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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 OSTI2022

r -process nucleosynthesis and kilonovae from hypermassive neutron star post-merger remnants

ABSTRACT We investigate r-process nucleosynthesis and kilonova emission resulting from binary neutron star (BNS) mergers based on a three-dimensional (3D) general-relativistic magnetohydrodynamic (GRMHD) simulation of a hypermassive neutron star (HMNS) remnant. The simulation includes a microphysical finite-temperature equation of state (EOS) and neutrino emission and absorption effects via a leakage scheme. We track the thermodynamic properties of the ejecta using Lagrangian tracer particles and determine its composition using the nuclear reaction network SkyNet. We investigate the impact of neutrinos on the nucleosynthetic yields by varying the neutrino luminosities during post-processing. The ejecta show a broad distribution with respect to their electron fraction Ye, peaking between ∼0.25–0.4 depending on the neutrino luminosity employed. We find that the resulting r-process abundance patterns differ from solar, with no significant production of material beyond the second r-process peak when using luminosities recorded by the tracer particles. We also map the HMNS outflows to the radiation hydrodynamics code SNEC and predict the evolution of the bolometric luminosity as well as broadband light curves of the kilonova. The bolometric light curve peaks on the timescale of a day and the brightest emission is seen in the infrared bands. This is the first direct calculation of the r-process yields and kilonova signal expected from HMNS winds based on 3D GRMHD simulations. For longer-lived remnants, these winds may be the dominant ejecta component producing the kilonova emission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Photometric calibration in u -band using blue halo stars

ABSTRACT We develop a method to calibrate u-band photometry based on the observed colour of blue Galactic halo stars. The Galactic halo stars belong to an old stellar population of the Milky Way and have relatively low metallicity. The ‘blue tip’ of the halo population – the main sequence turn-off (MSTO) stars – is known to have a relatively uniform intrinsic edge u-g colour with only slow spatial variation. In SDSS data, the observed variation is correlated with Galactic Latitude, which we attribute to contamination by higher metallicity disc stars and fit with an empirical curve. This curve can then be used to calibrate u-band imaging if g-band imaging of matching depth is available. Our approach can be applied to single-field observations at |b| > 30°, and removes the need for standard star observations or overlap with calibrated u-band imaging. We include in our method the calibration of g-band data with ATLAS-Refcat2. We test our approach on stars in KiDS DR 4, ATLAS DR 4, and DECam imaging from the NOIRLab Source Catalog (NSC DR2), and compare our calibration with SDSS. For this process, we use synthetic magnitudes to derive the colour equations between these data sets, in order to improve zero-point accuracy. We find an improvement for all data sets, reaching a zero-point precision of 0.016 mag for KiDS (compared to the original 0.033 mag), 0.020 mag for ATLAS (originally 0.027 mag), and 0.016 mag for DECam (originally 0.041 mag). Thus, this method alone reaches the goal of 0.02 mag photometric precision in u-band for the Rubin Observatory’s Legacy Survey of Space and Time (LSST).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Post maximum light and late time optical imaging polarimetry of type I superluminous supernova 2020znr

ABSTRACT Optical imaging polarimetry was conducted on the hydrogen poor superluminous supernova 2020znr during three phases after maximum light (≈ +34 d, +288 d, and +289 d). After instrumental and interstellar polarization correction, all measurements are consistent with null-polarization detection. Modelling the light curve with a magnetar spin-down model shows that SN2020znr has similar magnetar and ejecta parameters to other SLSNe. A comparison of the best-fitting values discussed in the literature on SN 2017egm and SN 2015bn, two hydrogen poor SLSNe showing an increase of polarization after maximum light, suggests that SN 2020znr has higher mass ejecta that may prevent access to the geometry of the inner ejecta with optical polarimetry. The combined information provided by spectroscopy and light-curve analysis of type I SLSNe may be an interesting avenue to categorize the polarization properties of this class of transients. This approach would require to expand the sample of SLSNe polarimetry data currently available with early and late time epochs new measurements.

