

The state-of-the art gamma-ray spectrometers such as AGATA and GRETA are using position sensitive multi-segmented HPGe crystals. Pulse-shape analysis (PSA) allows to retrieve the localisation of the gamma interactions and to perform gamma-ray tracking within germanium. The precision of the localisation depends on the quality of the pulse-shape database used for comparison. The IPHC laboratory developed a new fast scanning table allowing to measure experimental pulse shapes in the whole volume of any crystal. The results of the scan of an AGATA 36-fold segmented tapered coaxial detector are shown here, 48580 experimental pulse shapes are extracted within 2 weeks of scanning. These data will contribute to AGATA PSA performances, but have also applications for gamma cameras or Compton-suppressed detectors. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

A New Shape Optimization Approach for Lightweighting Electric Machines Inspired by Additive Manufacturing

Minimizing the mass in electric machines while maintaining superior performance is a new requirement for the advancement of drivetrains used in wind energy and electric mobility. Topology optimization (TO) for lightweighting electric machines using traditional approaches typically explores a restricted design space allowed by standard parametrizable geometry and manufacturing, while advanced methods, such as cell-based density approaches, suffer from a lack of robust manufacturability constraints during the optimization process. To overcome these drawbacks, we explore a grid-independent, boundary optimization where the outer shape of the magnet is parameterized using Bezier curves. We conduct a design of experiments (DOE) to study the effect of different magnet shapes on machine performance by varying the control points on the Bezier curves. A machine-learning-based surrogate model is constructed using the data from the DOE to quantify the relationship between the control points, air-gap torque, and mass. The control points are then optimized to maximize the torque density. The approach is used for minimizing electrical steel mass in the International Energy Agency (IEA) 15-MW radial flux direct-drive wind turbine generator. The new approach to shape optimization resulted in smooth and concise shapes that can be easily additively manufactured with up to a 20-ton reduction in electrical steel mass.

additive manufacturing↗

DOE OSTI2026

Measuring X-Ray Emission Line Shapes in Neutral Species for XRISM Calibration

Space X-ray spectrometers such as the Resolve instrument on XRISM require precise calibration in order to interpret the spectra of astrophysical objects. Key components of the calibration are the energy scale and the core line spread function, both of which vary with photon energy. A major issue in the calibration of high-resolution spectrometers is locating good calibrators with well-known and stable intrinsic line shapes. Neutral fluorescence is widely used, but inner-shell transitions in neutral atoms often exhibit complex, poorly documented line shapes that vary with excitation conditions. Here, in this study, we present empirical measurements of K-shell transitions in neutral O and F below 1 keV using an engineering model XRISM calorimeter array, an electron bombardment modulated X-ray source, and an electron beam ion trap (EBIT) to provide a precise energy reference. In addition, we report measurements of the Mo Lα complex with the transition-edge microcalorimeter spectrometer (TEMS), which reveal strong satellite structure and sensitivity of the line shape to the incident exciting spectrum. Together, these results demonstrate the need for empirical line-shape models, highlight the nonstationary nature of neutral fluorescence features, and define a path toward developing transfer standards for XRISM and future precision instruments such as Athena/X-IFU.

Astronomy and AstroPhysics↗

DOE OSTI2017

Net shape processing of alnico magnets by additive manufacturing

Alternatives to rare earth permanent magnets, such as alnico, will reduce supply instability, increase sustainability, and could decrease the cost of permanent magnets, especially for high temperature applications, such as traction drive motors. Alnico magnets with moderate coercivity, high remanence, and relatively high energy product are conventionally processed by directional solidification and (significant) final machining, contributing to increased costs and additional material waste. Additive manufacturing (AM) is developing as a cost effective method to build net-shape three-dimensional parts with minimal final machining and properties comparable to wrought parts. This work describes initial studies of net-shape fabrication of alnico magnets by AM using a laser engineered net shaping (LENS) system. High pressure gas atomized (HPGA) pre-alloyed powders of two different modified alnico “8” compositions, with high purity and sphericity, were built into cylinders using the LENS process, followed by heat treatment. The magnetic properties showed improvement over their cast and sintered counterparts. The resulting alnico permanent magnets were characterized using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), electron backscatter diffraction (EBSD), and hysteresisgraph measurements. Furthermore, these results display the potential for net-shape processing of alnico permanent magnets for use in next generation traction drive motors and other applications requiring high temperatures and/or complex engineered part geometries.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Microwave sintering of complex shapes: From multiphysics simulation to improvements of process scalability

