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At least 793 records · Page 44

Enabling integrated AI control on DIII-D: a control system design with state-of-the-art experiments

We present the design and application of a general algorithm for Prediction And Control using MAchiNe learning (PACMAN) in DIII-D. Machine learning (ML)-based predictors and controllers have shown great promise in achieving regimes in which traditional controllers fail, such as tearing mode (TM) free scenarios, ELM-free scenarios and stable advanced tokamak conditions. The architecture presented here was deployed on DIII-D to facilitate the end-to-end implementation of advanced control experiments, from diagnostic processing to final actuation commands. This paper describes the detailed design of the algorithm and explains the motivation behind each design point. We also describe several successful ML control experiments in DIII-D using this algorithm, including a reinforcement learning controller targeting advanced non-inductive plasmas, a wide-pedestal quiescent H-mode ELM predictor, an Alfvén Eigenmode controller, a Model Predictive Control plasma profile controller and a state-machine TM predictor-controller. There is also discussion on guiding principles for real-time ML controller design and implementation.

machine learning↗

Effect of outer divertor leg detachment on the high field side scrape-off layer in DIII-D and ASDEX Upgrade

In this work, evidence is presented that detachment of the outer divertor leg leads to a reduction of electron density and neutral pressure in the high-field side (HFS) scrape-off layer (SOL) of the ASDEX Upgrade (AUG) and DIII-D tokamaks with ion $B$ x $∇B$ drift directed toward the X-point (favorable configuration). These results are observed across multiple diagnostics and without the use of impurity seeding to reach detachment. In AUG, outer divertor leg detachment correlates with a decrease in electron density near the separatrix at the inner midplane, measured with HFS reflectometry. A concurrent reduction in inner divertor density and neutral pressure at the inner target is observed using divertor Thomson scattering and neutral pressure gauges. These effects are present in both L- and H-mode plasmas. In DIII-D, a similar reduction is detected through analysis of line-integrated hydrogenic emission measured by multiple diagnostics in the HFS SOL close to the separatrix. The consistent trends in both devices indicate that high electron density and strong hydrogenic emissivity in the HFS SOL are common features of H-mode plasmas in the favorable configuration, independent of wall material and divertor geometry. In L-mode plasmas, the reduction in electron density and neutral pressure is not observed in DIII-D, possibly due to differences in wall material. These results emphasize the importance of the divertor state in determining the two-dimensional neutral distribution and edge fueling.

detachment↗

Achievement of a high-density, high-confinement, and high-beta tokamak plasma regime in DIII-D, and implications for a lower-current path for ITER and FPP

Experiments on DIII-D have demonstrated a density-confinement synergy that enables sustainment of high performance in a previously unattained parameter regime of simultaneous very high energy confinement quality (H 98y2 ≥ 1.5), very high line-average density Greenwald fraction (ƒ Gr = πa 2 < n >/I P ≥ 1.4), and high toroidal beta (β T ≥ 3%). Tokamak operation in this regime is essential for a compact steady-state FPP, as well as for Q=10 with 500 MW of fusion power in ITER at I P << 15 MA. These experiments leveraged the knowledge that, in the high-poloidal-beta (β P ) regime, impurity and density gradients can enhance turbulence stabilization caused by high α MHD (α MHD ~(dβ P )⁄dr). This was described by theoretical predictions and gyrokinetic transport simulations [M.T. Kotschenreuther et al, 2024 Nucl. Fusion, 64 076033], and later confirmed by experiments on DIII-D [S. Ding et al, 2024 Nature 629 555]. To increase both β P and β T , the new experiments increased the ideal-wall stability β N -limit by using a smaller plasma-outer wall distance and higher triangularity in the plasma cross section (top/bottom average δ~0.9), enabled by the recent “shape & volume rise” (SVR) modification to the DIII-D divertor. The higher triangularity also contributed to achieving higher ƒ Gr by enabling higher pedestal density. At high density, the pedestal is ballooning limited and exhibits small and frequent ELMs, while the divertor is near detachment even without any impurity seeding. High plasma performance was attained and sustained reproducibly, with the eventual terminations brought about by an MHD mode destabilized as the current profile slowly continued to evolve. A path to stationary fully noninductive operation might include ECH injection to reduce both core impurity accumulation and the electron collisionality, thus increasing the bootstrap current. These experiments provide the first experimental demonstration of the ƒ Gr , H 98y2 , and β T values required simultaneously for ITER Q = 10 at I P < 10 MA, pointing to practical ways to improve the energy confinement in a fusion reactor.