2015bn↗
DOE OSTI2023

Core-collapse supernovae in the Dark Energy Survey: luminosity functions and host galaxy demographics

ABSTRACT We present the luminosity functions and host galaxy properties of the Dark Energy Survey (DES) core-collapse supernova (CCSN) sample, consisting of 69 Type II and 50 Type Ibc spectroscopically and photometrically confirmed supernovae over a redshift range 0.045 < z < 0.25. We fit the observed DES griz CCSN light curves and K-correct to produce rest-frame R-band light curves. We compare the sample with lower redshift CCSN samples from Zwicky Transient Facility (ZTF) and Lick Observatory Supernova Search (LOSS). Comparing luminosity functions, the DES and ZTF samples of SNe II are brighter than that of LOSS with significances of 3.0σ and 2.5σ, respectively. While this difference could be caused by redshift evolution in the luminosity function, simpler explanations such as differing levels of host extinction remain a possibility. We find that the host galaxies of SNe II in DES are on average bluer than in ZTF, despite having consistent stellar mass distributions. We consider a number of possibilities to explain this – including galaxy evolution with redshift, selection biases in either the DES or ZTF samples, and systematic differences due to the different photometric bands available – but find that none can easily reconcile the differences in host colour between the two samples and thus its cause remains uncertain.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Fundamental effective temperature measurements for eclipsing binary stars – IV. Selection of new benchmark stars and first results for HD 22064

I describe the selection and initial characterization of 20 eclipsing binary stars that are suitable for calibration and testing of stellar models and data analysis algorithms used by the PLATO mission and spectroscopic surveys. The binary stars selected are F-/G-type dwarf stars with M-type dwarf companions that contribute less than 2 per cent of the flux at optical wavelengths. The light curves typically show well-defined total eclipses with very little variability between the eclipses. I have used near-infrared spectra obtained by the APOGEE survey to measure the spectroscopic orbit for both stars in HD 22064. Combined with an analysis of the TESS light curve, I derive the following masses and radii: M 1 = 1.35 ± 0.03M ⊙ , M 2 = 0.58 ± 0.01M ⊙ , R 1 = 1.554 ± 0.014R ⊙ , R 2 = 0.595 ± 0.008R ⊙ . Using R 1 and the parallax from Gaia EDR3, I find that the primary star’s angular diameter is θ = 0.1035 ± 0.0009 mas. The apparent bolometric flux of the primary star is ${\mathcal {F}}_{{\oplus },0} = (7.51\pm 0.09)\times 10^{-9}$ erg cm -2 s -1 . Hence, this F2V star has an effective temperature $T_{\rm eff,1} = 6763{\rm \, K} \pm 39{\rm \, K}$. HD 22064 is an ideal benchmark star that can be used for ‘end-to-end’ tests of the stellar parameters measured by large-scale spectroscopic surveys or stellar parameters derived from asteroseismology with PLATO. The techniques described here for HD 22064 can be applied to the other eclipsing binaries in the sample in order to create an all-sky network of such benchmark stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The GMRT archive atomic gas survey – II. Mass modelling and dark matter halo properties across late-type spirals

Studying the kinematics and mass modelling of galaxies from H i 21 cm data provides valuable insights into the properties of both the baryonic components and the dark matter halo in nearby galaxies. Despite many observational studies, mass modelling of galaxies remains challenging due to different limitations. For example, most of the previous studies involving mass modelling are based on rotation curves derived from 2D velocity fields from H i or H α spectroscopic observation which are often affected by beam smearing and projection effect. However, kinematic modelling done by fitting the ‘Tilted ring model’ to 3D data cube is not affected by these issues. In this study, we present and compare 3D kinematic modelling of a pilot sample of 11 galaxies from the GMRT archive atomic gas survey (GARCIA) using two different publicly available pipelines. We model the observed H i rotation curve using 3.6-μm infrared data and SDSS r-band data for stellar contribution, H i surface density profile for gas, and Navarro–Frenk–White profile for dark matter halo; and employ the Markov chain Monte Carlo optimization method for parameter estimation. Further, to validate our analysis, we revisit important scaling relations, e.g. the M gas –M star relation, M star –M halo relation, M gas –M halo relation and Baryonic Tully–Fisher relation. Here, the scaling relations from our analysis are broadly consistent with that reported in the literature. A larger sample of galaxies from GARCIA in the near future will allow studying these scaling relations in greater details.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The IRX–β relation in kpc-sized star-forming regions in nearby galaxies

