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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Prompt-delayed γ-ray spectroscopy of neutron-rich 119.121 In isotopes

The Z = 50 shell closure, near N = 82, is unique in the sense that it is the only shell closure with the spin-orbit partner orbitals, π g 9 / 2 and π g 7 / 2 , enclosing the magic gap. The interaction of the proton hole/particle in the above-mentioned orbitals with neutrons in the νh 11/2 orbital is an important prerequisite to the understanding of the nuclear structure near N = 82 and the νπ interaction. To explore the structural similarity between the high-spin isomeric states in In ( Z = 49), Sn ( Z = 50), and Sb ( Z = 51) isotopes from a microscopic point of view. In addition, to understand the role of a proton hole or particle in the spin-orbit partner orbitals, π g 9 / 2 and π g 7 / 2 , respectively, with neutron holes in the ν h 11 / 2 orbital on these aforementioned isomers. The fusion and transfer induced fission reaction Be 9 ( U 238 , f ) with 6.2 MeV/u beam energy, using a unique setup consisting of AGATA, VAMOS++, and EXOGAM detectors, was used to populate through the fission process and study the neutron-rich In 119 , 121 isotopes. This setup enabled the prompt-delayed γ -ray spectroscopy of isotopes in the time range of 100 ns – 200 μ s . In the odd- A In 119 , 121 isotopes, indications of a short half-life 19/2 - isomeric state, in addition to the previously known 25/2 + isomeric state, were observed from the present data. Further, new prompt transitions above the 25/2 + isomer in In 121 were identified along with reevaluation of its half-life. The experimental data were compared with the theoretical results obtained in the framework of large-scale shell-model calculations in a restricted model space. Furthermore, the ( π g 9 / 2 ν h 11 / 2 ; I | H ^ | π g 9 / 2 ν h 11 / 2 ; I ) two-body matrix elements of residual interaction were modified to explain the excitation energies and the B ( E 2) transition probabilities in the neutron-rich In isotopes. The (i) decreasing trend of E (29/2 + ) - E (25/2 + ) in odd-In (with dominant configuration π g 9 / 2 - 1 ν h 11 / 2 - 2 and maximum aligned spin of 29/2 + ) and (ii) increasing trend of E (27/2 + ) - E (23/2 + ) in odd-Sb (with dominant configuration π g 7 / 2 + 1 ν h 11 / 2 - 2 and maximum aligned spin of 27/2 + ) with increasing neutron number could be understood as a consequence of hole-hole and particle-hole interactions, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Structure of rotational bands in 109 Rh

Rotational bands in 109 Rh are investigated in a simple model and in the interacting boson-fermion model. We have developed a solvable extended transitional Hamiltonian by adding a two-configuration mixing term. Results suggest that 109 Rh is a good candidate for triaxiality and shape coexistence. Mixing between 3/2 + states with K = 1/2 and 3/2 is found to be weak, as evidenced by the E2 strengths.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Solid-State Calcium-Ion Diffusion in Ca 1.5 Ba 0.5 Si 5 O 3 N 6

Rechargeable batteries based on multivalent working ions are promising candidates for next-generation high-energy-density batteries. Development of these technologies, however, is largely limited by the low diffusion rate of multivalent ions in solid-state materials, thereby necessitating a better understanding of the design principles that control multivalent-ion mobility. We report Ca 1.5 Ba 0.5 Si 5 O 3 N 6 as a potential calcium solid-state conductor and investigate its Ca migration mechanism by means of ab initio computations and neutron diffraction. This compound contains partially occupied Ca sites in close proximity to each other, providing a unique mechanism for Ca migration. Nuclear density maps obtained with the maximum entropy method from neutron powder diffraction data provide strong evidence for low-energy percolating one-dimensional pathways for Ca-ion migration. Ab initio molecular dynamics simulations further support a low Ca-ion migration barrier of ~400 meV when Ca vacancies are present and reveal a unique "vacancy-adjacent"concerted ion migration mechanism. This work provides a new understanding of solid-state Ca-ion diffusion and insights into the future design of novel cation configurations that utilize the interactions between mobile ions to enable fast multivalent-ion conduction in solid-state materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Coulomb excitation of 102 Ru with 12 C and 16 O