Garofalo, Andrea M. [General Atomics, San Diego, C↗

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

D–MOPH–25: diverse MOF–molecule pairs for Henry’s constants prediction

Computational methods like grand-canonical Monte Carlo simulations and machine learning (ML) have accelerated metal–organic frameworks (MOF) exploration but are typically limited to a narrow range of adsorbates due to data availability and force field constraints. In this study, we introduce a dataset of diverse MOF–molecule pairs for Henry’s constant prediction, D–MOPH–25, which systematically explores a diverse chemical space by combining 113 molecular adsorbates with over 5000 MOF structures through an active learning process. D–MOPH–25 constitutes the most diverse adsorbate dataset used in any ML study of molecular adsorption in MOFs to date. Our workflow builds a benchmark for predicting Henry’s constants at 300 K, leveraging conformal prediction for uncertainty quantification. Assessment through Shannon entropy and uniform manifold approximation and projection confirms the comprehensiveness of D–MOPH–25 while highlighting the importance of robust classification to filter out unphysical data points in regression tasks. Although future enhancements in model architecture and sampling criteria could improve predictive performance, our dataset already spans the target space using only 2.31% of total possibilities. This comprehensive dataset facilitates assessment of model generalizability across adsorbate species and can establish a foundation for high-throughput MOF screening and ML-driven separation processes.

active learning↗

PRISM3D: a 3-D reference seismic model for Iberia and adjacent areas

SUMMARY We present PRISM3D, a 3-D reference seismic model of P- and S-wave velocities for Iberia and adjacent areas. PRISM3D results from the combination of the most up-to-date earth models available for the region. It extends horizontally from 15°W to 5°E in longitude, 34°N to 46°N in latitude and vertically from 3.5 km above to 200 km below sea level, and is modelled on a regular grid with 10 and 0.5 km of grid node spacing in the horizontal and vertical directions, respectively. It was designed using models inferred from local and teleseismic body-wave tomography, earthquake and ambient noise surface wave tomography, receiver function analysis and active source experiments. It includes two interfaces, namely the topography/bathymetry and the Mohorovičić (Moho) discontinuity. The Moho was modelled from previously published receiver function analysis and deep seismic sounding results. To that end we used a probabilistic surface reconstruction algorithm that allowed to extract the mean of the Moho depth surface along with its associated standard deviation, which provides a depth uncertainty estimate. The Moho depth model is in good agreement with previously published models, although it presents slightly sharper gardients in orogenic areas such as the Pyrenees or the Betic-Rif system. Crustal and mantle P- and S-wave wave speed grids were built separately on each side of the Moho depth surface by weighted average of existing models, thus allowing to realistically render the speed gradients across that interface. The associated weighted standard deviation was also calculated, which provides an uncertainty estimation on the average wave speed values at any point of the grid. At shallow depths (<10 km), low P and S wave speeds and high VP/VS are observed in offshore basins, while the Iberian Massif, which covers a large part of western Iberia, appears characterized by a rather flat Moho, higher than average VP and VS and low VP/VS. Conversely, the Betic-Rif system seems to be associated with low VP and VS, combined with high VP/VS in comparison to the rest of the study area. The most prominent feature of the mantle is the well known high wave speed anomaly related to the Alboran slab imaged in various mantle tomography studies. The consistency of PRISM3D with previous work is verified by comparing it with two recent studies, with which it shows a good general agreement.The impact of the new 3-D model is illustrated through a simple synthetic experiment, which shows that the lateral variations of the wave speed can produce traveltime differences ranging from –1.5 and 1.5 s for P waves and from –2.5 and 2.5 s for S waves at local to regional distances. Such values are far larger than phase picking uncertainties and would likely affect earthquake hypocentral parameter estimations. The new 3-D model thus provides a basis for regional studies including earthquake source studies, Earth structure investigations and geodynamic modelling of Iberia and its surroundings.

