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DOE OSTI2024

Gravitational waveforms: A tale of two formalisms

We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton’s constant, ℎ ∼ 𝐺 + 𝐺 2 + 𝐺 3 (one-loop level), and correspondingly update its comparison with its classically derived multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion. We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [A. Georgoudis et al., J. High Energy Phys. 03 (2024) 089], the term quadratic in the amplitude in the observable-based formalism [D. A. Kosower et al., J. High Energy Phys. 02 (2019) 137] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional (𝑑 − 4)/(𝑑 − 4) finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order ℎ ∼ 𝐺 1 and at order ℎ ∼ 𝐺 3 when including disconnected diagrams in the observable-based formalism.

Astronomy & Astrophysics↗

DOE OSTI2019

Revealing the Nature of Antiferroquadrupolar Ordering in Cerium Hexaboride: CeB 6

The cerium hexaboride (CeB 6 ) f -electron compound displays a rich array of low-temperature magnetic phenomena, including a “magnetically hidden” order, identified as multipolar in origin via advanced x-ray scattering. From first-principles electronic-structure results, we find that the antiferroquadrupolar (AFQ) ordering in CeB 6 arises from crystal-field splitting and yields a band structure in agreement with experiments. With interactions of p electrons between Ce and B 6 being small, the electronic state of CeB 6 is suitably described as Ce(4 f 1 ) 3+ (e – )(B 6 ) 2– . The AFQ state of orbital spins is caused by an exchange interaction induced through spin-orbit interaction, which also splits the J = 5/2 state into a Γ 8 ground state and a Γ 7 excited state. Within the smallest antiferromagnetic (AFM) (111) configuration, an orbital-ordered AFQ state appears during charge self-consistency, and it supports the appearance of a “hidden” order. Furthermore hydrostatic pressure (either applied or chemically induced) stabilizes the AFM (AFQ) states over a ferromagnetic one, as observed at low temperatures.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Octupolar versus Néel Order in Cubic 5d 2 Double Perovskites

We report time-of-flight neutron spectroscopy and neutron and x-ray diffraction studies of the 5 d 2 double perovskite magnets, Ba 2 M OsO 6 ( M = Zn , Mg , Ca ). We find that these materials host antiferromagnetically coupled 5 d 2 Os 6 + ions decorating a face-centered cubic (fcc) lattice and are found to remain cubic down to the lowest temperatures. They all exhibit thermodynamic anomalies consistent with a single phase transition at a temperature T * , and a gapped magnetic excitation spectrum with spectral weight concentrated at wave vectors typical of type-I antiferromagnetic orders. However, while muon spin resonance experiments show clear evidence for time-reversal symmetry breaking below T * , we observe no corresponding magnetic Bragg scattering signal. These results are shown to be consistent with ferro-octupolar symmetry breaking below T * , and are discussed in the context of other 5 d double perovskite magnets and theories of exotic orders driven by multipolar interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Evaluation of Lattice Light Shift at Low 10 -19 Uncertainty for a Shallow Lattice Sr Optical Clock

A Wannier-Stark optical lattice clock has demonstrated unprecedented measurement precision for optical atomic clocks. Here, we present a systematic evaluation of the lattice light shift, a necessary next step for establishing this system as an accurate atomic clock. With precise control of the atomic motional states in the lattice, we report accurate measurements of the multipolar and the hyperpolar contributions and the operational lattice light shift with a fractional frequency uncertainty of 3.5×10 -19 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Spectroscopic Evidence of Kondo-Induced Quasiquartet in CeRh 2 As 2

CeRh 2 As 2 is a new multiphase superconductor with strong suggestions for an additional itinerant multipolar ordered phase. The modeling of the low-temperature properties of this heavy-fermion compound requires a quartet Ce 3 + crystal-field ground state. Here, we provide the evidence for the formation of such a quartet state using x-ray spectroscopy. Core-level photoelectron and x-ray absorption spectroscopy confirm the presence of Kondo hybridization in CeRh 2 As 2 . The temperature dependence of the linear dichroism unambiguously reveals the impact of Kondo physics for coupling the Kramer’s doublets into an effective quasiquartet. Nonresonant inelastic x-ray scattering data find that the | Γ 7 − ⟩ state with its lobes along the 110 direction of the tetragonal structure ( x y orientation) contributes most to the multiorbital ground state of CeRh 2 As 2 . Published by the American Physical Society 2024

Christovam, Denise S. (ORCID:0000000250698107)↗

DOE OSTI2024

Spin-Orbit-Lattice Entangled State in A 2 ⁢MgReO 6 (A = Ca, Sr, Ba) Revealed by Resonant Inelastic X-Ray Scattering

