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At least 55 records · Page 3

Geological activity shapes the microbiome in deep-subsurface aquifers by advection

Subsurface environments host diverse microorganisms in fluid-filled fractures; however, little is known about how geological and hydrological processes shape the subterranean biosphere. Here, we sampled three flowing boreholes weekly for 10 mo in a 1478-m-deep fractured rock aquifer to study the role of fracture activity (defined as seismically or aseismically induced fracture aperture change) and advection on fluid-associated microbial community composition. We found that despite a largely stable deep-subsurface fluid microbiome, drastic community-level shifts occurred after events signifying physical changes in the permeable fracture network. The community-level shifts include the emergence of microbial families from undetected to over 50% relative abundance, as well as the replacement of the community in one borehole by the earlier community from a different borehole. Null-model analysis indicates that the observed spatial and temporal community turnover was primarily driven by stochastic processes (as opposed to deterministic processes). We, therefore, conclude that the observed community-level shifts resulted from the physical transport of distinct microbial communities from other fracture(s) that outpaced environmental selection. Given that geological activity is a major cause of fracture activity and that geological activity is ubiquitous across space and time on Earth, our findings suggest that advection induced by geological activity is a general mechanism shaping the microbial biogeography and diversity in deep-subsurface habitats across the globe.

59 BASIC BIOLOGICAL SCIENCES↗

Structurally Driven Selective Adsorption of Hydrocarbons by Metal Substitution in Isostructural Rare-Earth Metal–Organic Frameworks

The design and realization of highly selective nanoporous materials are necessary to target critical separations across industries. By leveraging pore size, pore shape, and linker functionalization, the design of nanoporous solid adsorbents will enable the rapid production of energy efficient separation materials for high-value gas mixtures. This study uses a combination of modeling, synthesis, and gas adsorption testing to investigate a new class of small-pore isostructural rare-earth (RE) 2,5-dihydroxyterephthalic acid (DOBDC) metal–organic frameworks (MOFs) (RE: Pr-, Gd-, Er-, Yb; DOBDC = 2,5-dihydroxyterephthalic acid) and their adsorption selectivity for acetylene/ethylene mixtures. Density functional theory simulations identified that selective binding of acetylene over ethylene in the Gd-, Er-, and Yb-DOBDC MOFs was due to hydrogen-bonding between acetylene and the linker hydroxyl. Adsorption experiments validated the computational results by identifying mechanisms that control the acetylene/ethylene adsorption selectivity and high acetylene adsorption. Furthermore, dynamic column breakthrough experiments with the Gd-DOBDC MOF validated the simulations and indicated that ethylene can be separated from acetylene in a mixture containing 1 vol % acetylene and 39 vol % ethylene (balance argon). In conclusion, the results highlight the complexity of gas binding in functional porous materials and how combining modeling and experiment enables a fundamental understanding of gas–framework interactions that can be leveraged for the design of future separation materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Noncoordinating Secondary Sphere Ion Modulates Supramolecular Clustering of Lanthanides

The role of counterions in molecular recognition of lanthanides is underexplored, especially when they exhibit weak interactions with the metal cations. Here, we report a complementary and comprehensive investigation integrating theoretical calculations with X-ray absorption fine structure spectroscopy, dynamic light scattering, and small-angle X-ray scattering to reveal atomic-scale structural features beyond the immediate coordination sphere of a system used for rare-earth element separations. Here, our results indicate the formation of an unusual T-shaped outer-sphere lanthanide complex, containing two ligands and two nitrate ions in the first coordination sphere, whereas the third nitrate is weakly coordinated and resides in the second shell. This unique structural arrangement causes inhomogeneous charge distribution, leading to self-assembly of the complexes into larger nanoclusters through sterically directed electrostatic interactions in the nonpolar medium. Our findings point to the importance of "noncoordinating" anions in defining the degree of supramolecular aggregation and ion cluster assembly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimentally determined traits shape bacterial community composition one and five years following wildfire