Arroucau, P.↗

T d to 1 T' structural phase transition in the WTe 2 Weyl semimetal

Elastic neutron scattering on a single crystal combined with powder x-ray diffraction measurements were carried out to investigate how the crystal structure evolves as a function of temperature in the Weyl semimetal WTe 2 . Here, a sharp transition from the low-temperature orthorhombic phase T d to the high-temperature monoclinic phase 1T' was observed at ambient pressure in the single crystal near ~565 K. Unlike in MoTe 2 , the solid-solid transition from T d to 1T' occurs without the cell doubling of the intermediate T d * phase with AABB (or ABBA) layer stacking. In powders, however, the thermal transition from the Td to the 1T' phase was broadened and a two-phase coexistence was observed until 700 K, well above the structural transition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Mass enhancement in 3 d and s - p perovskites from symmetry breaking

In some d-electron oxides, the measured effective mass m* exptl has long been known to be significantly larger than the model effective mass m* model deduced from mean-field band theory, i.e., m* exptl =βm* model , where β>1 is the “mass-enhancement” or “mass-renormalization” factor. Previous applications of density functional theory (DFT), based on a symmetry-restricted structure with the smallest number of possible magnetic, orbital, and structural degrees of freedom, missed such mass enhancement. This fact has been taken as evidence of strong electronic correlation, often described via the symmetry-restricted dynamic mean-field approach of the many-body theory, being the exclusive enabling physics. This paper uses instead a static density functional approach that does not restrict positional or spin degrees of freedom (symmetry-broken structures). This approach analyzes the contributions of different symmetry-broken modalities to mass enhancement for a few nominally highly correlated d-electron perovskites as well as the nominally uncorrelated, closed-shell s-p bonding perovskites. It shows that the energy-lowering symmetry-broken spin effects (e.g., nonzero local moment in the paramagnetic phase) and structural effects (e.g., atomic displacement) as described in mean-field DFT already manifest mass enhancement for both electrons and holes in a range of d-electron perovskites SrVO 3 , SrTiO 3 , BaTiO 3 , and LaMnO 3 , as well as p-electron perovskites CsPbI 3 and SrBiO 3 , including both metals (SrVO 3 ) and insulators (the rest). This is revealed only when enlarged unit cells of the same parent global symmetry, which are large enough to allow for symmetry-breaking distortions and concomitant variations in spin order, are explored for their ability to lower the total energy. Positional symmetry breaking that leads to mass enhancement includes octahedral rotation in halide perovskites such as CsPbI 3 , Jahn-Teller-like Q${+}\atop{2}$ distortion in LaMnO 3 , and bond disproportionation in SrBiO 3 , while magnetic symmetry breaking resulting in mass enhancement includes the formation of a distribution of local moments in SrVO3 that averages to zero in the paramagnetic phase. Not all symmetry breaking leads to significant mass enhancement, e.g., the rather small octahedral rotations in the nearly perfectly cubic SrTiO 3 cause negligible mass enhancement, as do the paraelectric displacements in BaTiO 3 . In principle, by ergodicity, the two descriptions, i.e., the symmetry-restricted dynamic approach with a single time-fluctuating magnetic moment and the symmetry-broken mean-field approach with a static distribution of spatially fluctuated local moments, are not mutually exclusive but are a choice of representation and consequently, a choice of computational efficiency. In approximate implementations, the symmetry-broken mean-field approach appears to remove much of what was strong correlation in dynamically correlated symmetry-restricted solutions, leaving smaller (“weak”) residual correlation with respect to the exact solution.

