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At least 73 records · Page 4
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DOE OSTI2026

Transitions, Dynamics, and Driven States in Quantum Magnets (Final Report Revised)

Transitions into unusual electronic, optical, and magnetic states at the absolute zero of temperature display special properties that teach us about fundamental quantum mechanics and also underlie important technologies. These so-called quantum phase transitions intertwine the static and dynamical responses of the materials changing state. They are extremely sensitive to the effects of disorder and etch in high relief the role of quantum fluctuations. There are ample questions remaining about the character of such transitions and the nature of the competing quantum states. There are also opportunities to drive quantum materials out of equilibrium, with the possibility of new types of correlated and coherent order, and new ways to access the dynamical evolution of ground and excited states. We have investigated how the order develops in time and space, and the nature of the final configurations. We are able to compare and contrast classical and quantum excitations in our experimental system of choice, and thereby can trace the relative speed by which the system settles into its lowest-energy ground state. This comparison of quantum and classical annealing protocols lies at the heart of strategies for harnessing the power of quantum computers dedicated to optimization problems. A combination of magnetic susceptibility measurements at finite frequency where the magnetic spins are queried by an external ac field, dc magnetometry measurements that characterize the macroscopic strength of magnetic order and its resistance to change, noise measurements that reveal the microscopic fluctuations of the spins as they prepare to change state, and microwave spectroscopy to look at the response of both the electronic and nuclear degrees of freedom, have been performed as functions of temperature, magnetic field, frequency, excitation amplitude, magnetic spin concentration, and disorder. This combination of probes addresses issues of stability over time, overlap between spin states, the ability of the spins to respond independently or coherently, and the promise of control on the nanometer length scale. The research reported here provides insights into fundamental quantum physics. It also addresses the question of how best to use complex systems, such as magnetic solids, to stably process quantum information.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Quantum fluctuations drive nonmonotonic correlations in a qubit lattice

Abstract Fluctuations may induce the degradation of order by overcoming ordering interactions, consequently leading to an increase of entropy. This is particularly evident in magnetic systems characterized by nontrivial, constrained disorder, where thermal or quantum fluctuations can yield counterintuitive forms of ordering. Using the proven efficiency of quantum annealers as programmable spin system simulators, we present a study based on entropy postulates and experiments on a platform of programmable superconducting qubits to show that a low level of uncertainty can promote ordering in a system impacted by both thermal and quantum fluctuations. A set of experiments is proposed on a lattice of interacting qubits arranged in a triangular geometry with precisely controlled disorder, effective temperature, and quantum fluctuations. Our results demonstrate the creation of ordered ferrimagnetic and layered anisotropic disordered phases, displaying characteristics akin to the elegant order-by-disorder phenomenon. Extensive experimental evidence is provided for the role of quantum fluctuations in lowering the total energy of the system by increasing entropy and defect clustering. Our thorough and comprehensive application of an intentionally introduced noise on a quantum platform provides insight into the dynamics of defects and fluctuations in quantum devices, which may help to reduce the cost associated with quantum processing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Probing Oxidation-Driven Amorphized Surfaces in a Ta(110) Film for Superconducting Qubit

Recent advances in superconducting qubit technology have led to significant progress in quantum computing, but the challenge of achieving a long coherence time remains. Despite the excellent lifetime performance that tantalum (Ta) based qubits have demonstrated to date, the majority of superconducting qubit systems, including Ta-based qubits, are generally believed to have uncontrolled surface oxidation as the primary source of the two-level system loss in two-dimensional transmon qubits. Therefore, atomic-scale insight into the surface oxidation process is needed to make progress toward a practical quantum processor. Here, in this study, the surface oxidation mechanism of native Ta films and its potential impact on the lifetime of superconducting qubits were investigated using advanced scanning transmission electron microscopy (STEM) techniques combined with density functional theory calculations. The results suggest an atomistic model of the oxidized Ta(110) surface, showing that oxygen atoms tend to penetrate the Ta surface and accumulate between the two outermost Ta atomic planes; oxygen accumulation at the level exceeding a 1:1 O/Ta ratio drives disordering and, eventually, the formation of an amorphous Ta 2 O 5 phase. In addition, we discuss how the formation of a noninsulating ordered TaO 1–δ (δ < 0.1) suboxide layer could further contribute to the losses of superconducting qubits. Subsurface oxidation leads to charge redistribution and electric polarization, potentially causing quasiparticle loss and decreased current-carrying capacity, thus affecting superconducting qubit coherence. The findings enhance the comprehension of the realistic factors that might influence the performance of superconducting qubits, thus providing valuable guidance for the development of future quantum computing hardware.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Material and Interface Engineering Strategies to Mitigate Decoherence in Superconducting Qubits

