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DOE OSTI2022

Monitoring the propagation of mechanical discontinuity using data-driven causal discovery and supervised learning

Mechanical wave transmission through a material is influenced by the mechanical discontinuity in the material. The propagation of embedded discontinuities can be monitored by analyzing the wave-transmission measurements recorded by a multipoint sensor system placed on the surface of the material. The proposed workflow monitors the propagation of mechanical discontinuity through three stages, namely initial, intermediate, and final stages, by using supervised learning followed by data-driven causal discovery. To the end, the workflow processes the multipoint waveform measurements resulting from a single impulse source, while considering the effects of wave attenuation, dispersion and multiple wave-propagation modes due to the discontinuity and material boundaries. Among various feature reduction techniques ranging from decomposition methods to manifold approximation methods, the features derived based on statistical parameterizations of the measured waveforms lead to reliable monitoring that is robust to changes in precision, resolution, and signal-to-noise ratio of the multipoint sensor measurements. The numbers of zero-crossing, negative-turning, and positive turning in the waveforms are the strongest causal signatures of the propagation of mechanical discontinuity. Higher order moments of the waveforms, such as variance, skewness and kurtosis, are also strong causal signatures of the propagation. Finally, the newly discovered causal signatures confirm that the statistical correlations and conventional feature rankings are not always statistically significant indicators of causality.

42 ENGINEERING↗

DOE OSTI2025

Arbitrary-velocity laser pulses in plasma waveguides

Space-time structured laser pulses feature an intensity peak that can travel at an arbitrary velocity while maintaining a near-constant profile. These pulses can propagate in uniform media, where their frequencies are correlated with continuous transverse wave vectors, or in structured media, such as a waveguide, where their frequencies are correlated with discrete mode numbers. Here, we demonstrate the formation and propagation of arbitrary-velocity laser pulses in a plasma waveguide where the intensity can be orders of magnitude higher than in a solid-state waveguide. The flexibility to control the velocity of the peak intensity in a plasma waveguide enables new configurations for plasma-based sources of radiation and energetic particles, including THz generation, laser wakefield acceleration, and direct laser acceleration.

42 ENGINEERING↗

DOE OSTI2020

A Search for MeV to TeV Neutrinos from Fast Radio Bursts with IceCube

We present two searches for IceCube neutrino events coincident with 28 fast radio bursts (FRBs) and 1 repeating FRB. The first improves on a previous IceCube analysis - searching for spatial and temporal correlation of events with FRBs at energies greater than roughly 50 GeV - by increasing the effective area by an order of magnitude. The second is a search for temporal correlation of MeV neutrino events with FRBs. No significant correlation is found in either search; therefore, we set upper limits on the time-integrated neutrino flux emitted by FRBs for a range of emission timescales less than one day. These are the first limits on FRB neutrino emission at the MeV scale, and the limits set at higher energies are an order-of-magnitude improvement over those set by any neutrino telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Determining Catalytically Relevant Surfaces through Coverage-Dependent Lattice Gas Models: Carbon Adsorption on Fe(100)

Here, we have quantified the C–C lateral interactions on Fe(100) using a density functional theory (DFT)-parameterized lattice gas cluster expansion (LG CE) model trained using 265 unique configurations spanning a C coverage from 0 to 1 monolayer (ML). Our LG CE model shows high predictive accuracy with a leave-multiple-out cross-validation score of 10.2 and 16.6 meV/site for systems with and without the top two layers of Fe atoms fixed, respectively. Electronic ground-state structures identified from the lattice gas model (including the structures at 0 and 1 monolayers) were further used to generate ab initio phase diagrams under a range of temperatures and pressures. At low temperatures (<400 K), we found that the 1.0 monolayer structure is dominant, whereas at higher temperatures (>500 K), the 0.88 ML structure is most likely to form on the Fe surface. Interestingly, our model identified a c (2 × 2) ordered structure at 1/2 ML, which correlates well with previous DFT studies for carbon adsorption on iron surfaces and matches with the experimentally observed low-energy electron diffraction structure. Overall, the DFT-parameterized energies for the C/Fe system including effects of coverage and configurational space can further help in developing multiscale models for various heterogeneous reactions involving C–C and C–Fe interactions.