36 MATERIALS SCIENCE↗

Orthorhombic distortion drives orbital ordering in the antiferromagnetic 3$d$ 1 Mott insulator PrTiO 3

The orbital, which represents the shape of the electron cloud, very often strongly influences the manifestation of various exotic phenomena, e.g., magnetism, metal-insulator transition, colossal magnetoresistance, unconventional superconductivity, etc. in solid-state systems. The observation of the antiferromagnetism in $RE$TiO 3 ($RE$ = rare-earth) series has been puzzling since the celebrated Kugel-Khomskii model of spin-orbital superexchange predicts ferromagnetism in an orbitally degenerate $d$ 1 system. Further, the existence of the orbitally ordered vs. orbital liquid phase in both antiferromagnetic and paramagnetic phase have been unsettled issues thus far. To address these longstanding questions, we investigate single crystalline film of PrTiO 3 . Our synchrotron x-ray diffraction measurements confirm the retention of bulklike orthorhombic ($D_{2h}$) symmetry in the thin film geometry. We observe similar x-ray linear dichroism signal in both paramagnetic and antiferromagnetic phase, which can be accounted by ferro-orbital ordering (FOO). While the presence of $D_{2h}$ crystal field does not guarantee lifting of orbital degeneracy always, we find it to be strong enough in these rare-earth titanates, leading to the FOO state. Thus, our work demonstrates the orthorhombic distortion is the driving force for the orbital ordering of antiferromagnetic $RE$TiO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Reappraisal of SU(3)-flavor breaking in B → D P

In light of recently found deviations of the experimental data from predictions from QCD factorization for B ( s ) → D ( s ) P decays, where P = { π , K } , we systematically probe the current status of the SU ( 3 ) F expansion from a fit to experimental branching ratio data without any further theory input. We find that the current data are in agreement with the power counting of the SU ( 3 ) F expansion. While the SU ( 3 ) F limit is excluded at > 5 σ , amplitude-level SU ( 3 ) F -breaking contributions of ∼ 20 % suffice for an excellent description of the data. SU ( 3 ) F breaking is needed in tree ( > 5 σ ) and color-suppressed tree ( 2.4 σ ) diagrams. We are not yet sensitive to SU ( 3 ) F breaking in exchange diagrams. From the underlying SU ( 3 ) F parametrization we predict the unmeasured branching ratios B ( B ¯ s 0 → π − D + ) = 2 B ( B ¯ s 0 → π 0 D 0 ) = [ 0.3 , 7.2 ] × 10 − 6 of suppressed decays that can be searched for at the LHCb experiment. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

1-D Convolutional Graph Convolutional Networks for Fault Detection in Distributed Energy Systems

This paper presents a 1-D convolutional and graph convolutional networks for fault detection in microgrids. The combination of 1-D convolutional neural networks (1D-CNN) and graph convolutional networks (GCN) helps extract both spatial-temporal correlations from the voltage measurements in microgrids. The fault detection scheme includes fault event detection, fault type and phase classification, and fault location. There are five neural network model training to handle these tasks. Transfer learning and fine-tuning are applied to reduce training efforts. The combined 1-D convolutional and graph convolutional networks (1D-CGCN) is compared with the traditional ANN structure on the Potsdam 13-bus microgrid dataset. The accuracy of 99.5%, 98.4%, 99.2%, and 95.5% are achieved in fault event detection, fault type classification, fault phase identification, and fault location respectively. The detailed confusion matrices of fault type and fault phase classification are provided for validation.

deep neural network↗

Insights into Na + Diffusion in Silicon Modules under Operating Conditions: Measuring Low Concentrations by D-SIMS