Here, the Coulomb excitation of 102 Ru was performed with beams of 12 C and 16 O ions. The beam particles scattered at forward angles were momentum analyzed with a magnetic spectrograph. The resolution achieved enabled the populations of the $2^{+}_{1}$ state, the unresolved $2^{+}_{2}$/ $4^{+}_{1}$, and $2^{+}_{4}$/$3^{-}_{1}$, doublets of states, and the $3^{-}_{2}$ state to be determined as a function of the scattering angle. These populations are compared with gosia calculations, yielding B(E2; $2^{+}_{1}$→$0^{+}_{1}$) = 41.5 ± 2.3 W.u., B(E2; $2^{+}_{2}$→$0^{+}_{1}$) = 1.75 ± 0.11 W.u., B(E3; $3^{-}_{1}$→$0^{+}_{1}$) = 31.5 ± 3.5 W.u., and B(E3; $3^{-}_{2}$→$0^{+}_{1}$) = 6.8 ± 0.5 W.u. The B(E3; $3^{-}_{1}$→$0^{+}_{1}$) value is significantly larger than previously measured. The weakly populated $2^{+}_{3}$ state, presumed to be a member of the band built on the $0^{+}_{2}$ state, was observed clearly for a single angle only, and a fit to its population results in B(E2; $2^{+}_{3}$→$0^{+}_{1}$) = 0.053 ± 0.011 W.u. Using the known γ -ray branching ratios for the $2^{+}_{3}$ level, the B(E2; $2^{+}_{3}$→$0^{+}_{2}$) value is calculated to be 18 ± 4 W.u., substantially less than the B(E2; $2^{+}_{1}$→$0^{+}_{1}$) . This suggests that the deformation of the $0^{+}_{2}$ state is lower than that of the $0^{+}_{1}$ state. The results are compared with beyond-mean-field calculations with the Gogny-D1S interaction using the symmetry-conserving configuration-mixing method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Design and optimization of higher order mode couplers for the superconducting cavities of the PERLE energy recovery linac

The Powerful Energy Recovery Linac for Experiments (PERLE) is an energy recovery linac (ERL) facility based on superconducting radio-frequency (SRF) technology to be hosted at the Laboratoire de Physique des 2 Infinis Irène Joliot-Curie (IJCLab) in France. With a target beam power of 10 MW, PERLE aims to demonstrate the high-current, continuous wave, multi-pass operation to validate options for future high-energy machines, such as the 50 GeV ERL proposed for the Large Hadron electron Collider (LHeC) and the Future Circular electron-hadron Collider (FCC-eh), and host dedicated particle physics and nuclear experiments. In high-current ERLs, the regenerative Beam Breakup (BBU), emerging from the beam and cavity Higher Order Modes (HOMs) interaction, is a major concern for their stable operation. Beam-induced HOMs can increase the cavity heat load at cryogenic temperature and cause beam instabilities. HOM couplers are installed in the cavity beam pipes to absorb HOM energy and mitigate these effects. This thesis presents the design and optimization of several coaxial HOM couplers for the 5-cell 801.58 MHz elliptical Nb cavities of the 500 MeV PERLE ERL configuration. The RF transmission of the HOM couplers was optimized to enhance the damping of the most dangerous HOMs. The optimized HOM couplers were integrated into endgroups to simulate their damping performance and thermal behavior. The optimized HOM couplers were 3D-printed in epoxy and copper-coated. Low-power RF measurements were conducted on the produced HOM couplers installed in copper PERLE-type cavities to validate their damping performance and propose several endgroups for the PERLE 5-cell cavity to mitigate HOMs below the BBU instability limits.