08 HYDROGEN↗

DOE OSTI2021

A new hypothesis for the origin of Amazonian Dark Earths

Amazonian Dark Earths (ADEs) are unusually fertile soils characterised by elevated concentrations of microscopic charcoal particles, which confer their distinctive colouration. Frequent occurrences of pre-Columbian artefacts at ADE sites led to their ubiquitous classification as Anthrosols (soils of anthropic origin). However, it remains unclear how indigenous peoples created areas of high fertility in one of the most nutrient-impoverished environments on Earth. Here, we report new data from a well-studied ADE site in the Brazilian Amazon, which compel us to reconsider its anthropic origin. The amounts of phosphorus and calcium—two of the least abundant macronutrients in the region—are orders of magnitude higher in ADE profiles than in the surrounding soil. The elevated levels of phosphorus and calcium, which are often interpreted as evidence of human activity at other sites, correlate spatially with trace elements that indicate exogenous mineral sources rather than in situ deposition. Stable isotope ratios of neodymium, strontium, and radiocarbon activity of microcharcoal particles also indicate exogenous inputs from alluvial deposition of carbon and mineral elements to ADE profiles, beginning several thousands of years before the earliest evidence of soil management for plant cultivation in the region. Our data suggest that indigenous peoples harnessed natural processes of landscape formation, which led to the unique properties of ADEs, but were not responsible for their genesis. If corroborated elsewhere, this hypothesis would transform our understanding of human influence in Amazonia, opening new frontiers for the sustainable use of tropical landscapes going forward.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Analyzing rotational bands in odd-mass nuclei using effective field theory and Bayesian methods

We recently developed an Effective Field Theory (EFT) for rotational bands in odd-mass nuclei. Here we use EFT expressions to perform a Bayesian analysis of data on the rotational energy levels of 99 Tc, 155,157 Gd, 159 Dy, 167,169 Er, 167,169 Tm, 183 W, 235 U and 239 Pu. The error model in our Bayesian analysis includes both experimental and EFT truncation uncertainties. It also accounts for the fact that low-energy constants (LECs) at even and odd orders are expected to have different sizes. We use Markov Chain Monte Carlo (MCMC) sampling to explore the joint posterior of the EFT and error-model parameters and show both the LECs and the breakdown scale can be reliably determined. We extract the LECs up to fourth order in the EFT and find that, provided we correctly account for EFT truncation errors in our likelihood, results for lower-order LECs are stable as we go to higher orders. LEC results are also stable with respect to the addition of higher-energy data. We extract the expansion parameter for all the nuclei listed above and find a clear correlation between the extracted and the expected value of the inverse breakdown scale, W, based on the single-particle and vibrational energy scales. However, the W that actually determines the convergence of the EFT expansion is markedly smaller than would be naively expected based on those scales.

EFT↗

DOE OSTI2025

Measurement of correlated charge noise in superconducting qubits at an underground facility

The charge environment of superconducting qubits may be studied through the introduction of controlled, quantified amounts of ionizing radiation. We measure space- and time-correlated charge jumps on a four-qubit device, operating 107 meters below the Earth’s surface in a low-radiation, cryogenic facility designed for the characterization of low-threshold particle detectors. The rock overburden of this facility reduces the cosmic ray muon flux by over 99% compared to laboratories at sea level. Combined with 4π coverage of a movable lead shield, this facility enables quantifiable control over the flux of ionizing radiation on the qubit device. Long-time-series charge tomography measurements on these weakly charge-sensitive qubits capture discontinuous jumps in the induced charge on the qubit islands, corresponding to the interaction of ionizing radiation with the qubit substrate. The rate of these charge jumps scales with the flux of ionizing radiation on the qubit package, as characterized by a series of independent measurements on another energy-resolving detector operating simultaneously in the same cryostat with the qubits. Using lead shielding, we achieve a minimum charge jump rate of $0.19^{+0.04}_{-0.03}$ mHz, almost an order of magnitude lower than that measured in surface tests, but a factor of roughly seven higher than expected based on reduction of ambient gammas alone. We operate four qubits for over 22 consecutive hours with zero correlated charge jumps at length scales above three millimeters.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Effect of Cooling Rate on Nano-Eutectic Formation in Laser Surface Remelted and Rare Earth Modified Hypereutectic Al-20Si Alloys

