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DOE OSTI2026

Ecological Insights from Transferable Plant Biomass Mapping across the Arctic using High-resolution Structure-from-Motion and LiDAR Data

Warmer temperatures, permafrost thaw, and increased wildfire activity are driving rapid ecological change across the Arctic, significantly altering plant productivity and aboveground biomass (AGB). These rapid changes highlight the urgent need to improve monitoring of vegetation dynamics in the Earth’s northern ecosystems, where high spatiotemporal heterogeneity occurs at scales finer than those captured by traditional satellite observations. The growing use of Unoccupied Aerial Systems (UASs) presents an opportunity to overcome this limitation. Yet, the diversity of UAS platforms, sensors, and data collection and processing workflows presents challenges for developing standardized, generalizable approaches. To address this challenge, we compiled 672 AGB plots co-located with 183 UAS-based Structure-from-Motion (SfM) or Light Detection and Ranging (LiDAR) surveys collected across the Arctic. Here, we: (1) evaluated the generalizability of UAS-derived canopy structure derived from high-resolution SfM and LiDAR for estimating AGB, (2) assessed scaling errors and their sources in two recent satellite-based AGB products derived from Landsat and MODIS, and (3) demonstrated the use of high-resolution AGB maps to quantify biomass variation across tundra plant functional types (PFTs) and to monitor post-fire recovery. Our results show that both SfM and LiDAR accurately captured AGB and its variability across tundra PFTs using a Random Forest (RF) model (overall RMSE: 0.336 kg/m2), with mapping performance varying slightly by region and data source. Using UAS-derived AGB maps as a benchmark, we identified systematic biases in satellite-derived AGB products, largely attributable to the magnitude of AGB and structural heterogeneity within coarse-resolution pixels. Applying our model to repeat UAS surveys following a tundra fire on Seward Peninsula, we observed rapid AGB recovery in non-shrub patches, with biomass recovering to pre-fire levels within 2 years. In contrast, shrub patches recovered more slowly, with AGB gains continuing over 2–4 years through both in-patch growth and lateral expansion (via dispersal) into remaining burned areas. Overall, these findings demonstrate the generalizability of UAS-based SfM and LiDAR data for estimating tundra AGB and highlight the potential of our approach to be broadly applied to generate high-quality AGB data for ecological monitoring and model benchmarking across the Arctic.

Yang, Daryl [ORNL] (ORCID:0000000317057823)↗

DOE OSTI2025

Comparison of stress tolerance mechanisms between Saccharomyces cerevisiae and the multistress-tolerant Pichia kudriavzevii

Yeasts play a vital role in both research and industrial biomanufacturing. Saccharomyces cerevisiae has been extensively utilized as a model system. However, its application is often constrained by limited tolerance to the diverse stress conditions encountered in bioprocesses. These challenges have driven increasing interest in nonconventional, multistress-tolerant yeasts as alternative biomanufacturing hosts. This review highlights Pichia kudriavzevii as a promising nonconventional yeast for industrial applications. Unlike S. cerevisiae, P. kudriavzevii exhibits exceptional tolerance to high temperatures, elevated concentrations of furanic and phenolic inhibitors, osmotic stress, salinity, and extreme pH. These traits make it an attractive candidate for industrial processes without requiring extensive genetic modifications to enhance stress resistance. As a result, P. kudriavzevii has emerged as a flagship species for advancing bioeconomy. Despite its industrial potential, the molecular mechanisms underlying P. kudriavzevii's superior stress tolerance remain poorly understood. This review compiles current knowledge on P. kudriavzevii and compares its stress tolerance mechanisms with those of S. cerevisiae, providing insights into its innate resilience. By expanding our understanding of nonconventional yeasts, this review aims to facilitate their broader adoption as robust microbial platforms for industrial biomanufacturing.

Frousnoon, Thasneem Banu↗

DOE OSTI2026

Comprehensive earthquake catalogue update and spatiotemporal distribution analysis for Iraq and surrounding regions, northeastern Arabian Plate