While significant strides have been made to increase the coherence time of superconducting qubits, further advancements are essential for realizing scalable quantum computing. Decoherence is often a result of loss and noise stemming from two-level systems and excess quasiparticles, arising due to material defects, fabrication processes, and ambient exposure, particularly at surfaces and interfaces. Our recent efforts to mitigate these decoherence mechanisms have employed a variety of strategies, including low-loss surface encapsulation materials, advanced substrate preparation techniques, modifications to metal film growth, and the development of novel fabrication processes. The structural and chemical properties of materials, surfaces, and interfaces are studied using scanning probe microscopy, electron microscopy, photoelectron spectroscopy, mass spectrometry, and X-ray diffraction, which is correlated to device performance metrics, including superconducting resonator internal quality factor and qubit T1 time. This information is used to identify and understand material sources of loss and their origins in the device fabrication process. Through multi-institution efforts within SQMS we have identified the loss mechanism of interstitial hydrogen in niobium-based devices and shown how standard fabrication processes introduce these hydrides, developing strategies to mitigate their formation.1 Furthermore, we have characterized the metal-substrate interface, including the loss of niobium-silicides formed at that interface, and developed silicon surface treatments that reduce atomic scale roughness and oxygen content at the metal-substrate and Josephson junction interfaces.2-4 By developing the connection between materials properties and the overall performance of superconducting quantum circuitry, we can develop fabrication strategies to mitigate material losses, thus supporting the ongoing efforts to enhance coherence time in superconducting quantum devices. 1. Torres-Castanedo, C. G.*, Goronzy, D. P.*, et al., Adv. Funct. Mater., 2401365 (2024) 2. Lu, X., et al., Phys. Rev. Materials 6, 064402 (2022) 3. Berti, G., Appl. Phys. Lett. 122, 192605 (2023) 4. Kopas, C. J., Goronzy, D. P., et al., arXiv:2408.02863 (2024)

Goronzy, Dominic P.↗
DOE OSTI2023

Liouvillian dynamics of the open Schwinger model: String breaking and kinetic dissipation in a thermal medium

Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an antifermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. Here in this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal medium, treating the Schwinger model as an open quantum system coupled to a thermal environment. Within the regime of weak coupling between the system and environment, the real-time evolution of the system can be described by a Lindblad evolution equation. We analyze the Liouvillian gaps of this Lindblad equation and the time dependence of the system’s von Neumann entropy. We observe that the late-time relaxation rate decreases as the environment correlation length increases. Moreover, when the environment correlation length is infinite, the system exhibits two steady states, one in each of the sectors with definite charge-conjugation-parity (CP) quantum numbers. For parameter regimes where an initial string breaks in vacuum, we observe a delay of the string breaking in the medium, due to kinetic dissipation effects. Conversely, in regimes where an initial string remains intact in vacuum time evolution, we observe string breaking (melting) in the thermal medium. We further discuss how the Liouvillian dynamics of the open Schwinger model can be simulated on quantum computers and provide an estimate of the associated Trotter errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Modulating Oxide‐Based Quantum Materials by Ion Implantation