Abstract Wildfires represent major ecological disturbances, burning 2–3% of Earth’s terrestrial area each year with sometimes drastic effects above- and belowground. Soil bacteria offer an ideal, yet understudied system within which to explore fundamental principles of fire ecology. To understand how wildfires restructure soil bacterial communities and alter their functioning, we sought to translate aboveground fire ecology to belowground systems by determining which microbial traits are important post-fire and whether changes in bacterial communities affect carbon cycling. We employed an uncommon approach to assigning bacterial traits, by first running three laboratory experiments to directly determine which microbes survive fires, grow quickly post-fire and/or thrive in the post-fire environment, while tracking CO 2 emissions. We then quantified the abundance of taxa assigned to each trait in a large field dataset of soils one and five years after wildfires in the boreal forest of northern Canada. We found that fast-growing bacteria rapidly dominate post-fire soils but return to pre-burn relative abundances by five years post-fire. Although both fire survival and affinity for the post-fire environment were statistically significant predictors of post-fire community composition, neither are particularly influential. Our results from the incubation trials indicate that soil carbon fluxes post-wildfire are not likely limited by microbial communities, suggesting strong functional resilience. From these findings, we offer a traits-based framework of bacterial responses to wildfire.

54 ENVIRONMENTAL SCIENCES↗

Intermediate Bandgap (IB) Cu 3 VS x Se 4−x Nanocrystals as a New Class of Light Absorbing Semiconductors

A new family of highly uniform, cubic-shaped Cu 3 VS x Se 4−x (CVSSe; 0 ≤ x ≤ 4) nanocrystals based on earth-abundant materials with intermediate bandgaps (IB) in the visible range is reported, synthesized via a hot-injection method. The IB transitions and optical band gap of the novel CVSSe nanocrystals are investigated using ultraviolet-visible spectroscopy, revealing tunable band gaps that span the visible and near-infrared regimes. The composition-dependent relationships among the crystal phase, optical band gap, and photoluminescence properties of the novel IB semiconductors with progressive substitution of Se by S are examined in detail. High-resolution transmission electron microscopy and scanning electron microscopy characterization confirm the high crystallinity and uniform size (~19.7 nm × 17.2 nm for Cu 3 VS 4 ) of the cubic-shaped nanocrystals. Density functional theory (DFT) calculations based on virtual crystal approximation support the experimental findings, showing good agreement in lattice parameters and band gaps across the CVSSe series and lending confidence that the targeted phases and compositions have been successfully realized. A current conversion efficiency, i.e., incident photon-to-current efficiency, of 14.7% was achieved with the p-type IB semiconductor Cu 3 VS 4 . These novel p-type IB semiconductor nanocrystals hold promise for enabling thin film solar cells with efficiencies beyond the Shockley–Queisser limit by allowing sub-band-gap photon absorption through intermediate-band transitions, in addition to the conventional direct-band-gap transition.

Cu3VSxSe4−x↗

Geology and elevation shape bacterial assembly in Antarctic endolithic communities

Ice free areas of continental Antarctica are among the coldest and driest environments on Earth, and yet, they support surprisingly diverse and highly adapted microbial communities. Endolithic growth is one of the key adaptations to such extreme environments and often represents the dominant life-form. Despite growing scientific interest, little is known of the mechanisms that influence the assembly of endolithic microbiomes across these harsh environments. Here, we used metagenomics to examine the diversity and assembly of endolithic bacterial communities across Antarctica within different rock types and over a large elevation range. While granite supported richer and more heterogeneous communities than sandstone, elevation had no apparent effect on taxonomic richness, regardless of rock type. Conversely, elevation was clearly associated with turnover in community composition, with the deterministic process of variable selection driving microbial assembly along the elevation gradient. The turnover associated with elevation was modulated by geology, whereby for a given elevation difference, turnover was consistently larger between communities inhabiting different rock types. Overall, selection imposed by elevation and geology appeared stronger than turnover related to other spatially-structured environmental drivers. Our findings indicate that at the cold-arid limit of life on Earth, geology and elevation are key determinants of endolithic bacterial heterogeneity. This also suggests that warming temperatures may threaten the persistence of such extreme-adapted organisms.

