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At least 235 records · Page 13

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NASA NTRS1999

Developing a Fundamental Model for an Integrated GPS/INS State Estimation System with Kalman Filtering

This work will demonstrate the integration of sensor and system dynamic data and their appropriate models using an optimal filter to create a robust, adaptable, easily reconfigurable state (motion) estimation system. This state estimation system will clearly show the application of fundamental modeling and filtering techniques. These techniques are presented at a general, first principles level, that can easily be adapted to specific applications. An example of such an application is demonstrated through the development of an integrated GPS/INS navigation system. This system acquires both global position data and inertial body data, to provide optimal estimates of current position and attitude states. The optimal states are estimated using a Kalman filter. The state estimation system will include appropriate error models for the measurement hardware. The results of this work will lead to the development of a "black-box" state estimation system that supplies current motion information (position and attitude states) that can be used to carry out guidance and control strategies. This black-box state estimation system is developed independent of the vehicle dynamics and therefore is directly applicable to a variety of vehicles. Issues in system modeling and application of Kalman filtering techniques are investigated and presented. These issues include linearized models of equations of state, models of the measurement sensors, and appropriate application and parameter setting (tuning) of the Kalman filter. The general model and subsequent algorithm is developed in Matlab for numerical testing. The results of this system are demonstrated through application to data from the X-33 Michael's 9A8 mission and are presented in plots and simple animations.

Canfield, Stephen↗

NASA NTRS2001

Theoretical Studies of Possible Synthetic Routes for the High Energy Density Material Td N4: Excited Electronic States

Vertical electronic excitation energies for single states have been computed for the high energy density material (HEDM) Td N4 in order to assess possible synthetic routes that originate from excited electronic states of N2 molecules. Several ab initio theoretical approaches have been used, including complete active space self-consistent field (CASSCF), state averaged CASSCF (SA-CASSCF), singles configuration interaction (CIS), CIS with second-order and third-order correlation corrections [CIS(D)) and CIS(3)], and linear response singles and doubles coupled-cluster (LRCCSD), which is the highest level of theory employed. Standard double zeta polarized (DZP) and triple zeta double polarized (TZ2P) one-particle basis sets were used. The CASSCF calculations are found to overestimate the excitation energies, while the SA-CASSCF approach rectifies this error to some extent, but not completely. The accuracy of the CIS calculations varied depending on the particular state, while the CIS(D), CIS(3), and LRCCSD results are in generally good agreement. Based on the LRCCSD calculations, the lowest six excited singlet states are 9.35(l(sup)T1), 10.01(l(sup)T2), 10.04(1(sup)A2), 10.07(1(sup)E), 10.12(2(sup)T1), and 10.42(2(sup)T2) eV above the ground state, respectively. Comparison of these excited state energies with the energies of possible excited states of N2+N2 fragments, leads us to propose that the most likely synthetic route for Td N4 involving this mechanism arises from combination of two bound quintet states of N2.

Lee, Timothy J.↗

NASA NTRS2016

Analysis of Pilot Feedback Regarding the Use of State Awareness Technologies During Complex Situations

A flight simulation study was conducted at NASA Langley Research Center to evaluate flight deck systems that (1) predict aircraft energy state and/or autoflight configuration, (2) present the current state and expected future state of automated systems, and/or (3) show the state of flight-critical data systems in use by automated systems and primary flight instruments. Four new technology concepts were evaluated vis-à-vis current state-of-the-art flight deck systems and indicators. This human-in-the-loop study was conducted using commercial airline crews. Scenarios spanned a range of complex conditions and several emulated causal factors and complexity in recent accidents involving loss of state awareness by pilots (e.g. energy state, automation state, and/or system state). Data were collected via questionnaires administered after each flight, audio/video recordings, physiological data, head and eye tracking data, pilot control inputs, and researcher observations. This paper strictly focuses on findings derived from the questionnaire responses. It includes analysis of pilot subjective measures of complexity, decision making, workload, situation awareness, usability, and acceptability.