Sodium induced shunting under an electric field is a challenging reliability issue in crystalline Si solar modules. The source of this Potential-Induced Degradation of the Shunting type (PID-s) is well understood and its influence on power loss has been intensively studied based on phenomenological models on cell or module level relating the experimental power-loss to stressing parameters (time, temperature, voltage). However, little is known about the Na ion migration kinetics, responsible for PID on a microscopic level, and its quantitative relation to the efficiency degradation. In this paper we present our investigations of sodium ion migration in Ethylene-Vinyl Acetate (EVA) and silicon through Dynamic Secondary Ion Mass Spectroscopy (D-SIMS). Each sample was annealed at field relevant temperatures from 60-90 °C to address typical migration mechanisms of common PV installations. Analysis of the SIMS migration profiles revealed a diffusivity constant D 0,EVA = 0.09 ± 0.14 cm 2 /s and an activation energy E A,EVA = 0.85 ± .04 eV for Na in EVA and diffusivities higher than extrapolated literature values in silicon (D 0,Si = (3.03 ± 2.42)x10 -5 cm 2 /s, and E A,Si = 0.98 ± 0.02 eV). The new insight will be included in a drift-diffusion based degradation model accounting for the partition coefficient across all relevant interfaces. This model can assist in predicting PID-failure in the field based on the given model stack and the diffusion of Na + through each material. Furthermore, this tool can be used for process optimization as well as material selection significantly reducing the cost and time to validate a technology.

14 SOLAR ENERGY↗

Fabrication of a Nb-Ti Superconducting Closed-Loop Coil for the Next-Generation 45 GHz ECR Ion Source MARS-D

Electron Cyclotron Resonance Ion Sources (ECRISs) that utilize Nb-Ti superconducting coils for 28 GHz frequencies have been operating effectively for over twenty years. However, transitioning to higher frequencies demands stronger magnetic fields, and the conventional racetrack-and-solenoid ECRIS structures have reached their maximum capability with Nb-Ti. To address this, a Mixed Axial and Radial field System Demonstrator (MARS-D) is being developed at Lawrence Berkeley National Laboratory (LBNL). This system features an innovative Closed-Loop Coil (CLC) design that optimizes the use of the conductor fields, enabling the application of Nb-Ti in the next-generation 45 GHz ECRISs. The fabrication of the hexagonal CLC is particularly challenging due to its complex winding path and shape, the stiffness of the Nb-Ti superconducting wire, and the small bending radius. Here, to address these challenges, a series of unique fixtures and tools, as well as a pre-over-bending method, were developed for winding the CLC. To validate the winding fixtures, tools, procedures, and materials used in the coil assembly, a 4-layer practice CLC was wound, epoxy-impregnated, and then cold-tested using liquid nitrogen. The full-size MARS-D CLC is in the process of winding. This paper presents the structure of the MARS-D CLC, the winding fixtures and tools, the winding procedures, the quality control, the impregnation, the test results, and the potential future improvements.

ECR ion sources↗

Eddy Current Loss Model Unifying the Effects of Reaction Field and Non-Homogeneous 3-D Magnetic Field

In this article, a new analytical method is proposed to estimate eddy currents inside linear conductive materials. The novel closed-form formulation takes into account the effects of both conductor reaction field that dominates at high frequencies as well as the spatially non-homogeneous nature of the magnetic field penetrating the material. Although the model is suitable for most kinds of permanent magnet machines, it is particularly useful for Surface-mounted Permanent Magnet (SPM) machines where both of these phenomena are prominent. The numerical implementation of the proposed model, which consists of a combination of the method of images and 4-D Fourier transform, is presented. The model is then validated against 2-D and 3-D finite element models (FEMs) for a simple magnetic circuit, showing good agreement. Finally, the eddy current magnet loss in an SPM synchronous machine is evaluated and results are discussed.