54 ENVIRONMENTAL SCIENCES↗

Advanced Permanent Magnet Generator Topologies Using Multimaterial Shape Optimization and 3D Printing: Preprint

A vast majority of utility-scale wind turbine generators in the United States are dependent on foreign- sourced rare-earth permanent magnets that are vulnerable to supply chain uncertainties. Many small wind original equipment manufacturers are motivated to pursue continuous improvements to the generator design to lower the material and production costs and improve performance by lowering cogging torque and increasing the efficiency. Traditional design and manufacturing offer limited opportunities. In this work, we demonstrate advanced design approaches for a 15-kW baseline wind turbine generator by making use of recent progress in three-dimensional (3D) printing of polymer- bonded magnets and, electrical and structural steel. We explore three methods of magnet parametrization using Bezier curves resulting in symmetric, asymmetric and multimaterial magnet designs. We employ a multiphysics approach combining parametric computer-aided design modeling, finite- element analysis and targeted sampling to identify novel designs with more opportunities for reducing rare-earth material, improving efficiency and minimizing cogging torque. The results show that asymmetric-pole design and multimaterial-pole designs offer a greater opportunity to minimize rare-earth magnet materials by up to 35% with similar performance as the baseline generator, suggesting newer opportunities with design freedom beyond traditional limits of symmetry and as allowed by 3D printing.

Bezier curves↗

Evidence for autotrophic growth of purple sulfur bacteria using pyrite as electron and sulfur source

ABSTRACT Purple sulfur bacteria (PSB) are capable of anoxygenic photosynthesis via oxidizing reduced sulfur compounds and are considered key drivers of the sulfur cycle in a range of anoxic environments. In this study, we show that Allochromatium vinosum (a PSB species) is capable of autotrophic growth using pyrite as the electron and sulfur source. Comparative growth profile, substrate characterization, and transcriptomic sequencing data provided valuable insight into the molecular mechanisms underlying the bacterial utilization of pyrite and autotrophic growth. Specifically, the pyrite-supported cell cultures (“py”’) demonstrated robust but much slower growth rates and distinct patterns from their sodium sulfide-amended positive controls. Up to ~200-fold upregulation of genes encoding various c - and b -type cytochromes was observed in “py,” pointing to the high relevance of these molecules in scavenging and relaying electrons from pyrite to cytoplasmic metabolisms. Conversely, extensive downregulation of genes related to LH and RC complex components indicates that the electron source may have direct control over the bacterial cells’ photosynthetic activity. In terms of sulfur metabolism, genes encoding periplasmic or membrane-bound proteins (e.g., FccAB and SoxYZ) were largely upregulated, whereas those encoding cytoplasmic proteins (e.g., Dsr and Apr groups) are extensively suppressed. Other notable differentially expressed genes are related to flagella/fimbriae/pilin(+), metal efflux(+), ferrienterochelin(−), and [NiFe] hydrogenases(+). Characterization of the biologically reacted pyrite indicates the presence of polymeric sulfur. These results have, for the first time, put the interplay of PSB and transition metal sulfide chemistry under the spotlight, with the potential to advance multiple fields, including metal and sulfur biogeochemistry, bacterial extracellular electron transfer, and artificial photosynthesis. IMPORTANCE Microbial utilization of solid-phase substrates constitutes a critical area of focus in environmental microbiology, offering valuable insights into microbial metabolic processes and adaptability. Recent advancements in this field have profoundly deepened our knowledge of microbial physiology pertinent to these scenarios and spurred innovations in biosynthesis and energy production. Furthermore, research into interactions between microbes and solid-phase substrates has directly linked microbial activities to the surrounding mineralogical environments, thereby enhancing our understanding of the relevant biogeochemical cycles. Our study represents a significant step forward in this field by demonstrating, for the first time, the autotrophic growth of purple sulfur bacteria using insoluble pyrite (FeS2) as both the electron and sulfur source. The presented comparative growth profiles, substrate characterizations, and transcriptomic sequencing data shed light on the relationships between electron donor types, photosynthetic reaction center activities, and potential extracellular electron transfer in these organisms capable of anoxygenic photosynthesis. Furthermore, the findings of our study may provide new insights into early-Earth biogeochemical evolutions, offering valuable constraints for understanding the environmental conditions and microbial processes that shaped our planet’s history.