The effect of dust attenuation on a galaxy’s light depends on a number of physical properties, such as geometry and dust composition, both of which can vary across the faces of galaxies. To investigate this variation, we continue analysis on star-forming regions in 29 galaxies studied previously. We analyse these regions using Swift /UV Optical Telescope and Wide-field Infrared Survey Explorer images, as well as Sloan Digital Sky Survey/Mapping Nearby Galaxies at Apache Point Observatory emission line maps to constrain the relationship between the infrared excess (IRX) and the ultraviolet spectral index, β, for each star-forming region. This relationship can be used to constrain which dust attenuation law is appropriate for the region. We find that the value of D n (4000) for a region is correlated with both IRX and β, and that the gas-phase metallicity is strongly correlated with the IRX. This correlation between metallicity and IRX suggests that regardless of aperture, metal-rich regions have steeper attenuation curves. We also find that integrated galactic light follows nearly the same IRX–β relationship as that found for kpc-sized star-forming regions. Here, this similarity may suggest that the attenuation law followed by the galaxy is essentially the same as that followed by the regions, although the relatively large size of our star-forming regions complicates this interpretation because optical opacity and attenuation curves have been observed to vary within individual galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The simulated catalogue of optical transients and correlated hosts (SCOTCH)

ABSTRACT As we observe a rapidly growing number of astrophysical transients, we learn more about the diverse host galaxy environments in which they occur. Host galaxy information can be used to purify samples of cosmological Type Ia supernovae, uncover the progenitor systems of individual classes, and facilitate low-latency follow-up of rare and peculiar explosions. In this work, we develop a novel data-driven methodology to simulate the time-domain sky that includes detailed modelling of the probability density function for multiple transient classes conditioned on host galaxy magnitudes, colours, star formation rates, and masses. We have designed these simulations to optimize photometric classification and analysis in upcoming large synoptic surveys. We integrate host galaxy information into the snana simulation framework to construct the simulated catalogue of optical transients and correlated hosts (SCOTCH, a publicly available catalogue of 5-million idealized transient light curves in LSST passbands and their host galaxy properties over the redshift range 0 < z < 3. This catalogue includes supernovae, tidal disruption events, kilonovae, and active galactic nuclei. Each light curve consists of true top-of-the-galaxy magnitudes sampled with high (≲2 d) cadence. In conjunction with SCOTCH, we also release an associated set of tutorials and transient-specific libraries to enable simulations of arbitrary space- and ground-based surveys. Our methodology is being used to test critical science infrastructure in advance of surveys by the Vera C. Rubin Observatory and the Nancy G. Roman Space Telescope.

Astronomy & Astrophysics↗
DOE OSTI2023

Why the observed spin evolution of older-than-solar-like stars might not require a dynamo mode change

ABSTRACT The spin evolution of main-sequence stars has long been of interest for basic stellar evolution, stellar ageing, stellar activity, and consequent influence on companion planets. Observations of older-than-solar late-type main-sequence stars have been interpreted to imply that a change from a dipole-dominated magnetic field to one with more prominent higher multipoles might be necessary to account for the data. The spin-down models that lead to this inference are essentially tuned to the Sun. Here, we take a different approach that considers individual stars as fixed points rather than just the Sun. We use a time-dependent theoretical model to solve for the spin evolution of low-mass main-sequence stars that includes a Parker-type wind and a time-evolving magnetic field coupled to the spin. Because the wind is exponentially sensitive to the stellar mass over radius and the coronal base temperature, the use of each observed star as a separate fixed point is more appropriate and, in turn, produces a set of solution curves that produces a solution envelope rather than a simple line. This envelope of solution curves, unlike a single line fit, is consistent with the data and does not unambiguously require a modal transition in the magnetic field to explain it.