Evans, Emory↗

NASA NTRS2019

Evaluation of Technology Concepts for Energy, Automation, and System State Awareness in Commercial Airline Flight Decks

A pilot-in-the-loop flight simulation study was conducted at NASA Langley Research Center to evaluate flight deck systems that (1) provide guidance for recovery from low energy states and stalls, (2) present the current state and expected future state of automated systems, and/or (3) show the state of flight-critical data systems in use by automated systems and primary flight instruments. The study was conducted using 13 commercial airline crews from multiple airlines, paired by airline to minimize procedural effects. Scenarios spanned a range of complex conditions and several emulated causal and contributing factors found in recent accidents involving loss of state awareness by pilots (e.g., energy state, automation state, and/or system state). Three new technology concepts were evaluated while used in concert with current state-of-the-art flight deck systems and indicators. The technologies include a stall recovery guidance algorithm and display concept, an enhanced airspeed control indicator that shows when automation is no longer actively controlling airspeed, and enhanced synoptic pages designed to work with simplified interactive electronic checklists. An additional synoptic was developed to provide the flight crew with information about the effects of loss of flight critical data. Data was collected via questionnaires administered at the completion of flight scenarios, audio/video recordings, flight data, head and eye tracking data, pilot control inputs, and researcher observations. This paper presents findings derived from the questionnaire responses and subjective data measures including workload, situation awareness, usability, and acceptability as well as analyses of two low-energy flight events that resulted in near-stall conditions.

Kramer, Lynda J.↗

NASA NTRS2022

A validation of satellite derived cyanobacteria detections with state reported events and recreation advisories across U.S. lakes

Cyanobacteria harmful algal blooms (cyanoHABs) negatively affect ecological, human, and animal health. Traditional methods of validating satellite algorithms with data from water samples are often inhibited by the expense of quantifying cyanobacteria indicators in the field and the lack of public data. However, state recreation advisories and other recorded events of cyanoHAB occurrence reported by local authorities can serve as an independent and publicly available dataset for validation. State recreation advisories were defined as a period delimited by a start and end date where a warning was issued due to detections of cyanoHABs over a state’s risk threshold. State reported events were defined as any event that was documented with a single date related to cyanoHABs. This study examined the presence-absence agreement between 160 state reported cyanoHAB advisories and 1,343 events and cyanobacteria biomass estimated by a satellite algorithm called the Cyanobacteria Index (CI(cyano)). The true positive rate of agreement with state recreation advisories was 69% and 60% with state reported events. CI(cyano) detected a reduction or absence in cyanobacteria after 76% of the recreation advisories ended. CI(cyano) was used to quantify the magnitude, spatial extent, and temporal frequency of cyanoHABs; each of these three metrics were greater (r > 0.2) during state recreation advisories compared to non-advisory times with effect sizes ranging from small to large. This is the first study to quantitatively evaluate satellite algorithm performance for detecting cyanoHABs with state reported events and advisories and supports informed management decisions with satellite technologies that complement traditional field observations.

remote sensing↗

DOE OSTI2026

Exact Fock-State Preparation with $n^{1/4}$ Circuit Depth

Efficient, deterministic, and high-fidelity preparation of large Fock states is essential for scaling bosonic quantum technologies and exploring quantum phenomena at large excitation energies. We introduce a deterministic one-parameter (D1p) protocol that maps Fock-state preparation in an infinite-dimensional Hilbert space onto two-dimensional amplitude amplification. Starting from a coherent state with $|α|\simeq\sqrt{n}$, the initial target-state population scales as $n^{-1/2}$, yielding an iteration count and circuit depth of $\mathcal{O}(n^{1/4})$. Phase matching guarantees unit fidelity in the ideal model; remarkably, preparing $|{10^6}\rangle$ requires only 39 iterations. The protocol uses only displacements and number-selective phase operations, requires no numerical optimization, and further extends to state transfer, general superpositions, finite-dimensional systems, and multipartite entangled states. In the large-amplitude regime, its multi-target form prepares $L$-legged cat states with an iteration count determined only by $L$; cats with up to ten legs require only two iterations, independent of the coherent-state amplitude. This framework provides a broadly applicable route to highly excited bosonic states on platforms supporting these elementary controls.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗

DOE OSTI2025

Engineering long-lived entanglement through dissipation in quantum hybrid solid-state platforms