59 BASIC BIOLOGICAL SCIENCES↗

Improved Regional Moment Tensor Inversion for Moderately Large Earthquakes in the Western United States Using a 3D Earth Model Based on Full Waveform Tomography

The nature of seismic sources for moderately large (moment magnitude, M w 5.0–6.5) events are commonly characterized by their moment tensor (MT) solutions and obtained by inversion of regional distance (200–1600 km) long‐period (20–50 s) waveforms. Regional MT estimates are often calculated from average plane‐layered, one‐dimensional (1D) velocity models. However, 1D model calculations can produce misfits in the arrival times and waveform shapes that introduce errors, particularly at longer distances or for shorter periods, which are necessary for analyzing lower magnitude events. Approximate Earth models (e.g., 1D) representing broad areas may be inadequate, particularly in the crust and uppermost mantle of tectonically complex regions. In this study, we show how a three‐dimensional (3D) Earth model obtained from full waveform inversion tomography can improve waveform fits and decrease phase errors. We developed a platform and workflow to perform routine 3D MT inversions and inverted MTs for 25 earthquakes in the western United States and seven nuclear explosions using an average 1D and a recent 3D Earth model, WUS256 (Rodgers et al., 2022). Using the 3D model improves waveform fits (variance reduction and phase time shifts) compared with the 1D model, and the 3D MT solutions are stable across large distances. This study shows that 3D models obtained from full waveform tomography can improve MTs and source characterization especially at far regional distances (>800 km).

Geosciences↗

A Planetary Defense System For Responsive Space Missions

As King et al succinctly write, “Collision between the Earth and small objects in the solar system are known to occur regularly, and can result in extinction-level events at their most energetic or more commonly widespread loss of life or economic destruction even for relatively low-energy impacts.” Currently, the JPL Sentry System and the NASA NEO Surveyor mission track, identify, and monitor potential asteroid threats. The JPL Sentry System4 is an automated collision monitoring system which scans the current asteroid catalog for potential impact trajectories with Earth. A 2017 study led by P. Tricarico titled “The near-Earth asteroid population from two decades of observations” analyzes the combined observations of nine leading asteroid surveys. The NASA NEO Surveyor mission seeks to identify 90% of near-Earth objects (NEO) with diameters greater than 140 meters (460 feet) within 10 years. The NEO Surveyor combines data from two infrared imaging detectors to measure NEO size, composition, shape, rotational state, and orbits. Recently, the NASA Double Asteroid Redirection Test (DART) mission successfully altered the orbit of asteroid moon Dimorphos in 2022. This demonstrated that orbit alteration is possible. Thus, collisions between the Earth and asteroids are both likely and demonstrate potential for great harm. There is ongoing work to identify, catalog, and track potential threats. However, when a threat is identified there is not yet a system in place to target the threatening asteroid and defend the planet from potentially existential threats. Building on the DART Mission, we explore a planetary defense system to mitigate asteroid threats.

42 ENGINEERING↗

Rare‐Earth Reduction in High‐Speed PM‐Assisted Synchronous Reluctance Motors Using Hybrid Magnet Strategies and Design Optimisation for 800 V EVs

The trend towards electrifying transportation systems has stimulated research endeavours aimed at developing electric machines that are not only high speed and efficient but also low‐cost and compact. To support this transition, the US Department of Energy (DOE) has established ambitious targets of $7/kW cost and 12 kW/L power density for the electric drivetrains. This paper attempts to meet these targets by proposing high‐speed permanent magnet assisted synchronous reluctance machine (PMASynRM) topologies enabled by hybrid magnet strategies, combining rare‐earth (RE) magnets with low‐cost, RE‐free alternatives. Modified 2‐layer and 3‐layer U‐shaped rotor configurations, featuring structural reinforcements to withstand high mechanical stress at elevated speeds, are developed. A multi‐objective design optimisation framework is employed to optimise the rotor design, targeting reductions in RE magnet volume, magnet demagnetisation risk and torque ripple while achieving the desired electromagnetic performance. A comprehensive analysis of the optimised rotor designs, compared against a 16,000 rpm, 800 V baseline IPM motor, shows over 70% RE reduction, demagnetisation risk below 3.5% and torque ripple under 10%. Detailed analyses of performance trends across various magnet combinations and rotor configurations highlight the viability of hybrid magnet PMASynRM designs as cost‐effective, robust and energy‐efficient solutions for next‐generation EVs.