Astronomy & Astrophysics↗
DOE OSTI2024

Tracing back the birth environments of Type Ia supernova progenitor stars: a pilot study based on 44 early-type host galaxies

The environmental dependence of Type Ia supernova (SN Ia) luminosities is well established, and efforts are being made to find its origin. Previous studies typically use the currently observed status of the host galaxy. However, given the delay time between the birth of the progenitor star and the SN Ia explosion, the currently observed status may differ from the birth environment of the SN Ia progenitor star. In this paper, employing the chemical evolution and accurately determined stellar population properties of 44 early-type host galaxies, we, for the first time, estimate the SN Ia progenitor star birth environment, specifically [Fe/H] Birth and [α/Fe] Birth . We show that [α/Fe] Birth has a $30.4^{\text{+10.6}}_{-10.1}{{\ \rm per\ cent}}$ wider range than the currently observed [α/Fe] Current , while the range of [Fe/H] Birth is not statistically different ($17.9^{\text{+26.0}}_{-27.1}{{\ \rm per\ cent}}$) to that of [Fe/H] Current . The birth and current environments of [Fe/H] and [α/Fe] are sampled from different populations (p-values of the Kolmogorov–Smirnov test <0.01). We find that light-curve fit parameters are insensitive to [Fe/H] Birth (<0.9σ for the non-zero slope), while a linear trend is observed with Hubble residuals (HRs) at the 2.4σ significance level. With [α/Fe] Birth , no linear trends (<1.1σ) are observed. Interestingly, we find that [α/Fe] Birth clearly splits the SN Ia sample into two groups: SN Ia exploded in [α/Fe] Birth -rich or [α/Fe ]Birth -poor environments. SNe Ia exploded in different [α/Fe] Birth groups have different weighted-means of light-curve shape parameters: 0.81 ± 0.33 (2.5σ). They are thought to be drawn from different populations (p-value = 0.01). Regarding SN Ia colour and HRs, there is no difference (<1.0σ) in the weighted-means and distribution (p-value > 0.27) of each [α/Fe] Birth group.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The ambiguous AT2022rze: changing-look AGN mimicking a supernova in a merging galaxy system

AT2022rze is a luminous, ambiguous transient located south-east of the geometric centre of its host galaxy at redshift $z = 0.08$. The host appears to be formed by a merging galaxy system. The observed characteristics of AT2022rze are reminiscent of active galactic nuclei (AGNs), tidal disruption events, and superluminous supernovae. The transient reached a peak absolute magnitude of $-$20.2 $\pm$ 0.2 mag, showing a sharp rise (t$_{\mathrm{rise,1/e}} = 27.5 \pm 0.6$ d) followed by a slow decline (t$_{\mathrm{dec,1/e}} = 382.9 \pm 0.6$). Its bumpy light curve and narrow Balmer lines indicate the presence of gas (and dust). Its light curve shows rather red colours, indicating that the transient could be affected by significant host extinction. The spectra reveal coronal lines, indicative of high-energy (X-ray/UV) emission. Archival data reveal no prior activity at this location, disfavouring a steady-state AGN, although an optical spectrum obtained prior to the transient is consistent with an AGN classification of the host. Based on this, we conclude that the transient most likely represents a changing-look AGN at the centre of the smallest component of the merging system.