Spin squeezing, a form of many-body entanglement, is a crucial resource in quantum metrology and information processing. While experimentally viable protocols for generating stable spin squeezing have been proposed in quantum optics setups, there is growing interest in quantum hybrid solid-state systems as alternative platforms for both engineering and exploring many-body quantum phenomena. In this work, we propose a scheme to generate long-lived spin squeezing in an ensemble of solid-state qubits interacting with electromagnetic noise emitted by a squeezed solid-state bath. We identify the conditions under which quantum correlations within the bath can be transferred to the qubit array, driving it into an entangled state independently of its initial configuration. To assess the experimental feasibility of our approach, we analyze the dynamics of an array of solid-state spin defects coupled to a common ferromagnetic bath, which is driven into a non-equilibrium squeezed state through its interaction with a surface acoustic wave mode. Our results demonstrate that the ensemble can exhibit steady-state spin squeezing under suitable conditions, opening new pathways for the generation of robust many-body entanglement in solid-state spin ensembles.

NV centers↗

DOE OSTI2025

Solid-state platform for cooperative quantum dynamics driven by correlated emission

While traditionally regarded as an obstacle to quantum coherence, recent breakthroughs in quantum optics have shown that the dissipative interaction of a qubit with its environment can be leveraged to protect quantum states and synthesize many-body entanglement. Inspired by this progress, here we set the stage for the—as yet uncharted—exploration of analogous cooperative phenomena in hybrid solid-state platforms. We develop a comprehensive formalism for the quantum many-body dynamics of an ensemble of solid-state spin defects interacting with the magnetic field fluctuations of a common solid-state reservoir. Our framework applies to any solid-state reservoir whose fluctuating spin, pseudospin, or charge degrees of freedom generate magnetic fields. To understand whether correlations induced by dissipative processes can play a relevant role in a realistic experimental setup, we apply our model to a qubit array interacting via the spin fluctuations of a ferromagnetic bath. Our results show that the low-temperature collective relaxation rates of the qubit ensemble can display clear signatures of super- and subradiance, i.e., forms of cooperative dynamics traditionally achieved in atomic ensembles. We find that the solid-state analog of these cooperative phenomena is robust against spatial disorder in the qubit ensemble and thermal fluctuations of the magnetic reservoir, providing a route for their feasibility in near-term experiments. Finally, our work lays the foundation for a multiqubit approach to quantum sensing of solid-state systems and the direct generation of many-body entanglement in spin-defect ensembles. Furthermore, we discuss how the tunability of solid-state reservoirs opens up novel pathways for exploring cooperative phenomena in regimes beyond the reach of conventional quantum optics setups.

NV centers↗

DOE OSTI2026

The two radiative states of the Arctic atmosphere and their impacts on the surface energy budget of sea ice

The surface energy budget (SEB) is a central regulator of Arctic climate and sea ice evolution, yet its processes remain poorly constrained due to sparse observations and complex, coupled surface-atmosphere interactions. This study leverages year-long measurements from the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) to provide the most comprehensive assessment to date of the central Arctic SEB and its modulation by atmospheric variability. Ship- and ice-based observations from October 2019 to September 2020 were used to directly measure or tightly constrain each term of the SEB, leading to exceptional energetic closure with the seasonal snow and ice mass balance. The analysis reveals strong seasonal transitions in atmosphere-surface energy transfer that are modulated by the atmospheric state and constrained by the ability of the surface temperature to respond. Classification of the atmosphere into its two dominant radiative states—the semi-transparent (ST) and opaque (OP)—highlights the central role of synoptic-scale variability in clouds. The ST atmospheric state dominated the long winter ice growth season, with limited cloudiness supporting persistent surface radiative cooling and ice growth. The OP state, associated with liquid-containing or thick ice clouds, became dominant in spring, with the combination of increased solar heating and cloud surface longwave warming driving ice and snow melt. Eddy covariance versus bulk approaches for deriving surface turbulent heat fluxes provide vastly different perspectives on the role of turbulence in modulating the SEB. These results establish a high-quality benchmark dataset for Arctic SEB studies and demonstrate how the balance of atmospheric radiative states exerts a first-order control on the annual evolution of the sea ice. The findings have broad implications for advancing observing technologies, understanding Arctic amplification, improving climate models, and predicting future sea ice change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Near-Infrared Photoluminescence from Spin-Flip Excited States of π-Conjugated Tris(quinolinolate) Chromium(III) Complexes