Ion implantation has emerged as a powerful tool for manipulating and investigating oxide quantum materials, where strong electron correlations give rise to exotic phases and functionalities. This Review examines how controlled ion bombardment enables targeted modulation of structural, electronic, and magnetic properties in complex oxides. Recent advances in ion beam techniques is analyzed that provide unprecedented control over defect profiles, from point defects to extended damage cascades. In application, ion irradiation has demonstrated the ability to tune quantum phenomena including metal‐insulator transitions, magnetism, and superconductivity through selective doping, defect creation, and lattice strain. The ability to write quantum states with nanoscale precision using focused ion beams is opening new paths for quantum device fabrication. Challenges in understanding radiation damage mechanisms in strongly correlated systems is discussed, and identify opportunities for designing quantum functionality through defect‐engineering approaches. The technique's demonstrated capability to write quantum states with nanoscale precision, combined with its compatibility with existing semiconductor processing infrastructure, suggests a clear pathway for translating fundamental discoveries in quantum materials into practical technological applications.

defect engineering↗
DOE OSTI2023

Synthesis and Characterization of Amorphous Lawsone Polymer Dots for Fluorescent Applications

In this work, a two-step hydrothermal/solvothermal process was developed to generate highly fluorescent lawsone polymer dots (LPDs) utilizing an inexpensive and abundant starting material, 2-hydroxy-1,4-napththoquinone (lawsone). This hydrothermal/solvothermal process produces LPDs that have excitation independent emission with well-defined electronic transitions. This two-step protocol provides a straightforward approach to remove unwanted small molecular fluorescence, which has plagued carbon dot systems, without the need for advanced chromatographic purification methods or steps. A series of spectroscopic, electrochemical, and theoretical experiments suggest that this process proceeds via a sequential dehydration and dehydrogenation pathway to cross-link the lawsone into a carbon dot structure. This polymerization process helps to stabilize and favor certain electronic transitions inherently present in the lawsone monomer. The generation of the LPDs results in a 2 order of magnitude increase in the emission intensity and a quantum yield of 37%. This behavior is likely the result of the cross-linked structure shielding these electronic states from deactivation caused by nonradiative processes such as vibrational coupling and excited state quenching from thermal deactivation and solvent collisions. This finding is consistent with a cross-linked enhanced emission (CEE) mechanism, as previously observed for other similar systems. The LPDs were then incorporated into a TiO2 photoanode and utilized as a photosensitizer in a dye-sensitized solar cell (DSSC) which showed an enhancement in photocurrent density over pure TiO2. We also prepared a derivative of the LPDs utilizing a diethylene triamine additive (nitrogen-doped lawsone polymer dots (N-LPDs)) using the same two-step protocol and demonstrated its potential as a fluorescence microscopy dye for imaging MDA-MB-231 cancer cells.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Similarity Metric for Data Optimization and Efficient Training of Reactive Machine Learning Force Fields for Hydrocarbon Radiolysis

Radiolysis is a common approach to sterilize polymers, chemically modify them for upcycling, and accelerate their decomposition for recycling purposes. Reactive molecular dynamics (MD) simulations provide a powerful tool to generate atomic-level trajectories of the reactive processes and quantify radiolytic chemical degradation pathways. For this, machine learning (ML) surrogate models for reactive force fields with quantum mechanical accuracy are now widely used, which require ML training data sets that can provide information on atomic environments for target chemical systems. However, radiolysis chemistry can be highly complex and diverse, which poses significant challenges for generating training data to parametrize ML models. In this regard, we developed a method for optimizing the training data set using a cosine similarity metric to help guide training set selection for radiolysis of polyethylene, a model hydrocarbon polymer, as well as to enhance the transferability of our reactive ML force field (MLFF) to a variety of molecular and polymeric systems. Our approach performs atom-by-atom comparisons between local atomic environments to pinpoint important data points associated with rare and localized events, such as radiolysis damage within structures. We apply this approach to train the Chebyshev Interaction Model for Efficient Simulation (ChIMES) MLFF model, which expresses the atomic interaction potentials in terms of linear combinations of many-body Chebyshev polynomials. We first show that our method can reduce our training set size by ∼70% while improving overall accuracy compared to more standard MD model fitting approaches. We then validate our optimum model against diverse hydrocarbon simulation data, including simple alkanes and systems with unsaturated carbon bonds, over a wide range of thermodynamic conditions. Finally, we use our ChIMES model to perform MD simulations of radiolytic damage with large-scale systems that help avoid system size effects. Overall, our approach yields an MD force field that retains most of the accuracy of the underlying quantum method while yielding many orders of improvement in computational efficiency. In conclusion, our efforts will have impact on future hydrocarbon polymer radiolysis studies, where the chemical details of the polymer–radiation interactions can have a strong effect on the resulting products observed in experiments.