The microwave sintering homogeneity of large and complex shape specimens is analyzed. A new approach enabling the fabrication of complex shapes ceramics via 3D printing and microwave sintering is presented. The use of a dental microwave cavity is shown to enable a substantial level of densification of complex shape components while restricting the grain growth. The homogeneity of the processed samples during microwave sintering is studied by an electromagnetic-thermal-mechanical simulation. The realistic densification behavior, that phenomenologically takes into account the microwave effect, is included in the modeling framework. We observe that the simulation indicates the sharp correlation between the microwave field distribution in the cavity, the temperature profile, and the specimen's shape distortion.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Review—Drag Coefficients of Non-Spherical and Irregularly Shaped Particles

Abstract The knowledge of simple and relatively accurate closure equations for the drag coefficients of nonspherical particles is very important for Eulerian multiphase numerical codes that require such inputs for the solution of the momentum equation. However, the existing correlations for the drag coefficients are laden with high uncertainty, which propagates in the numerical results. This review paper examines critically the state of our knowledge of the drag coefficients of nonspherical particles starting with our understanding of the “size” and “shape” of particles. Lengthscales and other parameters that have been used to characterize sizes of nonspherical particles are presented. Shape factors and shape descriptors that have been used in past correlations are also presented together with an appraisal of their applicability. Several correlations that have been developed for the determination of the drag coefficients of nonspherical particles with regular and irregular shapes are also presented together with available information on their accuracy and applicability. Based on the review of the available correlations general recommendations are offered on the use of the correlations as closure equations and inputs in computatioal fluid dynamics (CFD) codes.

Engineering↗

DOE OSTI2015

Effects of the shape of the foil corners on the irradiation performance of U10Mo alloy based monolithic mini-plates

Monolithic plate-type fuel is a fuel form being developed for high performance research and test reactors to minimize the use of enriched material. These fuel elements are comprised of a high density, low enrichment, U-Mo alloy based fuel foil, sandwiched between Zirconium liners and encapsulated in Aluminum cladding. The use of a high density fuel in a foil form presents a number of fabrication and operational concerns, such as: foil centering, flatness of the foil, fuel thickness variation, geometrical tilting, foil corner shape etc. To benchmark this new design, effects of various geometrical and operational variables on irradiation performance have been evaluated. As a part of these series of sensitivity studies, the shape of the foil corners were studied. To understand the effects of the corner shapes of the foil on thermo-mechanical performance of the plates, a behavioral model was developed for a selected plate from RERTR-12 experiments (Plate L1P785). Both fabrication and irradiation processes were simulated. Once the thermo-mechanical behavior the plate is understood for the nominal case, the simulations were repeated for two additional corner shapes to observe the changes in temperature, displacement and stress-strain fields. The results from the fabrication simulations indicated that the foil corners do not alter the post-fabrication stress-strain magnitudes. Furthermore, the irradiation simulations revealed that post-fabrication stresses of the foil would be relieved very quickly in operation. While, foils with chamfered and filleted corners yielded stresses with comparable magnitudes, they are slightly lower in magnitudes, and provided a more favorable mechanical response compared with the foil with sharp corners.

Finite Element Analysis↗

DOE OSTI2022

Practical guide to understanding goodness-of-fit metrics used in chemical state modeling of x-ray photoelectron spectroscopy data by synthetic line shapes using nylon as an example

Chemical state analysis of a sample surface through fitting bell-shaped curves to x-ray photoelectron spectroscopic polymer data is reviewed using nylon to introduce and discuss aspects of data analysis. Different strategies for modeling chemistry in nylon spectra are presented and in so doing, a case is made to include in published science the design logic and implementation in terms of line shapes and optimization parameter constraints between components in a peak model. Imperfections in line shape relative to the true shape for photoemission lines, when compensated for using constraints to optimization parameters, are shown to provide chemical state information about a sample that justify, for peak models constructed with these limitations, metrics for goodness-of-fit different from those expected for pulse-counted data.

Materials Science↗

DOE OSTI2023

Shape tuning of large area silicon nanotip arrays through reactive ion etching

Nanostructures formed in silicon form an important class of structures that span a broad spectrum of application areas. Of these, columnar structures of silicon featuring tiplike apexes have their own niche applications. Here, the ability to afford shape tunability for these structures further enhances their application potential. In this paper, we present our findings on the large area fabrication of silicon nanotips defined through microsphere lithography and shape tuned through a combination of different reactive ion etching (RIE) techniques. The self-sharpening mechanism of the tips when using nonplanar etch masks (microspheres) under anisotropic etching conditions is elucidated. We further show that depending on the manner of etching (continuous versus discrete multistep etch), identical anisotropic etching recipes produce vastly different tip morphologies. Hourglass-shaped silicon tips were obtained when silicon was subjected to anisotropic followed by isotropic etching conditions. Sharp silicon tips with tip apex radii on the order of 2 nm have been successfully realized when the RIE shape tuned tips were subjected to a series of oxidative sharpening steps.

74 ATOMIC AND MOLECULAR PHYSICS↗