Tuning metal–ligand covalency offers promising design strategies to tailor the photoluminescence (PL) emission energies of metal-centered, spin-flip excited states. Herein, we report a series of tris(quinolinolate) chromium(III) complexes that exhibit record-low near-infrared II emission energies in a fluid solution at room temperature, afforded by their strong metal–ligand covalencies. Appending π-conjugated arylethynyl substituents to quinolinolate ligands resulted in minimal changes to metal–ligand bond lengths, facilitating nearly indiscriminate metal–ligand covalencies for each tris(quinolinolate) chromium(III) complex. As a result, near-infrared II emission was observed across the series, while simultaneously affording careful tuning of the 4 LMCT/ 4 ( 1 ILCT) electronic transition energies across the visible region. Here, detailed analyses of ground-state electronic structures and excited-state electronic transitions revealed that PL arises from a ligand-field, 2 E excited state, admixed with charge-transfer character. This assignment was supported by solvent-dependent near-infrared emission energies and long excited-state lifetimes, consistent with spin-forbidden relaxation (ranging from 115 ± 5 to 123 ± 1 ns across the series). Utilizing spectroscopic data, ligand-field parameters were quantified, further rationalizing the role of strong metal–ligand covalency in enabling near-infrared II emission. Supported by these results, this study presents a new class of ligands that enable room-temperature near-infrared II emission in chromium(III)-based spin-flip excited states.

Absorption spectroscopy↗

DOE OSTI2025

Extended quantum anomalous Hall states in graphene/hBN moiré superlattices

Electrons in topological flat bands can form new topological states driven by correlation effects. The pentalayer rhombohedral graphene/hexagonal boron nitride (hBN) moiré superlattice was shown to host fractional quantum anomalous Hall effect (FQAHE) at approximately 400 mK, triggering discussions around the underlying mechanism and role of moiré effects. In particular, new electron crystal states with non-trivial topology have been proposed. Here, in this paper, we report electrical transport measurements in rhombohedral pentalayer and tetralayer graphene/hBN moiré superlattices at electronic temperatures down to below 40 mK. We observed two more fractional quantum anomalous Hall (FQAH) states and smaller R xx values in pentalayer devices than those previously reported. In the new tetralayer device, we observed FQAHE at moiré filling factors v = 3/5 and 2/3. With a small current at the base temperature, we observed a new extended quantum anomalous Hall (EQAH) state and magnetic hysteresis, where R xy = h/e 2 and vanishing R xx spans a wide range of v from 0.5 to 1.3. At increased temperature or current, EQAH states disappear and partially transition into the FQAH liquid. Furthermore, we observed displacement field-induced quantum phase transitions from the EQAH states to the Fermi liquid, FQAH liquid and the likely composite Fermi liquid. Our observations established a new topological phase of electrons with quantized Hall resistance at zero magnetic field and enriched the emergent quantum phenomena in materials with topological flat bands.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Simplified calculation of the area specific impedance for solid-state battery design

Simplified algebraic area specific impedance (ASI) correlations have been developed for solid-state composite battery electrodes made of a single ion conducting electrolyte, conductive additive, and intercalation active material. Two ASI expressions were developed, one for short times ( i.e. , pulsed power operation) and another for the pseudo steady state operation (i.e., sustained discharge for energy estimation). A full electrochemical model based on porous electrode theory was developed to examine the accuracy of the simplified ASI expressions. The simplified expressions agree favorably with full model results over a wide range of parameters (i.e. , electrode thicknesses, electrolyte conductivities, solid-state diffusion coefficients, specific surface areas, etc.) and conditions (i.e. , C-rates, states of charge, and pulse times). Under most conditions, the error between the full model and the correlations is well below 7 %. Higher errors were observed for the pseudo steady state expression at high/ low states of charge where the assumption of uniform reaction distributions loses validity. Here, the short time ASI has higher error at low states of charge due to the nonlinearity of the open circuit voltage equation, which is assumed linear in the formulation of the simplified algebraic expression.