Laser Surface Remelting (LSR) was applied to arc-melted Al-20Si-0.2Sr, Al-20Si-0.2Ce, and Al-20Si hypereutectic alloys to refine microstructures. Experiments revealed that microstructures in the melt pool varied from fully eutectic to a mixture of Al dendrites and inter-dendritic eutectic. We calculated cooling rates using the Eagar-Tsai model and correlated cooling rates with characteristic microstructures, revealing that a cooling rate on the order of 104 K/s could lead to maximized fully eutectic microstructure morphology. Due to rapid solidification, the Si composition in the LSR eutectic was measured at 18.2 wt.%, higher than the equilibrium eutectic composition of 12.6 wt.%Si. Compared to Al-20Si, Ce addition had no significant effect on the volume fraction of the fully eutectic structure but refined Si fibers to approximately 30 nm in diameter. Sr addition did not further refine the diameter of eutectic Si fibers compared to Al-20Si but increased the volume fraction of the fully eutectic microstructure morphology. The refinement ratio (φ) of the Si fiber diameter from the bottom of the melt pool to the surface for the three alloys was similar, at around 28%. The established correlation between the cooling rate and the size and morphology of the microstructure within the melt pool will enable tailoring of the microstructure in laser-processed as well as deposited alloys for high strength and plasticity.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Rate-dependent strength and deformation heterogeneity of B4C-reinforced Al composite: Time-resolved imaging with synchrotron X-rays

Dynamic (up to 5500 s -1 ) and quasi-static compression tests are conducted on a 15 wt% B4C particle-reinforced Al (B 4 C/Al) composite. In situ, high-speed synchrotron X-ray phase contrast imaging and digital image correlation are employed to map mesoscale deformation fields at μm and μs scales. The bulk stress–strain curves show significant strain and strain-rate hardening under dynamic compression. The strain-rate sensitivity exponent is an order of magnitude higher at high strain rates (> 10 3 s -1 ) than that at low strain rates (< 10 -2 s -1 ). Strain field mapping demonstrates distinct compressive strain localizations for both quasi-static and dynamic loading. Nevertheless, compressive strain localizations appear denser in spacing under dynamic loading, owing to spontaneous dislocation nucleation in both weak and strong zones. This results in a higher density of geometrically necessary dislocations, which contributes to the higher strain and strain-rate hardening of B 4 C/Al under dynamic loading. Additionally, the ratio of the maximum local strain to the bulk average is 1.5, and the local strain-rate enhancement cannot explain the increased rate sensitivity of B 4 C/Al under dynamic loading. Therefore, the rate-dependent deformation heterogeneity dominates the strain-rate hardening of B 4 C/Al. Postmortem analyses help correlate deformation features to particle- and grain-scale microstructures, yielding consistent results with mesoscale strain fields.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Identification and quantification of distinct active sites in Hf-Beta zeolites for transfer hydrogenation catalysis

Despite the significant progress made in characterizing different framework heteroatom sites that exist in Lewis acidic zeolites with probe molecule adsorption and spectroscopy, methods to reliably quantify site counts remain indefinite and have been primarily limited to Sn and Ti Lewis acid sites. Here, methods to quantify framework Lewis acidic Hf 4+ sites in zeolite Beta (Hf-Beta) with two Lewis base titrants (pyridine, deuterated acetonitrile) were developed using infrared (IR) spectroscopy. Lewis acid site counts for Hf-Beta zeolites were validated by measuring integrated molar extinction coefficients (IMECs; ε, cm μmol –1 ) on Sn-Beta zeolites using identical Lewis base titrants to benchmark site counts with established literature procedures to quantify Lewis acid sites in Beta zeolites from IR spectra. Highlighting the importance of benchmarking active site counts against well-established experimental protocols, IMECs of CD 3 CN bound to open (ε(Sn; 2316 cm –1 ): 1.80 ± 0.25) and closed (ε(Sn; 2308 cm –1 ): 3.76 ± 0.33) Sn sites were ~1.8x larger than those previously reported while total Lewis acid site counts agreed with those measured by pyridine (ε(Sn; 1451 cm –1 ): 1.58 ± 0.16) on six different Sn-Beta zeolites. IMECs measured for IR peaks reflecting pyridine bound to Lewis acidic Hf sites (ε(Hf; 1448 cm –1 ): 1.54 ± 0.21) and CD 3 CN bound to open (ε(Hf; 2313 cm –1 ): 2.40 ± 0.22) and closed (ε(Hf; 2307 cm –1 ): 3.55 ± 0.41) Hf sites, gave similar counts for the total number of Lewis acidic sites across six Hf-Beta zeolites (Si/Hf = 100–413). Consistent with previous reports with Sn-Beta catalysts where open Sn sites are responsible for catalytic turnover, apparent first and zero-order MPVO rate constants (0.01–1 M cyclohexanone in 2-butanol; per total Hf, 373 K) correlated with the total number of open Hf sites, per total Hf, but not with the total number of closed Hf sites or total Lewis acid site counts. Measured initial MPVO rates (0.1 M cyclohexanone in 2-butanol, per open Hf, 373 K) were ~25x higher on hydrophobic Hf-Beta-F than on hydrophilic Hf-Beta-OH zeolites. Overall, the apparent first-order MPVO rate constants (2-butanol solvent, per open Hf, 373 K) were ~6x higher on Hf-Beta-F than on Hf-Beta-OH zeolites. The characterization methods reported here enable normalization of MPVO turnover rates on Sn- and Hf-Beta zeolites by their number of open sites. Finally, this enables performing quantitative rate comparisons across Lewis acid zeolites of varying active site identity, solvation, and pore topology used in liquid-phase catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