Hydrocarbons↗
DOE OSTI2024

Accurate numerical simulations of open quantum systems using spectral tensor trains

Decoherence between qubits is a major bottleneck in quantum computations. Decoherence results from intrinsic quantum and thermal fluctuations as well as noise in the external fields that perform the measurement and preparation processes. With prescribed colored noise spectra for intrinsic and extrinsic noise, we present a numerical method, Quantum Accelerated Stochastic Propagator Evaluation (Q-ASPEN), to solve the time-dependent noise-averaged reduced density matrix in the presence of intrinsic and extrinsic noise. Q-ASPEN is arbitrarily accurate and can be applied to provide estimates for the resources needed to error-correct quantum computations. We employ spectral tensor trains, which combine the advantages of tensor networks and pseudospectral methods, as a variational ansatz to the quantum relaxation problem and optimize the ansatz using methods typically used to train neural networks. Here, the spectral tensor trains in Q-ASPEN make accurate calculations with tens of quantum levels feasible. We present benchmarks for Q-ASPEN on the spin-boson model in the presence of intrinsic noise and on a quantum chain of up to 32 sites in the presence of extrinsic noise. In our benchmark, the memory cost of Q-ASPEN scales as a low-order polynomial in the size of the system once the number of system states surpasses the number of basis functions used in the spectral expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Nonlinear multi-magnon scattering in artificial spin ice

Abstract Magnons, the quantum-mechanical fundamental excitations of magnetic solids, are bosons whose number does not need to be conserved in scattering processes. Microwave-induced parametric magnon processes, often called Suhl instabilities, have been believed to occur in magnetic thin films only, where quasi-continuous magnon bands exist. Here, we reveal the existence of such nonlinear magnon-magnon scattering processes and their coherence in ensembles of magnetic nanostructures known as artificial spin ice. We find that these systems exhibit effective scattering processes akin to those observed in continuous magnetic thin films. We utilize a combined microwave and microfocused Brillouin light scattering measurement approach to investigate the evolution of their modes. Scattering events occur between resonance frequencies that are determined by each nanomagnet’s mode volume and profile. Comparison with numerical simulations reveals that frequency doubling is enabled by exciting a subset of nanomagnets that, in turn, act as nanosized antennas, an effect that is akin to scattering in continuous films. Moreover, our results suggest that tunable directional scattering is possible in these structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Backaction-evading receivers with magnetomechanical and electromechanical sensors

Today's mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise originating from the process of measurement itself—the quantum-mechanical backaction of measurement—and go below this ‘standard’ limit, possibly approaching the Heisenberg limit. One of the ways to eliminate this noise is by measuring a quantum nondemolition variable such as the momentum in a free-particle system. Here, we propose and characterize theoretical models for direct velocity measurement that utilize traditional electric and magnetic transducer designs to generate a signal while enabling this backaction evasion. We consider the general readout of this signal via electric or magnetic field sensing by creating toy models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme—voltage or current—for each mechanical detector configuration implies access to either the position or velocity of the mechanical subsystem. This in turn suggests a path forward for key fundamental physics experiments such as the direct detection of dark matter particles. Published by the American Physical Society 2024

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Enhancement of vibrationally assisted energy transfer by proximity to exceptional points, probed by fluorescence-detected vibrational spectroscopy