25 ENERGY STORAGE↗

DOE OSTI2025

Unraveling the Surface Termination and Evolution of Surface States for Electrocatalyst PtSn 4 in Alkaline HER

Semimetal PtSn 4 has been experimentally demonstrated as a promising topological electrocatalyst for the hydrogen evolution reaction (HER) under both acidic and alkaline conditions. While two possible mechanisms have been proposed to explain its activity, the role of its surface states in HER remains unclear. It is indeed in question how the surface states of this alloy evolve as HER proceeds. In this study, we investigate the surface termination that sustains conducting surface states on PtSn 4 , and we track their evolution during HER catalysis. We show that a reconstructed surface with a Sn-poor termination reproduces the scanning tunneling microscopy pattern observed in experiments and sustains a conducting surface. Through phase diagram and geometric structure analysis, we outline the HER profile following the Volmer–Heyrovsky mechanism. As hydrogen atoms adsorb onto the surface, the structure undergoes further reconstruction to an equilibrium phase with a coverage of two hydrides per unit cell. Meanwhile, the surface electronic bands evolve in response to interactions with the adsorbed hydrogen atoms. A hybridization diagram is further proposed for understanding the surface state evolution based on wave function and chemical bonding analyses. While the Pt atoms serve as conventional sites for hydrogen binding, the surface states of PtSn 4 are essential for stabilizing the hydrogen antibonding states via in-phase electronic interactions with the Sn components. This stabilization results in frontier surface bands that are responsible for driving the HER catalysis. Here, our findings provide a detailed description for the direct involvement of surface states on PtSn4 when employed as a catalyst for HER.

catalysts↗

DOE OSTI2025

On-chip terahertz emission from Floquet-Bloch states [Invited]

Floquet engineering uses time-periodic electromagnetic fields to modify the electronic properties of quantum materials via the creation of Floquet-Bloch states. These photon-dressed states inherit features from both the material and the driving field, enabling the exploration and control of quantum phenomena in light-matter hybrid systems. In non-centrosymmetric materials, shift currents can arise from the quantum geometric properties of electronic wavefunctions. However, shift currents from Floquet-Bloch states remain experimentally unexplored. Here, we employ an on-chip optoelectronic circuit to detect intrinsic terahertz emission from Floquet-Bloch states in T d -WTe 2 under intense optical driving. We observe strong edge-localized terahertz emission that scales linearly with the driving field, consistent with the theoretical prediction for shift currents generated by Floquet-Bloch states. The results advance our understanding of strongly driven quantum materials and provide insights for developing efficient, bias-free terahertz sources for future optoelectronic technologies.

Li, Xinyu [Max Planck Institute for the Structure ↗

DOE OSTI2025

Robust quantification of the diamond nitrogen-vacancy center charge state via photoluminescence spectroscopy

Nitrogen vacancy (NV) centers in diamond are at the heart of many emerging quantum technologies, all of which require control over the NV charge state. Hence, methods for quantification of the relative photoluminescence intensities of the NV 0 and NV − charge states, i.e., a charge state ratio, are vital. Several approaches to quantify NV charge state ratios have been reported but are either limited to bulk-like NV diamond samples or yield qualitative results. We propose an NV charge state quantification protocol based on the determination of sample- and experimental setup-specific NV 0 and NV − reference spectra. The approach employs blue (400–470 nm) and green (480–570 nm) excitation to infer pure NV 0 and NV − spectra, which are then used to quantify NV charge state ratios in subsequent experiments via least squares fitting. We test our dual excitation protocol (DEP) for a bulk diamond NV sample and 20 and 100 nm nanodiamond particles and compare results with those obtained via other commonly used techniques such as zero-phonon line fitting and non-negative matrix factorization. We find that DEP can be employed across different samples and experimental setups and yields consistent and quantitative results for NV charge state ratios that are in agreement with our understanding of NV photophysics. By providing robust NV charge state quantification across sample types and measurement platforms, DEP will support the development of NV-based quantum technologies.