Barbagallo, Carmelo↗
DOE OSTI2025

Lattice-Renormalized Tunneling Models for Superconducting Qubit Materials

We present a lattice-renormalized formalism for configurational tunneling two-level systems (TLS) that overcomes limitations of minimum-energy-path and light-particle models. Derived from the nuclear Hamiltonian, our formulation introduces composite phonon coordinates to capture lattice distortions between degenerate potential wells. This approach resolves deficiencies in prior models and enables accurate computation of tunnel splittings and excitation spectra for hydrogen-based TLS in bcc Nb. Our results bound experimental tunnel splittings and reveal strong anharmonic couplings between tunneling atoms and lattice phonons, establishing a direct link between TLS dynamics and phonon-mediated strain interactions. The formalism further generalizes to multi-level systems (MLS), providing insight into defect-induced decoherence in superconducting qubits and guiding strategies for materials design to suppress TLS-related loss.

Pritchard, P. G. [Northwestern U.]↗
DOE OSTI2024

Development and Implementation of a Bag Degradation Predictive Tool at Los Alamos National Laboratory

Nuclear material packaging involves many complex variables derived from the stored material's properties, the storage environment, and the synergistic interaction of said material and its environment on the containment boundary. In the Plutonium Facility (PF-4) at Los Alamos National Laboratory (LANL) the typical containment boundary found, starting from the stored material itself to the outermost containment layer, consists of the material contained within a stainless steel (typically 304) slip-lid (or other equivalent stainless steel packaging layer) wrapped in an sPVC bag-out bag contained within a facility approved outer container stored within the boundaries of an approved facility (i.e., a building designed and approved to store nuclear material). This packaging configuration, though occasionally deviated from in the past, represents the current procedurally enforced, expected containment structure for all interim nuclear material containment outside of an engineered control barrier (e.g., a glovebox). Over the life of containerization research at LANL, packaging engineers have become increasingly concerned with the degradation of the sPVC bag-out bag, which can cause corrosion to the outermost packaging layer as well as possible exposure to alpha contamination if the bag-out bag layer is degraded to the point of containment failure. A bag-out bag degradation predictive tool (BDT) is therefore needed to assess the current and future nuclear material inventory for possible bag degradation in order to continue to ensure safe operations for the facility and its workers to deliver on the vital national security mission of 30 PPY.

42 ENGINEERING↗
DOE OSTI2024

Capturing Correlation Effects in Positron Binding to Atoms and Molecules

A major challenge in contemporary electronic structure theory involves the development of methods to describe in a balanced manner the contribution of correlation effects to energy differences. This challenge can be even greater for multicomponent systems containing more than one type of quantum particle. In the present work, we describe a flexible code for carrying out self-consistent field and configuration interaction (CI) calculations on multicomponent systems and use it to generate trial wave functions for use in diffusion Monte Carlo (DMC) calculations of the positron affinity of Be, Be 2 , Be 4 , Mg, CS 2 , and benzene. The resulting positron affinities (PAs) are in good agreement with the best values from the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Modeling fission dynamics at the barrier in a discrete-basis formalism

A configuration-interaction model is presented for the barrier region of induced fission. The configuration space is composed of seniority-zero configurations constructed from self-consistent mean-field wave functions. The Hamiltonian matrix elements between configurations include diabatic and pairing interactions between particles. Other aspects of the Hamiltonian are treated statistically, guided by phenomenological input of compound-nucleus transmission coefficients. In this exploratory study the configuration space is restricted to neutron excitations only. A key observable calculated in the model is the fission-to-capture branching ratio. We find that both pairing and diabatic interactions are important for achieving large branching to the fission channels. In accordance with the transition-state theory of fission, the calculated branching ratio is found to be quite insensitive to the fission decay widths of the pre-scission configurations. Furthermore, the barrier-top dynamics appear to be quite different from transition-state theory in that the transport is distributed over many excited configurations at the barrier top.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

First Estimation of Model Parameters for Neutrino-Induced Nucleon Knockout Using Simulation-Based Inference