galaxies: active↗
DOE OSTI2025

SN 2021foa: the bridge between SN IIn and Ibn

ABSTRACT We present the long-term photometric and spectroscopic analysis of a transitioning SN IIn/Ibn from –10.8 d to 150.7 d post V-band maximum. SN 2021foa shows prominent He i lines comparable in strength to the H $\alpha$ line around peak, placing SN 2021foa between the SN IIn and SN Ibn populations. The spectral comparison shows that it resembles the SN IIn population at pre-maximum, becomes intermediate between SNe IIn/Ibn, and at post-maximum matches with SN IIn 1996al. The photometric evolution shows a precursor at –50 d and a light curve shoulder around 17 d. The peak luminosity and colour evolution of SN 2021foa are consistent with most SNe IIn and Ibn in our comparison sample. SN 2021foa shows the unique case of an SN IIn where the narrow P-Cygni in H $\alpha$ becomes prominent at 7.2 d. The H $\alpha$ profile consists of a narrow (500–1200 km s$^{-1}$) component, intermediate width (3000–8000 km s$^{-1}$) and broad component in absorption. Temporal evolution of the H $\alpha$ profile favours a disc-like CSM geometry. Hydrodynamical modelling of the light curve well reproduces a two-component CSM structure with different densities ($\rho \propto$ r$^{-2}$–$\rho \propto$ r$^{-5}$), mass-loss rates (10$^{-3}$–10$^{-1}$ M$_{\odot }$ yr$^{-1}$) assuming a wind velocity of 1000 km s$^{-1}$ and having a CSM mass of 0.18 M$_{\odot }$. The overall evolution indicates that SN 2021foa most likely originated from an LBV star transitioning to a WR star with the mass-loss rate increasing in the period from 5 to 0.5 yr before the explosion or it could be due to a binary interaction.

Gangopadhyay, Anjasha (ORCID:0000000238845637)↗
DOE OSTI2026

Stacked reverberation mapping of high-redshift quasars in DESI. I. Feasibility analysis

The broad-line region of quasars has long been probed by reverberation mapping techniques that measure time lags between continuum and broad emission-line variations. Stacked reverberation mapping has been proposed as a less observationally expensive alternative to traditional methods. This ensemble approach also reduces biases from small-number statistics. The Dark Energy Spectroscopic Instrument (DESI) is conducting the most extensive spectroscopic survey of quasars to date. We create mock light curves emulating expected DESI quasar observations at redshifts $1.48\lt z\lt 5.2$ and luminosities $44.68 \le \log \lambda L_{1350 \mathring{\rm A}{}} / \mathrm{erg\, s^{-1}} \le 45.99$ to test stacked reverberation mapping feasibility using sparse spectroscopic data paired with well-sampled photometric data. The pipeline, using the lag estimation code JAVELIN (Just Another Vehicle for Estimating Lags In Nuclei), successfully recovers the simulated C IV lags within 1σ of the true values using spectroscopic light curves composed of only a few spectral epochs (2–10) with irregular cadences. We investigate how observational factors, including C IV flux error magnitude, number of stacked quasars, and spectral epoch count, affect performance. This work motivates a pathway for future stacked reverberation mapping projects with large-scale spectroscopic surveys of quasars having $\ge 2$ spectroscopic observations. Our results suggest an economical alternative for constraining and extending the radius–luminosity relation to higher redshifts and luminosities. Subsequently, this relation can be employed more reliably in single-epoch black hole mass measurements and quasar cosmology in these distant regimes.

quasars: general, quasars: supermassive black hole↗
DOE OSTI2026

Collapse of magnetized white dwarfs as site of heavy-element formation and kilonova signal

We present the first end-to-end calculation connecting the accretion-induced collapse (AIC) of a magnetized, rapidly rotating white dwarf to observable kilonova signatures, combining two-dimensional (2D) general-relativistic neutrino-magnetohydrodynamic simulations, followed by radiation hydrodynamics with in-situ nuclear network and 2D Monte Carlo radiative transfer with spatially resolved heating rates. Unlike all previous unmagnetized AIC models – which predicted proton-rich, $^{56}$Ni-dominated ejecta – strong magnetic fields eject ${\approx }\, 0.2\, \mathrm{ M}_\odot$ of neutron-rich material ($\langle Y_e \rangle \sim 0.24$) on dynamical time-scales, before neutrino irradiation can raise the electron fraction, enabling strong r-process nucleosynthesis up to and beyond the third peak. The resulting kilonova is lanthanide-rich ($X_{\rm lan} \approx 8~{{\ \rm per\ cent}}$) and dominated by near-infrared emission. We compute synthetic light curves in the Large Synoptic Survey Telescope and J ames Webb Space Telescope bands and find striking agreement, without parameter tuning, between the observations of AT 2023vfi/GRB 230307A and our broadband light curves for polar viewing angles. These results establish magnetized AIC as a viable channel for heavy r-process element production and a compelling progenitor candidate for long-duration gamma-ray bursts with kilonova signatures.