The 5d 1 ordered double perovskites present an exotic playground for studying novel multipolar physics due to large spin-orbit coupling. Here, we present Re L 3 edge resonant inelastic Xray scattering (RIXS) results that reveal the presence of the dynamic Jahn-Teller effect in the A 2 MgReO 6 (A = Ca, Sr, Ba) family of 5d 1 double perovskites. The spin-orbit excitations in these materials show a strongly asymmetric lineshape and exhibit substantial temperature dependence, indicating that they are dressed with lattice vibrations. Our experimental results are explained quantitatively through a RIXS calculation based on a spin-orbit-lattice entangled electronic ground state with the dynamic Jahn-Teller effect taken into consideration. We find that the spin-orbitlattice entangled state is robust against magnetic and structural phase transitions as well as against significant static Jahn-Teller distortions. Our results illustrate the importance of including vibroniccoupling for a complete description of the ground state physics of 5d 1 double perovskites.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Close Proximity to a Quantum Phase Transition in TmZn2⁢GaO5

TmZn2⁢GaO5 is a newly synthesized triangular lattice magnet that exhibits a unique quantum phase characterized by strong Ising anisotropy, a pseudodoublet crystal electric field ground state, and a low-energy gapped excitation at the 𝐾 point. Unlike its well-known counterparts, TmMgGa⁢O4 and YbMgGa⁢O4, this material crystallizes in a distinct hexagonal structure, leading to a platform for investigating frustrated magnetism. Magnetic susceptibility, heat capacity, and inelastic neutron scattering measurements confirm the absence of long-range magnetic order down to 50 mK, placing TmZn2⁢GaO5 in a distinct region of the transverse-field Ising model phase diagram. Theoretical calculations based on spin-wave theory and mean-field modeling reproduce key experimental observations, reinforcing the material’s placement in a quantum disordered or multipolar state near a quantum critical point that separates it from the low-energy phase of TmMgGa⁢O4. These results highlight its potential for exploring quantum disordered states, anisotropic excitations, and exotic quantum phases in frustrated spin systems.

Ennis, Matthew [Department of Physics, Duke Univer↗

DOE OSTI2025

Renormalized classical theory of quantum magnets

Here, we derive a renormalized classical spin (RCS) theory for 𝑆 >1/2 quantum magnets by constraining a generalized classical theory that includes all multipolar fluctuations to a reduced CP 1 phase space of dipolar SU(2) coherent states. When the spin Hamiltonian $\hat{ℋ}$(𝑆) is linear in the spin operators $\hat{𝑺}$ 𝑗 for each lattice site 𝑗, the RCS Hamiltonian $\tilde{ℋ}$ cl coincides with the usual classical model ℋ cl = lim 𝑆→∞⁡ $\hat{ℋ}$(𝑆). In the presence of nonlinear terms, however, the RCS theory is more accurate than ℋ cl . For the many materials modeled by spin Hamiltonians with (nonlinear) single-ion anisotropy terms, the use of the RCS theory is essential to accurately model phase diagrams and to extract the correct Hamiltonian parameters from neutron-scattering data.

magnetic anisotropy↗

DOE OSTI2025

Diffuse scattering from correlated electron systems

The role of inhomegeneity in determining the properties of correlated electron systems is poorly understood because of the dearth of structural probes of disorder at the nanoscale. Advances in both neutron and x-ray scattering instrumentation now allow comprehensive measurements of diffuse scattering in single crystals over large volumes of reciprocal space, enabling structural correlations to be characterized over a range of length scales from 5 to 200 angstroms or more. When combined with new analysis tools, such as three-dimensional difference pair-distribution functions, these advanced capabilities have produced fresh insights into the interplay of structural fluctuations and electronic properties in a broad range of correlated electron materials. This review describes recent investigations that have demonstrated the importance of understanding structural inhomogeneity pertaining to phenomena as diverse as superconductivity, charge density wave modulations, metal-insulator transitions, and multipolar interactions.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Isoscalar and Isovector Giant Resonances in Closed Shells Nuclei and Bulk Properties of Nuclear Matter

Centroid energies, E CEN , of the isoscalar (T = 0) and isovector (T = 1) giant resonances of multipolarities L = 0 – 3 in 40,48 Ca, 68 Ni, 90 Zr, 116 Sn, 144 Sm and 208 Pb, were calculated within the fully self-consistent spherical Hartree-Fock (HF)-based random phase approximation (RPA) theory, using 33 different energy density functionals associated with Skyrme-type effective nucleon-nucleon interactions of the standard form commonly employed in the literature. Here, we also calculate the Pearson linear correlation coefficients between each E CEN and each bulk property of nuclear matter (NM), associated with the Skyrme interactions used in the calculations, and determine the sensitivity of E CEN to bulk properties of NM. By comparing the calculated values of E CEN to the experimental data, we constrain the values of the bulk NM properties. We find that interactions associated with the values of the NM effective mass, m* / m = 0.70 to 0.90, incompressibility coefficient, K NM = 210 to 240 MeV, and the enhancement coefficient of the energy weighted sum rule of the isovector giant dipole resonance, κ = 0.25 to 0.70, best reproduce the experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Propagation of Plasma Bunches through a Transverse Magnetic Barrier