To enable an accurate determination of oscillation parameters, accelerator-based neutrino experiments require detailed simulations of nuclear interaction physics in the GeV regime. While substantial effort from both theory and experiment is currently being invested to improve the fidelity of these simulations, their present deficiencies typically oblige experimental collaborations to resort to empirical tuning of simulation model parameters. As the precision requirements of the field continue to become more stringent, machine learning techniques may provide a powerful means of handling corresponding growth in the complexity of future neutrino interaction model tuning exercises. To study the suitability of simulation-based inference (SBI) for this physics application, in this paper we revisit a tuned configuration of the GENIE neutrino event generator that was originally developed by the MicroBooNE collaboration. Despite closely reproducing the adopted values of four physics parameters when confronted with the tuned cross-section predictions as input, we find that our trained SBI algorithm prefers modestly different values (within MicroBooNE's assigned uncertainties) and achieves slightly better goodness-of-fit when inference is run on the experimental data set originally used by MicroBooNE. We also find that our trained algorithm can create a fair approximation of an alternative neutrino scattering simulation, NuWro, that shares only a subset of its physics model parameters with GENIE.

Tame-Narvaez, Karla [Fermilab] (ORCID:000000022249↗
DOE OSTI2024

Spin Decoherence in VOPc@graphene Nanoribbon Complexes

Carbon nanoribbons or nanographene qubit arrays can facilitate quantum-to-quantum transduction between light, charge, and spin, making them an excellent testbed for fundamental science in quantum coherent systems and for the construction of higher-level qubit circuits. Here, in this work, we study spin decoherence due to coupling with a surrounding nuclear spin bath of an electronic molecular spin of a vanadyl phthalocyanine (VOPc) molecule integrated onto an armchair-edged graphene nanoribbon (GNR). Density functional theory (DFT) is used to obtain ground-state atomic configurations. Decay of spin coherence in Hahn echo experiments is then simulated using the cluster correlation expansion method with a spin Hamiltonian involving hyperfine and electric field gradient tensors calculated from DFT. We find that the decoherence time T 2 is anisotropic with respect to magnetic field orientation and determined only by the hydrogen nuclear spins on both VOPc and GNR. Large electron spin echo envelope modulation (ESEEM) due to nitrogen and vanadium nuclear spins is present at specific field ranges and can be completely suppressed by tuning the magnetic field. The relation between these field ranges and the hyperfine interactions is analyzed. The effects of interactions with the nuclear quadrupole moments are also studied, validating the applicability and limitations of the spin Hamiltonian when they are disregarded.

Hamiltonians↗
DOE OSTI2025

Neutrino Physics Opportunities with Pion and Kaon Decay-at-Rest Neutrino Source

Low-energy neutrino sources, such as those from stopped-pion, stopped-kaon or core-collapse supernova, interact with target nuclei in detectors through either coherent elastic or inelastic scattering processes. These interactions provide valuable insights into various Standard Model and Beyond the Standard Model phenomena, with significant implications for nuclear physics, particle physics, and astrophysics. The precision of coherent elastic scattering, where the nucleus remains in its ground state, depends on the accuracy of the underlying weak form factor of the nucleus. In contrast, inelastic scattering, where neutrinos excite the target nucleus to low-lying nuclear states, involves complex nuclear structures and dynamics and are quite poorly constrained. In this talk, I will present the physics opportunities offered by these neutrino sources, produced as secondary beams in an electron beam dump configuration at Jefferson Lab, and discuss their synergy with global neutrino experiments.

Pandey, Vishvas [Fermilab]↗
DOE OSTI2022

Precision half-life determination for the β + emitter N 13

A new precision half-life measurement of 13 N has been conducted using the TwinSol β-counting station at the University of Notre Dame. Here, the measured value of $t^{new}_{1/2}$ = 597.05(19) s differs from the previous world value by about 2.8σ. An evaluation of the 13N half-life results in a $t^{world}_{1/2}$ = 597.19(22) s. Updated Standard Model predictions for the Fermi to Gamow-Teller mixing ratio ρ and its associated correlation parameters have been calculated using the new 13 N world half life in preparation for a future measurement of the mixing ratio. Finally, an ab initio no-core configuration interaction (NCCI) calculation for the B(GT) of this decay, carried out using the Daejeon16 interaction, has been carried out, revealing the need for higher-order chiral corrections.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Preconceptual Design of Irradiated Fuel Salt Management System