Emulation of energy transfer processes in natural systems on quantum platforms can further our understanding of complex dynamics in nature. One notable example is the demonstration of vibrationally assisted energy transfer (VAET) on a trapped-ion quantum emulator, which offers insights for the energetics of light harvesting. In this work, we expand the study of VAET simulation with trapped ions to a non-Hermitian quantum system comprising a 𝒫⁢𝑇-symmetric chromophore dimer weakly coupled to a vibrational mode. We first characterize exceptional points (EPs) and non-Hermitian features of the excitation energy transfer processes in the absence of the vibration, finding a degenerate pair of second-order EPs. Exploring the non-Hermitian dynamics of the whole system including vibrations, we find that energy transfer accompanied by absorption of phonons from a vibrational mode can be significantly enhanced near such a degenerate EP. Our calculations reveal a unique spectral feature accompanying the coalescing of eigenstates and eigenenergies that provides a unique approach to probe the degenerate EP by fluorescence-detected vibrational spectroscopy. Enhancement of the VAET process near the EP is found to be due to maximal favorability of phonon absorption at the degenerate EP, enabling multiple simultaneous excitations. Our work on improving VAET processes in non-Hermitian quantum systems paves the way for leveraging non-Hermiticity in quantum dynamics related to excitation energy transfer.

Non-Hermitian systems↗
DOE OSTI2025

Designs for scalable construction of hybrid quantum photonic cavities

Nanophotonic resonators are central to numerous applications, from efficient spin–photon interfaces to laser oscillators and precision sensing. A leading approach consists of photonic crystal (PhC) cavities, which have been realized in a wide range of dielectric materials. However, translating proof-of-concept devices into a functional system entails a number of additional challenges, inspiring new approaches that combine resonators with wavelength-scale confinement and high quality factors; scalable integration with integrated circuits and photonic circuits; electrical or mechanical cavity tuning; and, in many cases, a need for heterogeneous integration with functional materials such as III–V semiconductors or diamond color centers for spin–photon interfaces. Here we introduce a concept that generates a finely tunable PhC cavity at a selected wavelength between two heterogeneous optical materials whose properties satisfy the above requirements. The cavity is formed by stamping a hard-to-process material with simple waveguide geometries on top of an easy-to-process material consisting of dielectric grating mirrors and active tuning capability. We simulate our concept for the particularly challenging design problem of multiplexed quantum repeaters based on arrays of cavity-coupled diamond color centers, achieving theoretically calculated unloaded quality factors of 106, mode volumes as small as 1.2(λ/neff)3, and maintaining >60% total on-chip collection efficiency of fluorescent photons. We further introduce a method of low-power piezoelectric tuning of these hybrid diamond cavities, simulating optical resonance shifts up to ∼760 GHz and color center fluorescence tuning of 5 GHz independent of cavity tuning. These results will motivate integrated photonic cavities toward larger scale systems-compatible designs.

Greenspon, Andrew S. (ORCID:0000000296317568)↗
DOE OSTI2023

Tracking Photochemical and Photophysical Processes for Solar Energy Conversion Via Multidimensional Visible and Vibrational Spectroscopic Methods

This project was motivated by an overarching goal to elucidate the mechanism of energy and electron transfer that governs the efficient charge separation in photosystem I (PSI) complexes. PSI is a natural light harvesting complex that drives oxygenic photosynthesis in plants, algae, and cyanobacteria. It uses ~300 tightly packed chlorophylls (Chls) to absorb photons, transfer the excitation energy to the reaction center (RC), and generate a charge separated state with near unity quantum efficiency (QE). A better understanding of the mechanism of energy transfer and charge separation in PSI is required for understanding the high QE of natural light harvesting complexes, and it could lead to the further development of artificial photosynthetic systems for solar energy conversion. We applied two-dimensional electronic spectroscopy (2DES) to different cyanobacterial photosystem I complexes to map energy transfer pathways to gain insight into the efficient light harvesting of PSI. We interpreted the 2DES spectra through a global analysis procedure, finding two ultrafast equilibration processes involving red-shifted Chl states. The analysis procedure is general and can be readily applied to other natural and artificial light harvesting systems. In addition to investigating PSI complexes, we also performed measurements on model systems to establish general data analysis procedures for interpreting 2D spectra.