A Quenched Disorder in the Quantum-Critical Superconductor CeCoIn 5

Emergent inhomogeneous electronic phases in metallic quantum systems are crucial for understanding high- T c superconductivity and other novel quantum states. In particular, spin droplets introduced by nonmagnetic dopants in quantum-critical superconductors (QCSs) can lead to a novel magnetic state in superconducting phases. However, the role of disorders caused by nonmagnetic dopants in quantum-critical regimes and their precise relation with superconductivity remain unclear. Here, the systematic evolution of a strong correlation between superconductive intertwined electronic phases and antiferromagnetism in Cd-doped CeCoIn 5 is presented by measuring current–voltage characteristics under an external pressure. In the low-pressure coexisting regime where antiferromagnetic (AFM) and superconducting (SC) orders coexist, the critical current ( I c ) is gradually suppressed by the increasing magnetic field, as in conventional type-II superconductors. At pressures higher than the critical pressure where the AFM order disappears, I c remarkably shows a sudden spike near the irreversible magnetic field. In addition, at high pressures far from the critical pressure point, the peak effect is not suppressed, but remains robust over the whole superconducting region. These results indicate that magnetic islands are protected around dopant sites despite being suppressed by the increasingly correlated effects under pressure, providing a new perspective on the role of quenched disorders in QCSs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Non-linear flow modes of identified particles in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}} $ = 5.02 TeV

The pT-differential non-linear flow modes, v 4,22 , v 5,32 , v 6,33 and v 6,222 for π ± , K ± , K$^0_S$ , $p + \bar{p}, Λ + \bar{Λ}$ and &straightphi;-meson have been measured for the first time at $\sqrt{s_{NN}}$ = 5.02 TeV in Pb-Pb collisions with the ALICE detector at the Large Hadron Collider. The results were obtained with a multi-particle technique, correlating the identified hadrons with reference charged particles from a different pseudorapidity region. These non-linear observables probe the contribution from the second and third order initial spatial anisotropy coefficients to higher flow harmonics. All the characteristic features observed in previous p T -differential anisotropic flow measurements for various particle species are also present in the non-linear flow modes, i.e. increase of magnitude with increasing centrality percentile, mass ordering at low p T and particle type grouping in the intermediate p T range. Hydrodynamical calculations (iEBE-VISHNU) that use different initial conditions and values of shear and bulk viscosity to entropy density ratios are confronted with the data at low transverse momenta. These calculations exhibit a better agreement with the anisotropic flow coefficients than the non-linear flow modes. These observations indicate that non-linear flow modes can provide additional discriminatory power in the study of initial conditions as well as new stringent constraints to hydrodynamical calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

The role of RF-induced E×B flows in the mitigation of scrape-off-layer convective transport during ion cyclotron resonance heating

Abstract While multiple experiments have reported a decrease in intermittent fluctuations in the far Scrape-Off-Layer (SOL) during ion cyclotron resonance heating (Antar et al 2010 Phys. Rev. Lett. 105 165001, Li et al 2022 Nucl. Eng. Technol. 54 207–19, Antar et al 2012 Nucl. Fusion 52 103005), the physical mechanism behind this observation has not been fully established yet. In this work, we demonstrate, for the first time, a direct correlation between the amplitude of RF-induced E×B flows and turbulence suppression in the far SOL. Using the Gas Puff Imaging (GPI) diagnostic on Alcator C-Mod, we show again that Ion Cyclotron Range of Frequencies can significantly alter the flow in the SOL and introduce a shear layer in regions magnetically connected close to the antenna (Cziegler et al 2012 Plasma Phys. Control. Fusion 54 105019). With the 4-strap field-aligned antenna operated in dipole phasing, the ratio of the power coupled by the central two straps to the power coupled by the outer two straps was varied. The resulting RF-induced radial electric field magnitude thus varied, and we show that the impact on the far SOL turbulence correlates with the modified E×B velocity. We then apply a newly-developed blob tracking algorithm (Han et al 2022 Sci. Rep. 12 18142) to higher-resolution GPI videos in order to directly observe the process of blob shearing by RF-induced E×B flows. We show that the radially sheared poloidal flows act as a transport barrier by stretching, stopping, and destroying filaments, which is consistent with the observed difference in turbulence statistics.