Color center laser spectroscopy↗

DOE OSTI2026

Role of the Character of the Excited State of Singly Reduced Rh 2 (II,II) Intermediates on Photocatalytic Activity

Singly reduced intermediates have recently been implicated as photoactive intermediates in a number of important reactions; however, their photophysical properties remain poorly understood. A series of dirhodium(II,II) complexes, cis-[Rh 2 (p-R-Form) 2 (bncn) 2 ] 2+ (bncn = benzo[c]cinnoline; p-R-Form = N,N′-di-p-R-phenylformamidinate), where R = −OCH 3 (1), −CH 3 (2), −H (3), −F (4), −Cl (5), and −CF 3 (6), and their respective radical anions were prepared and their excited state properties were investigated. Complex 3 acted as a singlemolecule photocatalyst for H 2 production with red light. Substitution on the formamidinate ligands in 1−6 affected the energy of the Rh 2 (δ*)/Form(π,nb) highest occupied molecular orbital (HOMO), consistent with the metal/ligand-to-ligand charge transfer ( 1 ML-LCT) absorption maxima and the 3 ML-LCT excited state lifetime, ranging from 1.6 ns in 1 to 54 ns in 6 in CH 3 CN. The highest turnover number for photocatalytic H 2 evolution was observed for 3, and the lowest values were for 1 and 6. The radical anion, [Rh 2 ] − , formed during photocatalysis, was shown to absorb a photon and undergo a second reduction. The lifetimes of the doublet excited states of [3] − and [6] − were 0.49 and 0.24 ns, respectively. Calculations showed that the lowest energy excited state in [3] − was 2 ML-LCT, whereas that in [6] − was a bncn − → Rh 2 (σ*) ligand-to-metal charge transfer ( 2 LMCT) state. The 2 LMCT state stabilized across the series from [1] − to [6] − , pointing at its role in modulating the photophysical properties. This work highlights the importance of the reductive quenching of [Rh 2 ] − and the generation of the doubly reduced species to effectively catalyze hydrogen evolution.

Absorption↗

DOE OSTI2026

Scattering theory of frequency-entangled biphoton states facilitated by cavity polaritons

The use of quantum light to probe exciton properties in semiconductor and molecular nanostructures typically occurs in the low-intensity regime. A substantial enhancement of exciton-photon coupling can be achieved with photonic cavities, where excitons hybridize with cavity modes to form polariton states. Here, to provide a theoretical framework for interpreting emerging experimental efforts in this direction, we develop a scattering theory describing the interaction of frequency-entangled photon pairs with cavity polariton and bipolariton states under various coupling regimes. Employing the Tavis-Cummings model in combination with our scattering approach, we present a quantitative analysis of how the interaction of the entangled photon pair with the polariton or bipolariton modifies its joint spectral amplitude (JSA). Specifically, we examine the effects of the cavity-mode steady-state population, exciton-cavity coupling strength, and different forms of the input photon JSA. Our results show that the entanglement entropy of the scattered photons is highly sensitive to the interplay between the input JSA and the spectral line shapes of the polariton resonances, emphasizing the cavity filtering effects. We suggest that biphoton-scattering quantum light spectroscopy best serves as a sensitive probe of polariton and bipolariton states in the photon-vacuum cavity state. Our approach is not only robust to various regimes of cavity-exciton coupling, but also amenable to extensions beyond the Tavis-Cummings model, enabling the representation of a broad class of molecular systems and solid state quantum materials.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Lifetimes of negative parity states in 162 Dy

Lifetimes of excited states in 162 Dy were measured using the (n,n’$γ$) reaction with the Doppler-Shift Attenuation Method (DSAM) at the University of Kentucky’s Accelerator Laboratory. A total of eighteen level lifetimes were obtained, including eleven negative-parity states, seven of which are new. These measurements significantly expand the experimental database of transition probabilities for negative-parity bands in the well-deformed rare earth region of nuclei. The extracted B(E1) and B(E2) values reveal enhanced interband E1 (10 -3 or 10 -4 ) W.u. and E2 strengths (several W.u.) between negative- and positive parity bands, particularly for the K π = $2^{-}_{1,2}$ bands decaying to the K π = $2^+_γ$ band, consistent with signatures of octupole-quadrupole coupling. In contrast, the K π = $0^{-}_1$ and K π = $1^{-}_3$ bands, which exhibit strong E1 transitions to the ground state band, are indicative of octupole-vibrational excitations built on the deformed ground state. Comparison of transition rates with Alaga rules supports this interpretation and distinguishes collective excitations from likely quasi-particle states. These new results establish 162 Dy as the most extensively characterized rare-earth nucleus for negative parity lifetimes and provide critical experimental benchmarks for theoretical models.

Aprahamian, A. [University of Notre Dame, IN (Unit↗