The National Reactor Innovation Center was established by the U.S. Department of Energy to accelerate the demonstration and deployment of advanced nuclear reactors. To meet this mission, the National Reactor Innovation Center has developed the Laboratory for Operations and Testing in the U.S. (LOTUS) to support the first fast-spectrum molten salt reactor demonstration. The goal of this research is to understand the system requirements that may be applied to a molten salt reactor experiment in the LOTUS test bed and to perform systems analyses and preconceptual development of a storage container for the management of the irradiated molten salt fuel. This study proposes a set of irradiated fuel salt management processes for the molten salt reactor, from defueling to storage or disposal. For that, the historic Molten Salt Reactor Experiment (MSRE) at Oak Ridge National Laboratory has served as a crucial source of data for a mock application. This paper proposes a potential geometry for storing irradiated fuel salt based on MSRE data and the Monte Carlo N-Particle radiation transport code. The geometry was analyzed for criticality safety under abnormal situations, such as water ingress and interaction between containers. Based on the determined configuration of the storage system, the decay heat produced from the irradiated fuel salts was calculated to provide a reasonable time scale of the dormancy period. Using the same geometry assumed above, the neutron and gamma dose rates from the irradiated fuel salt at the end of the dormancy period were estimated, which will be useful for understanding the handling and radiation protection requirements for handling the irradiated fuel salt. Lastly, a reactor in the LOTUS test bed could use chloride-based fuel as opposed to the fluoride-based fuel used in MSRE. Thus, a literature study provided data to understand the similarities and differences between the characteristics of fluoride- and chloride-based salts in terms of salt chemistry, material characteristics, postirradiation behavior, neutronics, thermal hydraulics, and heat removal. This study, together with the proposed irradiated fuel salt management processes, preliminary criticality calculations, decay heat, and dose rate estimates, provides a strong basis for future investigation into the management of irradiated fuel salts generated during molten salt reactor technology demonstrations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Insights into Supported Subnanometer Catalysts Exposed to CO via Machine-Learning-Enabled Multiscale Modeling

Subnanometer catalysts offer high noble metal utilization and superior performance for several reactions. However, understanding their structures and properties on an atomic scale under working conditions is challenging due to the large configurational space. Here, we introduce an efficient multiscale framework to predict their stability exposed to an adsorbate. The framework integrates a comprehensive toolset including density functional theory (DFT) calculations, cluster expansion, machine learning, and structure optimization. The end-to-end machine-learning workflow guides DFT data generation and enables significant computational acceleration. We demonstrate the approach for CO-adsorbed Pdn (n = 1–55) clusters on CeO 2 (111). Simulation results reveal that CO can facilitate restructuring by stabilizing smaller planar structures and bilayer structures of specific intermediate sizes, consistent with experimental reports. Metal–support interactions, preferential CO adsorption, and metal nuclearity and structure control catalyst stability. As a result, the framework allows automatic discovery of stable catalyst structures and a systematic strategy to exploit properties in the subnanometer scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Large radiation back-flux from Monte Carlo simulations of fusion neutron–material interactions

Abstract Fusion power reactors will generate intense neutron fluxes into plasma-facing and structural materials (SMs). Radiation back-fluxes, generated from neutron–material interactions under these fluxes, can dramatically impact the plasma dynamics, e.g. by seeding runaway electrons during disruptions via Compton scattering of background electrons by wall-emitted gamma radiation. Here, we quantify these back-fluxes, including neutrons, gamma rays, and electrons, using Monte Carlo calculations for a range of SM candidates and first wall (FW) thicknesses. The radiation back-flux magnitudes are remarkably large, with neutron and gamma radiation back-fluxes on the same order of magnitude as the incident fusion neutron flux. Electron back-fluxes are two orders of magnitudes lower, but are emitted at sufficiently high energies to impact the sheath and boundary plasma dynamics. Material configuration plays a key role in determining back-flux magnitudes. The SM chiefly determines the neutron back-flux magnitude, while the FW thickness principally attenuates the gamma ray and electron back-fluxes. In addition to prompt back-fluxes, which are emitted immediately after fusion neutrons impact the surface, significant delayed gamma ray and electron back-fluxes arise from nuclear decay processes in the activated materials. These delayed back-flux magnitudes range from 2% to 7% of the prompt back-fluxes, and remain present during transients when fusion no longer occurs. During disruptions, build-up of delayed gamma radiation back-flux represents potential runaway electron seeding mechanisms, posing additional challenges for disruption mitigation in a power reactor compared with non-nuclear plasma operations. This work highlights the impact of these radiation back-fluxes plasma performance and demonstrates the importance of considering back-flux generation in materials selection for fusion power reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Actinide opacities for modelling the spectra and light curves of kilonovae