Diab, R. (ORCID:0000000342065868)↗

DOE OSTI2024

Medium-induced photon bremsstrahlung in neutrino-nucleus, antineutrino-nucleus, and electron-nucleus scattering from multiple QED interactions

Interactions of charged leptons with nuclei and the naive tree-level kinematics of these processes are affected by radiation of photons induced by the QED nuclear medium. We evaluate cross section modifications at leading orders of the number of correlated interactions inside the nucleus, known as the opacity expansion. We derive results for soft and collinear types of the bremsstrahlung at the first three orders in opacity and generalize them to higher orders. We present the leading in opacity energy spectra of soft and collinear photons and radiative energy loss inside the nucleus for experiments with lepton kinematics in the GeV energy range. At leading power of the Glauber soft-collinear effective field theory, the soft radiation is further resummed to all orders both in opacity and in the electromagnetic coupling constant. We find that the soft and collinear medium-induced radiation is vacuumlike, and additional corrections are power suppressed. Despite the negligible modification to the induced photon spectra, the nuclear medium-induced radiation sizably affects the broadening of charged leptons in the direction orthogonal to their propagation. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Embedded random phase approximation for magnetic systems: H 2 dissociative adsorption on Fe(110)

The random phase approximation (RPA), a method for treating electron correlation, has been shown to be superior to standard density functional theory (DFT) approximations in numerous cases. However, the RPA’s computational cost is substantially higher than that of DFT, particularly restricting its application to extended surfaces. The recently introduced embedded RPA (emb-RPA) approach [Wei et al., J. Chem. Phys. 159(19), 194108 (2023)] reduces this computational cost by approximately two orders of magnitude. While previous applications of emb-RPA focused on non-spin-polarized systems, here we extend the approach to ferromagnetic ones. Unlike other embedded correlated wavefunction methods, such as embedded complete active space self-consistent field theory, emb-RPA is advantageous for spin-polarized systems because the RPA is compatible with unrestricted DFT solutions, which are eigenfunctions of the spin angular momentum operator S z but not the total spin-squared operator S 2 . By applying emb-RPA with specific magnetization constraints, we achieved a speedup of two to three orders of magnitude (one order when accounting for the one-time embedding potential optimization cost) with only small errors (∼50 meV) compared to full periodic RPA. Moreover, emb-RPA significantly reduces the over-binding errors of DFT approximations. In conclusion, we anticipate that the acceleration enabled by the spin-polarized emb-RPA approach will broaden the applicability of RPA to magnetic materials.

Density functional theory↗

DOE OSTI2026

Adsorption, charge transfer and a coverage-driven transition of alkali metals on rutile TiO 2 (110)

The interaction of alkali metals with metal oxide surfaces is central to tuning surface reactivity in heterogeneous catalysis and photocatalysis. Here we present a comprehensive DFT+U study of the adsorption of alkali metals (Li, Na, K, Rb, Cs) on the (110) surface of rutile TiO 2 . At low coverage (θ = 1/8), all alkali metals bind preferentially to bridging oxygen sites with adsorption energies in the range −4.06 to −3.33 eV, transferring nearly one full electron (0.92–0.99 |e|) to the substrate and inducing Ti 4+ → Ti 3+ reduction. The excess charge localizes preferentially at subsurface Ti sites in the form of small polarons. Diffusion barriers indicate facile motion along bridging-oxygen rows, whereas inter-row hopping is strongly hindered. Coverage effects were examined systematically for potassium: adsorption energy and charge transfer per K atom decrease monotonically with increasing θ. Strikingly, a sharp energy discontinuity occurs between θ = 4/8 and θ = 5/8 (ΔE ≈ 1 eV per atom), which we identify as a coverage-driven structural transition arising from steric packing constraints and enhanced K–K electrostatic repulsion once every (1×1) surface cell is occupied. This structural transition perfectly correlates with a dramatic drop in the work function down to an ultra-low minimum of 0.84 eV at θ=5/8, followed by a metallization- driven recovery at higher coverages. Ab initio molecular dynamics simulations confirm zigzag K arrangements at moderate coverage (θ = 1/3), while at high coverage (θ = 2/3) short-range K–K correlations emerge without long-range order. These results provide atomistic insight into the structure–activity relationships underlying alkali promotion effects on oxide-supported catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Strongly-overdoped $\mathrm{La}$ 2- $_{x}$$\mathrm{Sr}$$_{x}$$\mathrm{CuO}$ 4 : Evidence for Josephson-coupled grains of strongly-correlated superconductor