The injection of a plasma bunch into a multipolar trap can be applied to fill the trap with a plasma. The injection of the bunch into a tokamak-like trap can be considered an additional means for controlling the processes of plasma heating and fuel delivery to the central zone of a thermonuclear reactor. In both cases, the bunch is injected normally to the magnetic field of the trap. It has been shown theoretically, experimentally, and by numerical simulation that the depth of plasma bunch penetration into the magnetic field varies in direct proportion to the bunch energy and in inverse proportion to the magnetic pressure and the cross-sectional area of the plasma bunch. The data of this work allow researchers to estimate the values of plasma bunch parameters at which the bunch will be trapped. As a result, the process of plasma bunch trapping has been optimized.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Dielectric metasurfaces made from vertically oriented nanoresonators

Dielectric metasurfaces control optical wavefronts via nanoscale resonators laid out across a surface. However, most metasurfaces are, by design, planar. In this work, we demonstrate the ability to fabricate dielectric metasurfaces with vertically oriented dielectric resonators using membrane projection lithography. We first numerically characterize the resonant modes of an array of vertically oriented germanium ellipses with no substrate and identify a narrowband region where the resonators satisfy the first Kerker condition. We then fabricate seven metasurfaces by depositing germanium ellipses onto walls of a 3D micrometer-sized silicon nitride photonic scaffold and characterize their transmission. We find that signatures of the multipolar modes seen in the unsupported array persist in the supported array, but the overall behavior is more complicated due to the scaffold. Further, we show that for a conceptual metasurface containing two coupled, vertically oriented ellipses, the ellipses can generate a sharp resonance with a quality factor of 240.

Gennaro, Sylvain D. (ORCID:0000000222090831)↗

DOE OSTI2020

Energy density functional and sensitivity of energies of giant resonances to bulk nuclear matter properties

The development of a modern and more realistic nuclear energy density functional (EDF) for accurate predictions of properties of nuclei is the subject of enhanced activity, since it is very important for the study of properties of nuclear matter (NM), giant resonances and, in particular, of properties of rare nuclei with unusual neutron-to-proton ratios. Here, we provide a short review of the current status of the nuclear EDF and the theoretical results obtained for properties of nuclei and nuclear matter. We will first describe a method for determining the parameters of the EDF, associated with the Skyrme type effective interaction, by carrying out a Hartree-Fock based fit to extensive set of data of ground state properties and constraints. Next we will describe the fully self-consistent Hartree-Fock (HF) based random-phase-approximation (RPA) theory for calculating the strength functions S(E) and centroid energies E CEN of giant resonances and the folding model (FM) distorted wave Вorn approximation (DWBA) to calculate the excitation cross section of giant resonances by α scattering. Then we will provide results for: (i) the Skyrme parameters of the KDE0v1 EDF; (ii) consequences of violation of self-consistently in HF-based RPA; (iii) FM-DWBA calculation of excitation cross section; (iv) values of the E CEN of isoscalar and isovector giant resonances of multipolarities L=0–3 for a wide range of spherical nuclei, using 33 EDFs associated with standard form of the Skyrme type interactions, commonly employed in the literature; and (v) the sensitivities E CEN of the giant resonances to bulk properties of NM. We also determine constraints on NM properties, such as the incompressibility coefficient and effective mass, by comparing with experimental data on E CEN of giant resonances.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Evaluated Nuclear Structure Data File (ENSDF)

Contains recommended nuclear structure and decay data for all the known nuclides, which are obtained following a critical review of all available experimental data, supplemented with systematic trend studies and theoretical models. ENSDF data include (i) nuclear level properties, such as observation source, energy, half-life, decay modes, spin and parity; (ii) gamma ray energies, intensities, multipolarities, mixing ratios and conversion coefficients; (iii) nuclear radiation energy and intensity as well as radiation-specific data for different radiation types, such as such as gammas, alphas, betas and neutrons. Data for about 220 nuclides are fully evaluated each year; additionally, many datasets are partially updated each year. Nearly all the evaluation work is supported by the US Nuclear Data Program. The National Nuclear Data Center at Brookhaven National Laboratory is responsible for coordinating the evaluation effort as well as its web and journal dissemination.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Cyber Deterrence and Stability