33 ADVANCED PROPULSION SYSTEMS↗

Small-amplitude Compressible Magnetohydrodynamic Turbulence Modulated by Collisionless Damping in Earth’s Magnetosheath: Observation Matches Theory

Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales and affects energetic particle transport. Recent advances in the understanding of compressible magnetohydrodynamic (MHD) turbulence demonstrate the important role of damping in shaping energy distributions on small scales, yet its observational evidence is still lacking. This study provides the first observational evidence of substantial collisionless damping (CD) modulation on the small-amplitude compressible MHD turbulence cascade in Earth’s magnetosheath using four Cluster spacecraft. Based on an improved compressible MHD decomposition algorithm, turbulence is decomposed into three eigenmodes: incompressible Alfvén modes and compressible slow and fast (magnetosonic) modes. Our observations demonstrate that CD enhances the anisotropy of compressible MHD modes because CD has a strong dependence on wave propagation angle. The wavenumber distributions of slow modes are mainly stretched perpendicular to the background magnetic field (B 0 ) and weakly modulated by CD. In contrast, fast modes are subjected to a more significant CD modulation. Fast modes exhibit a weak, scale-independent anisotropy above the CD truncation scale. Below the CD truncation scale, the anisotropy of fast modes enhances as wavenumbers increase. As a result, fast-mode fractions in the total energy of compressible modes decrease with the increase of perpendicular wavenumber (to B 0 ) or wave propagation angle. Our findings reveal how the turbulence cascade is shaped by CD and its consequences for anisotropies in the space environment.

97 MATHEMATICS AND COMPUTING↗

Comparative Life Cycle Assessment of Injection Molded and Big Area Additive Manufactured NdFeB Bonded Permanent Magnets

Permanent magnets are expected to play a crucial role in the realization of the clean economy. In particular, the neodymium-iron-boron (Nd2Fe14B or NdFeB) magnets, which have the highest energy density among rare earth permanent magnets, are needed for building more efficient windmill generators, electric vehicle motors, etc. Currently, near-net shape magnets can be either made through sintering and compression molding with extensive post machining or directly through injection molding. However, injection molding has a loading volume fraction limitation of 0.65 for nylon binders. A novel method of manufacturing bonded permanent magnets with loading fraction greater than 0.65 has been demonstrated using Big Area Additive Manufacturing (BAAM) printers. As energy density is directly proportional to the square of the magnet loading fraction, magnets produced using BAAM printers require less volume and magnetic material compared to that of injection molded magnets on average. A comparative LCA shows that this difference in magnetic powder consumption nearly constitutes the difference in the environmental impact categories. Even after assuming recycled magnetic input, the BAAM magnets perform better environmentally than injection molded magnets, especially in the ozone depletion category. Since BAAM printers can accommodate even higher loading fractions, at scale, BAAM printers possibly can bring about a significant decrease in rare earth mineral consumption and environmental emissions. So furthermore, single screw extrusion enables BAAM printers to have high print speeds and allow them to be economically competitive against injection molding. Therefore, BAAM printed magnets show promise in transitioning towards the clean economy.

36 MATERIALS SCIENCE↗

Impacts of Mean State Ocean Heat Transport on Climate and Its Response to CO 2 Forcing

Simulations of the slab ocean configuration of the coupled Energy Exascale Earth System Model (E3SM) were used to isolate the role of poleward ocean heat transport (OHT) in shaping the climate and its response to CO 2 forcing. Imposed changes to mean-state OHT produce compensating changes in atmospheric heat transport (AHT) that are mediated by changes in surface evaporation. A reduction of maximum OHT by 0.56 PW (32%) reduces the global mean surface air temperature by 3.6°C. However, this cooler mean state exhibits 1.2°C more warming under CO 2 quadrupling, with the largest differences occurring at high latitudes. The amplified warming arises from stronger surface albedo and lapse rate feedbacks in polar regions and a shortwave cloud feedback in the southern midlatitudes. These results highlight the critical role of mean-state OHT in modulating mean-state climate, the partitioning between the OHT and AHT, and climate sensitivity.