The interpretation of how superconductivity disappears in cuprates at large hole doping has been controversial. To address this issue, here we present an experimental study of single-crystal and thin film samples of La 2-x Sr x CuO 4 (LSCO) with x ≥0.25. In particular, measurements of bulk susceptibility on LSCO crystals with x = 0.25 indicate an onset of diamagnetism at T c1 =38.5 K, with a sharp transition to a phase with full bulk shielding at T c2 =18 K, independent of field direction. Strikingly, the in-plane resistivity only goes to zero at T c2 . Inelastic neutron scattering on 0.25 crystals confirms the presence of low-energy incommensurate magnetic excitations with reduced strength compared to lower doping levels. The ratio of the spin gap to T c2 is anomalously large. Our results are consistent with a theoretical prediction for strongly overdoped cuprates by Spivak, Oreto, and Kivelson, in which superconductivity initially develops within disconnected self-organized grains characterized by a reduced hole concentration, with bulk superconductivity occurring only after superconductivity is induced by proximity effect in the surrounding medium of higher hole concentration. Beyond the superconducting-to-metal transition, local differential conductance measurements on an LSCO thin film suggest that regions with pairing correlations survive, but are too dilute to support superconducting order. Future experiments will be needed to test the degree to which these results apply to overdoped cuprates in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Beyond $\rho ^{2/3}$ scaling: microscopic origins and multimessengers of high-density nuclear symmetry energy

The nature and Equation of State (EOS) of dense neutron-rich matter are still very poorly known, while they have broad impacts on many interesting issues in both astrophysics and nuclear physics. In particular, the nuclear symmetry energy $E_{\textrm{sym}}(\rho )$ encoding the cost to make nuclear matter more neutron-rich has been the most uncertain component of the EOS of dense neutron-rich nucleonic matter. It significantly affects the radii, tidal deformations, cooling rates, and frequencies of various oscillation modes of isolated neutron stars as well as the strain amplitude and frequencies of gravitational waves from their mergers, besides its many effects on the structures of nuclei as well as the dynamics and observables of their collisions. Siemens (1970s) observed that $E_{\textrm{sym}}(\rho )$ scales as $(\rho /\rho _0)^{2/3}$ near the saturation density $\rho _0$ of nuclear matter, since both the kinetic part and the potential contribution (quadratic in momentum) exhibit this dependence. The scaling holds if: (1) the nucleon isoscalar potential is quadratic in momentum, and (2) the isovector interaction is weakly density-dependent. After examining many empirical evidences and understanding theoretical findings in the literature, we conclude that: (1) Siemens’ $\rho ^{2/3}$ scaling is robust and serves as a valuable benchmark for both nuclear theories and experiments up to $2\rho _0$ but breaks down at higher densities, (2) Experimental and theoretical findings about $E_{\textrm{sym}}(\rho )$ up to $2\rho _0$ are broadly consistent, but uncertainties remain large for its curvature $K_{\textrm{sym}}(\rho )$ and higher-order parameters, (3) Above $2\rho _0$ , uncertainties grow due to poorly constrained spin-isospin-dependent tensor and three-body forces as well as the resulting nucleon short-range correlations. Looking forward, combining signals from both observations of neutron stars and terrestrial heavy-ion reaction experiments is the most promising path to finally constraining the high-density $E_{\textrm{sym}}(\rho )$ and the EOS of supradense neutron-rich matter. Multiple examples of community efforts to further constrain the high-density $E_{\textrm{sym}}(\rho )$ using both real and mocked data of present and future high-precision observations of neutron stars, as well as heavy-ion collisions involving high-energy rare isotopes, are briefly reviewed.

Li, Bao-An [East Texas A & M Univ., Commerce, TX (↗