MHD↗
DOE OSTI2025

Disorder-induced spin excitation continuum and spin-glass ground state in the inverse spinel CuGa 2 O 4

Spinel-structured compounds serve as prototypical examples of highly frustrated systems and are promising candidates for realizing the long-sought quantum spin liquid (QSL) state. However, structural disorder is inevitable in many real QSL candidates and its impact remains a topic of intense debate. In this work, we conduct comprehensive investigations on CuGa 2 ⁢ O 4 , a spinel compound with significant structural disorder, focusing on its thermodynamic properties and spectroscopic behaviors. No long-range magnetic order is observed down to ∼80 mK, as evidenced by magnetic susceptibility, specific-heat, and elastic neutron scattering measurements. More intriguingly, inelastic neutron scattering experiments reveal a broad gapless continuum of magnetic excitations around the Brillouin zone boundary, resembling the magnetic excitation spectra expected for a QSL. Nevertheless, a spin-freezing transition at 𝑇 f ≈ 0.88 K is identified from the cusp in the dc susceptibility curves, where a bifurcation between zero-field-cooling and field-cooling curves occurs. Furthermore, ac susceptibility measurements show a peak close to 𝑇 f at low frequency, which shifts to higher temperature with increasing frequency. These results show that CuGa 2 ⁢ O 4 has a spin-glass ground state, consistent with the establishment of short-range order inferred from the specific-heat measurements. Collectively, these results illustrate the crucial role of disorder in defining the excitation spectrum out of the disordered ground state. Furthermore, our findings shed light onto the broader class of 𝐴⁢𝐵 2 ⁢O 4 spinels and advance our understanding of the spin dynamics in magnetically disordered systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Temperature and conductivity in shock compressed bridgmanite MgSiO 3 up to 2 TPa

The melting behavior and transport properties of MgSiO 3 at multi-megabar pressures remain poorly constrained despite their importance for high-pressure silicate physics. Here we report the first direct measurements of temperature and optical reflectivity in shock-compressed bridgmanite (MgSiO 3 ) using laser-driven decaying shock compression combined with velocimetry and optical pyrometry. Temperature and reflectivity data spanning approximately 4000–60 000 K were used to constrain the MgSiO 3 melting curve and to infer its electrical conductivity. We find that the MgSiO 3 melting curve becomes shallower than that of iron above 400 GPa, yielding lower melting temperatures in planetary mantles than predicted by several previous theoretical estimates. Across the solid-liquid transition, the inferred electrical conductivity increases significantly, reaching ∼2000 Ω cm −1 . These results provide experimental benchmarks for theoretical models of silicate melting and transport under extreme pressure-temperature conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Absolute dissociative electron attachment cross-section measurement of difluoromethane

Dissociative electron attachment (DEA) to difluoromethane (CH 2 F 2 ) has been studied in the electron energy range of 0 to 16 eV. Two resonant states around 2 and 11.4 eV leading to three different fragment anions (F - , CHF - , and F 2 - ) are observed. Ion-yield curves of the negative ions help us to locate the position of the resonant states. In the ion-yield curve of F - ions, one small hump near 9.8 eV followed by a peak around 15.2 eV is also observed. Absolute DEA cross sections of the F - ion is measured by using the well-known relative flow technique. Dissociation channels associated with each resonant states are identified by density-functional theory (DFT) calculations of the threshold energies. The theory matches quite well within the experimental uncertainty.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Phonon dispersion of Mo-stabilized γ -U measured using inelastic x-ray scattering

We have measured the room-temperature phonon spectrum of Mo-stabilized γ–U. The dispersion curves show unusual softening near the H point, q = [1/2,1/2,1/2], which may derive from the metastability of the γ–U phase or from strong electron-phonon coupling. Near the zone center, the dispersion curves agree well with theory, though significant differences are observed away from the zone center. The experimental phonon density of states is shifted to higher energy compared to theory and high-temperature neutron scattering. As a result, the elastic constants of γ-UMo are similar to those of body-centered cubic elemental metals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