Sahu, Raj↗

DIII-D Electron Cyclotron Heating and Current Drive System Status and Plans

The DIII-D 110 GHz Electron Cyclotron Heating and Current Drive (ECH/ECCD) System supports a wide range of experiments at the DIII-D National Fusion Facility and is pioneering innovative new techniques for future fusion reactors. Here, the system currently includes 8 sockets with 4 installed gyrotrons, 31.75 mm circular corrugated transmission lines, four dual real time steerable launchers plus two Top Launchers. After the successful testing of the first Top Launcher, that injects the EC waves downward nearly parallel to the resonance layer with double current drive efficiency and a long absorption path, a second new Top Launcher was designed and installed with an upgraded design. Some of the operational limitations encountered for the 110 GHz X-mode second harmonic resonance scenario launched in over-dense plasmas were overcome with the alternative use of O-mode second harmonic launch. Two new gyrotrons in a new series manufactured by CPI were installed and tested, bringing up the total installed power to 3 MW. The installation of repaired and new gyrotrons will increase the number of installed gyrotrons to 7 in 2023. An addition to the DIII-D building will be completed in early 2022 to provide the space to expand the ECH/ECCD system to ten gyrotron systems, plus an extra gyrotron test socket.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Implementation of a Doppler-Free Saturation Spectroscopy (DFSS) Diagnostic for Helicon Wave Electric Field Vector Measurement in Edge Plasma in DIII-D

A laser-based technique known as Doppler-free saturation spectroscopy (DFSS) has been designed, fabricated, and installed on the DIII-D National Fusion Facility to measure the helicon wave electric field vector in the edge plasma. These experimental measurements quantify phenomena resulting in decreased current drive efficiency due to wave/edge plasma interactions. This implementation of DFSS on DIII-D is the first of its kind on a tokamak and thus presents unique engineering challenges, including integration of the system onto an existing multidiagnostic port flange without impacts to system serviceability, as well as maintaining precise laser alignment over a 2-m distance during disruptions and thermal drift of the vessel. Further, these challenges were resolved using innovative design approaches such as a novel decoupled shutter system to facilitate serviceability of the in-vessel mirror assemblies without the need for personnel vessel entry, as well as an ex-vessel piezo-mirror-based optical system for laser beam shaping and real-time steering of the measurement location. The solutions to these engineering challenges were demonstrated during the successful installation and operation of these diagnostic components during the 2022 DIII-D vent and subsequent experimental campaign.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Geothermal Energy R&D: An Overview of the U.S. Department of Energy’s Geothermal Technologies Office

Geothermal energy can provide answers to many of America’s essential energy questions. The United States has tremendous geothermal resources, as illustrated by the results of the DOE GeoVision analysis, but technical and non-technical barriers have historically stood in the way of widespread deployment of geothermal energy. The U.S. Department of Energy’s Geothermal Technologies Office within the Office of Energy Efficiency and Renewable Energy has invested more than $470 million in research and development (R&D) since 2015 to meet its three strategic goals: (1) unlock the potential of enhanced geothermal systems, (2) advance technologies to increase geothermal energy on the U.S. electricity grid, and (3) support R&D to expand geothermal energy opportunities throughout the United States. Here, we describe many of those R&D initiatives and outlines future directions in geothermal research.

energy storage systems↗

Excitation functions and isomeric cross-section ratios of (d,xn) reactions on 86 Sr

Excitation functions of the 86 Sr(d,n) 87m,87g Y, 86 Sr(d,2n) 86m,86g Y and 86 Sr(d,3n) 85m,85g Y reactions on enriched 86 Sr target were measured by the activation technique up to deuteron energies of 49 MeV. The isomeric cross-section ratios as a function of projectile energy were deduced from the measured data for 87m Y, 87g Y(cum), 86m Y, 86g Y(cum), 85m Y and 85g Y pairs for the same energy range. All measurements are reported for the first time. The experimental data were compared with the data from the TENDL library which is based on TALYS calculation with default parameters. No satisfactory agreement was observed. Nuclear model calculations were then performed using the codes TALYS and EMPIRE with some parameter adjustments, and compared with the experimental data. The quality of the agreement between experimental data and model calculations was numerically quantified. In general, the data as well as the isomeric cross-section ratios are partially reproduced by the model calculations, provided the input model parameters are properly chosen and the level structure of the product nucleus is thoughtfully considered.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