ABSTRACT We extend previous ab initio calculations of lanthanide opacities to include a complete set of actinide opacities for use in the modelling of kilonova (KN) light curves and spectra. Detailed, fine-structure line features are generated using the configuration-interaction approach. These actinide opacities display similar trends to those observed for lanthanide opacities, such as the lighter actinides producing higher opacity than the heavier ones for relevant conditions in the dynamical ejecta. A line-binned treatment is employed to pre-compute opacity tables for 14 actinide elements (89 ≤ Z ≤ 102) over a grid of relevant temperatures and densities. These tabular opacities will be made publicly available for general usage in KN modelling. We demonstrate the usefulness of these opacities in KN simulations by exploring the sensitivity of light curves and spectra to different actinide abundance distributions that are predicted by different nuclear theories, as well as to different choices of ejecta mass and velocity. We find very little sensitivity to the two considered distributions, indicating that opacities for actinides with Z ≥ 99 do not contribute strongly. On the other hand, a single actinide element, protactinium, is found to produce faint spectral features in the far-infrared at late times (5–7 d post merger). More generally, we find that the choice of ejecta mass and velocity have the most significant effect on KN emission for this study.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Electromagnetic production of kaons on the nucleon

Studies of the electromagnetic production of strange quarks started in the 1950s as something of a curiosity that puzzled experimentalists and theorists alike. Eventually, a nascent understanding of these processes began to take shape through the first pioneering experiments dedicated to explore photo- and electroproduction that were carried out in the period from the 1950s to the 1980s. As the datasets increased, concomitant advances in theoretical models were realized. However, these initial studies also made clear that more precise data was essential to continue to move forward. A paradigm shift occurred in the 1990s with the development of second-generation facilities at ELSA, MAMI, SPring-8, and JLab. High-intensity, high duty-factor accelerators, coupled with novel detector systems and advances in computing and readout electronics, brought nuclear physics experiments forward by orders of magnitude in counting statistics compared to the first-generation efforts. This was an utter boon to strangeness physics investigations, and to date, more than 50 dedicated experiments in kaon photo- and electroproduction have been completed at facilities around the world, leading to a host of experimental observables that have enabled significant advances in the exploration of strongly interacting systems that decay via $s\bar{s}$ quark pair creation. These data have proven to be an essential complementary pathway to study the spectrum and structure of the excited states of the nucleon, and the search for missing and exotic baryon configurations. As well, investigations in these channels are requisite for exploring hypernuclear production as a probe of the $YN$ interaction and for studies of the electromagnetic form factors of strange mesons. This review was designed to provide the first-ever in-depth overview of both the experimental and theoretical progress in the field of the electromagnetic production of strangeness. This work looks back over 70 years of past developments, discusses ongoing work and near-term plans, and details future possibilities being considered for third-generation facilities. Extensive lists of the available datasets and theoretical models are provided, together with a comprehensive supporting bibliography of the field. Throughout this work, the primary impacts of these explorations are highlighted, along with connections to a wide range of related phenomenological applications. An important goal of this review is to provide a complete, (reasonably) self-contained guide into this field prepared at a level that is relevant for both new and seasoned scientists, whether experimentalists, phenomenologists, or theorists, to better understand what has been accomplished by so many dedicated folks-each building on what has come before-and to appreciate the exciting future potential for continued studies in this area.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