14 SOLAR ENERGY↗
DOE OSTI2022

Ultrastrong Coupling of Band‐Nested Excitons in Few‐Layer Molybdenum Disulphide

Abstract The 2D transition‐metal dichalcogenides (2D TMDCs) are an intriguing platform for studying strong light–matter interactions because they combine the electronic properties of conventional semiconductors with the optical resonances found in organic systems. However, the coupling strengths demonstrated in strong exciton–polariton coupling in the 2D TMDCs remain much lower than those found in organic systems. In this paper, a new approach is taken by utilizing the large oscillator strength of the above‐band gap C exciton in few‐layer molybdenum disulphide (FL‐MoS 2 ). A k ‐space Rabi splitting of 293 meV is shown when coupling FL‐MoS 2 C excitons to surface plasmon polaritons at room temperature. This value is 11% of the uncoupled exciton energy (2.67 eV or 464 nm), ≈2× what is typically seen in the TMDCs, placing the system in the ultrastrong coupling regime. The results take a step toward finally achieving the efficient quantum coherent processes of ultrastrong coupling in a CMOS‐compatible system—the 2D TMDCs—in the visible spectrum.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Basic Research Needs in Quantum Computing and Networking

Employing quantum mechanical resources in computing, information processing, and networking opens the door to potential exponential advantages over classical counterparts. However, quantifying and realizing such advantages poses extensive scientific and engineering challenges. Department of Energy (DOE) investments have driven steady progress in addressing such challenges. Recently developed quantum algorithms offer asymptotic exponential advantages in speed or accuracy for fundamental scientific problems. These problems include simulating physical systems, solving systems of linear equations, differential equations, and optimization problems. Empirical demonstrations on nascent quantum hardware suggest better performance on contrived computational tasks than classical analogs. However, the requirements for a quantum computer or network to demonstrate an end-to-end rigorously quantifiable performance improvement over classical analogs remains a grand challenge, especially for problems of practical value. In particular, what will be required for quantum technology to ultimately exhibit scalable, rigorous, and transformative performance advantages for practical applications? In July 2023, DOE’s Advanced Scientific Computing Research program in the Office of Science convened the Workshop on Basic Research Needs in Quantum Computing and Networking, where major opportunities and grand challenges were identified. The following five priority research directions (PRDs) were identified as a result of the workshop.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum physics of stars

Stars are slowly developing objects; the lifetimes of the different burning phases are determined by the strength of nuclear reactions, which in turn are defined by the quantum structure of the associated nuclei at the threshold and the respective reaction mechanisms. Stars, from the nuclear physics perspective, are cold environments where only a few of the key nuclear reactions have been measured at the actual stellar plasma temperatures. This is also the case for more dynamic astrophysical phenomena from the big bang to stellar explosions. Most of the nuclear reaction rates are therefore based on theoretical extrapolations. A number of discrepancies between these predictions and the associated stellar signatures have been observed, and many may be due to low-energy or near-threshold quantum effects. These effects need to be understood in order to reliably model nuclear reaction processes, not only for stars but also for low-temperature plasma environments such as controlled magnetic or inertial confinement fusion systems, which operate in similar temperature regimes. This review summarizes the various theoretical techniques presently used for deriving reaction rates and discusses possible quantum effects that may impact the reaction cross section near the reaction threshold. These resemble enhanced single-particle and cluster structures near threshold and associated interference effects. New experimental techniques such as deep-underground accelerators or the study of transfer reactions to mimic the quantum-mechanical transition strength, the so-called Trojan horse method, provide ways to directly or indirectly probe the reaction features that determine the reaction rates at stellar energies. Furthermore, this is demonstrated on a number of key nuclear reactions for different nucleosynthesis environments. Finally, current inconsistencies between experimental predictions and observations are discussed.

Models & methods for nuclear reactions↗