Throughout the 20th and early 21st centuries, deterrence and arms control have been cornerstones of strategic stability between the superpowers. However, the weaponization of the cyber realm by State actors and the multipolar nature of cyber conflict now undermines that stability. Strategic stability is the state in which nations believe that if they act aggressively to undermine U.S. national interests and the post-World War II liberal democratic order, the consequences will outweigh the benefits. The sense of lawlessness and lack of consequences in the cyber realm embolden States to be more aggressive in taking actions that undermine stability. Accordingly, this paper examines 1) the role of deterrence and arms control in securing cyber stability, and 2) the limitations and challenges associated with these traditional national security paradigms as applied to this emerging threat domain. This paper demonstrates that many 20th-century deterrence and arms control concepts are not particularly applicable in the cyber realm. However, they are not entirely irrelevant. The United States can distill lessons learned from this rich deterrence and arms control experience to develop and deploy a strategy to advance cyber stability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Higher Order Multipole Analysis of Beam Crabbing Mode at 197 MHz for Electron-Ion Collider

In the local crabbing scheme for Electron Ion Collider interaction region, beam rotation is initiated by one set of crab cavities at a high beta region with near 90 deg phase advance to the interaction point (IP), and ceased by an identical set of cavities on the symmetrically opposite side. The fundamental mode of all crab cavities is designed to apply a momentum kick to the particle bunches to complete this half cycle of rotation in the horizontal plane, meanwhile the electromagnetic (EM) field can be expanded into a series of harmonics. Despite the lowest dipole mode, higher harmonics cause instabilities during beam operation and loss of particles. We used SimTrack, which is the 6-d symplectic element-by-element tracking code developed at Brookhaven National Laboratory in 2015, to study the threshold of each higher-order harmonic multipolar mode with the criteria of maintaining a dynamic aperture of 6 σ or greater for the Hadron Storage Ring (HSR). In this paper, we showed the threshold for each higher harmonic multipole and their comparison with the multipole strength for the current crab cavity design.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Exploring Multilayer Network Models to Build a Scientific Basis for Integrated Deterrence: Final Report

The emerging multipolar international security environment represents a fundamental restructuring of global nuclear balance of power to include two nuclear peer competitors, growing non-peer nuclear threats, and concerns of nuclear latency from both allies and adversaries. Conflicts in the grey zone, cyber operations, mis- and disinformation campaigns, and emerging disruptive technologies like drones, and hypersonic missiles are becoming more prevalent. These present a risk of cross-domain and multi-domain conflicts that may not follow known escalatory patterns. In order to prepare for the new deterrence environment, it is critical to have quantitative and qualitative understandings of these cross-domain conflicts, their potential for escalation, and which systems they may impact. To that end, our team created a Multi-Layer Network (MLN) model of ‘integrated deterrence’ where instruments of national power are modeled as individual network graph layers that include efforts from all domains. We then evaluate the potential for escalation against escalation scenarios. Analysis of the escalation scenarios is then used to identify insights of potential risk and escalation within integrated deterrence.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2025

From Stewardship to Transformation: Toward a Nuclear Enterprise for the 21st Century

The erosion of the global security environment over the last two decades has been rapid and dramatic. It appears also to be accelerating. There are deep and widening concerns in the United States and among its allies and partners that deterrence too has eroded at both the conventional and nuclear levels. The Strategic Posture Commission captured the essence of the problem in its October 2023 report—the United States seeks to meet the challenges of complex multipolar nuclear rivalry in the 21 st century with a slimmed down version of a nuclear deterrent designed in the middle of the 20 th century. With great urgency, the Commission recommended that something more and/or different is needed than simply the replacement of legacy systems with modern variants. But the U.S. nuclear security enterprise was reshaped after the Cold War to support the stockpile stewardship mission—not renewed designed, engineering, and production at scale. It has long fallen short of the agility, flexibility, and adaptiveness periodically asked of it by national leaders. In recent years, however, the message of urgency has been clearly received in the enterprise. Its culture has begun to shift. It has also been received by those in Washington D.C. responsible for funding and guiding the enterprise. The result is an enterprise in transition. Stockpile stewardship has given way to stockpile transformation. Risk aversion is giving way to risk management. Innovation and adaptation have been embraced. Experience to date has yielded some important lessons about what works and what doesn’t in terms of accelerating and delivering the needed innovation and adaptation. It has revealed the enduring character of some challenges. But it has also revealed that a much more agile and effective enterprise is within the national reach—something that will pay important dividends for deterrence, assurance, strategic stability, and peace.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