Atmosphere-ocean-ice interactions↗

The Arctic

Arctic observations in 2023 provided clear evidence of rapid and pronounced climate and environmental change, shaped by past and ongoing human activities that release greenhouse gases into the atmosphere and push the broader Earth system into uncharted territory. This chapter provides a snapshot of 2023 and summarizes decades-long trends observed across the Arctic, including warming surface air and sea-surface temperatures, decreasing snow cover, diminishing sea ice, thawing permafrost, and continued mass loss from the Greenland Ice Sheet and Arctic glaciers. These changes are driving a transition to a wetter, greener, and less frozen Arctic, with serious implications for Arctic peoples and ecosystems, as well as for low- and midlatitudes

54 ENVIRONMENTAL SCIENCES↗

Alkaline Earth-Based Ternary Chalcogenide Nanocrystals: Cadmium- and Lead-Free Optical Materials

As some of the most abundant elements on the Earth’s crust, alkaline earths bear great potential in Cd- and Pb-free catalytic, energy conversion, and light-emitting devices. Further, because large electropositive alkaline earths (Ae) can adopt high coordination numbers, they offer structural complexity beyond the tetrahedral (c-Si, II–VI, III–V) or octahedral (IV–VI) atomic sites that─with the notable exception of halide perovskites─are ubiquitous among nanocrystalline semiconductors. Here, in this work, we present a general route to photoluminescent 6–125 nm nanocrystals of ternary AeIn 2 Ch 4 semiconductors (Ae = Sr, Ba; Ch = S, Se) featuring eight- (Ae) as well as four-coordinate (In and Ch) atomic sites. Powder X-ray diffraction, electron microscopy, optical absorption, photoluminescence, and solid-state (ss)NMR spectroscopies attest to the ternary composition and phase purity of the nanocrystals. Continuous shape measures pinpoint the degree of distortion of individual crystallographic sites from ideal coordination polyhedra, allowing us to identify two very distinct types of Se coordination environments. Based on their higher order, pseudo-3-fold rotational symmetry, we assign 77 Se ssNMR peaks with negligible chemical shift anisotropy (CSA) to pyramidalized Se sites with vacant-trigonal bipyramid-like geometries and those with larger CSA to lower symmetry Se sites with seesaw-distorted geometries. Calculations help to better understand the electronic band structure of these materials. The nanocrystals are stable at room temperature in open air for several weeks, and some compositions up to 1000 °C under Ar, making them strong candidates for practical applications.

alkaline earth↗

Evidence for flare-accelerated particles in large scale loops in the behind-the-limb gamma-ray solar flare of September 29, 2022

We report on the detection of the gamma-ray emission above 100 MeV from the solar flare of September 29, 2022, by Fermi LAT with simultaneous coverage in HXR by Solar Orbiter STIX. The Solar Orbiter-Earth separation was 178° at the time of the flare as seen from Earth, with Solar Orbiter observing the east limb. Based on STIX imaging, the flare was located 16° behind the eastern limb as seen from Earth. The STIX and GBM non-thermal emission and the LAT emission above 100 MeV all show similarly shaped time profiles, and the Fermi profiles peaked only 20 s after the STIX signal from the main flare site, setting this flare apart from all the other occulted flares observed by Fermi LAT. The radio spectral imaging based on the Nançay Radioheliograph and ORFEES spectrograph reveal geometries consistent with a magnetic structure that connects the parent active region behind the limb to the visible disk. We studied the basic characteristics of the gamma-ray time profile, in particular, the rise and decay times and the time delay between the gamma-ray and HXR peak fluxes. We compared the characteristics of this event with those of four Fermi LAT behind-the-limb flares and with an on-disk event and found that this event is strikingly similar to the impulsive on-disk flare. Based on multiwavelength observations, we find that the gamma-ray emission above 100 MeV originated from ions accelerated in the parent active region behind the limb and was transported to the visible disk via a large magnetic structure connected to the parent active region behind the limb. Our results strongly suggest that the source of the emission above 100 MeV from the September 29, 2022 flare cannot be the CME-driven shock.

79 ASTRONOMY AND ASTROPHYSICS↗

The convergence of quadrupole rotational invariants from the nuclear shell model

Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of convergence is addressed. Shell-model calculations performed in the sd- and pf-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states using the first 40 states of the relevant spins. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined. It is found that, on average, the inclusion of four intermediate states results in the leading-order invariant, $\langle\hat{Q^2}\rangle$, converging to within 10% of its true value and the triaxiality term, cos (3δ), converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly. The convergence of quadrupole rotationally invariant sum rules was quantified in the sd- and pf-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Finally, larger spaces, such as the rare-earth region, potentially offer faster convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