The updated earthquake catalogue for Iraq covers the period from 1900 to the end of 2021 and includes over 37 000 recorded earthquakes. To create this comprehensive catalogue, five key steps were taken: compiling bulletins, calculating moment magnitudes, harmonizing magnitudes, establishing empirical conversion relations and evaluating the completeness of the catalogue. A notable enhancement in this update is the direct calculation of moment magnitudes for approximately 2800 earthquakes, achieved through the coda envelope technique and waveform data from the Mesopotamian Seismological Network (MPSN) in Iraq. This updated catalogue serves as a valuable resource for examining the spatiotemporal distribution of earthquakes, with respect to earthquake density, maximum moment magnitude and seismogenic depths. Additionally, the Gutenberg–Richter relationship was applied to calculate the a- and b-values specific to Iraq. The findings show that the Zagros Fold-Thrust Belt has a seismogenic layer (source) that ranges from 2 to 33 km deep and experiences high seismic activity. In contrast, the Mesopotamian Foredeep has a seismogenic layer ranging from 1 to 25 km deep and has lower seismic activity. The greatest seismic activity is concentrated around the Mandili-Badra-Teeb fault, which has experienced significant ruptures over time. The Outer Arabian Platform is identified as the main area of seismic activity, while additional activity occurs on the Inner Arabian Platform. Three major tectonic boundaries define the distribution of earthquakes in the northeastern Arabian Plate. These boundaries are defined by the Main Zagros Reverse Fault, the Zagros Foredeep Fault and the Anah Graben and Abu Jir-Euphrates Fault Zone. These boundaries highlight variations in seismicity levels and the spatial distribution of deformation in the region. The updated earthquake catalogue presented in this study is expected to play a vital role in regional seismicity assessments and seismic hazard analyses for Iraq and its surrounding areas.

58 GEOSCIENCES↗

DOE OSTI2025

Mapping the cosmic gamma-ray horizon: the 1CGH catalogue of Fermi -LAT detections above 10 GeV

ABSTRACT We present the First Cosmic Gamma-ray Horizon (1CGH) catalogue, featuring $\gamma$-ray detections above 10 GeV based on 16 yr of observations with the Fermi Large Area Telescope (Fermi-LAT) satellite. After carefully selecting a sample of blazars and blazar candidates from catalogues in the literature, we performed a binned likelihood analysis and identified 2791 $\gamma$-ray emitters above 10 GeV, at >3$\sigma$ level, including 62 that are new $\gamma$-ray detections. For each source, we estimated the mean energy of the highest energy bin and analysed them in the context of the cosmic gamma-ray horizon. By adopting a reference model for the extragalactic background light (EBL), we identified a subsample of 525 sources where moderate to severe $\gamma$-ray absorption could be detected across the redshift range of 0–3. This work provides the most up-to-date compilation of detections above 10 GeV, along with their redshift information. We condense extensive results from the literature, including reports on observational campaigns dedicated to blazars and $\gamma$-ray sources, thereby delivering an unprecedented review of the redshift information for sources detected above 10 GeV. Additionally, we highlight key 1CGH sources where redshift information remains incomplete, offering guidance for future optical observation campaigns. The 1CGH catalogue aims to track the most significant sources for studying the $\gamma$-ray transparency of the Universe. Furthermore, it provides a targeted subsample where the EBL optical depth, $\tau _{(E,z)}$, can be robustly measured using Fermi-LAT data.

Arsioli, Bruno (ORCID:0000000181666602)↗

DOE OSTI2025

Comparing the DES-SN5YR and Pantheon+ SN cosmology analyses: investigation based on ‘evolving dark energy or supernovae systematics’?

Recent cosmological analyses measuring distances of type Ia supernovae (SNe Ia) and baryon acoustic oscillations (BAO) have all given similar hints at time-evolving dark energy. To examine whether underestimated SN Ia systematics might be driving these results, Efstathiou (2025) compared overlapping SN events between Pantheon+ and DES-SN5YR (20 per cent SNe are in common), and reported evidence for an $\sim$0.04 mag offset between the low- and high-redshift distance measurements of this subsample of events. If this offset is arbitrarily subtracted from the entire DES-SN5YR sample, the preference for evolving dark energy is reduced. In this paper, we show that this offset is mostly due to different corrections for Malmquist bias between the two samples; therefore, an object-to-object comparison can be misleading. Malmquist bias corrections differ between the two analyses for several reasons. First, DES-SN5YR used an improved model of SN Ia luminosity scatter compared to Pantheon+ but the associated scatter-model uncertainties are included in the error budget. Secondly, improvements in host mass estimates in DES-SN5YR also affected SN standardized magnitudes and their bias corrections. Thirdly, and most importantly, the selection functions of the two compilations are significantly different, hence the inferred Malmquist bias corrections. Even if the original scatter model and host properties from Pantheon+ are used instead, the evidence for evolving dark energy from CMB, DESI BAO Year 1 and DES-SN5YR is only reduced from 3.9$\sigma$ to 3.3$\sigma$, consistent with the error budget. Finally, in this investigation, we identify an underestimated systematic uncertainty related to host galaxy property uncertainties, which could increase the final DES-SN5YR error budget by 3 per cent. In conclusion, we confirm the validity of the published DES-SN5YR results.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Methods to Track Effective Doses from Airborne Radioactive Emissions for Compliance with 40 CFR 61, SUBPART H

US Department of Energy national laboratories can play an integral role in not only the advancement of science but also in the treatment of various medical conditions through research and development activities conducted at radioisotope production facilities. Here, a project has been underway at Oak Ridge National Laboratory since 2016 whose mission is to produce and supply the radioisotope 227 Ac, which is used in a radiopharmaceutical developed to treat certain types of prostate cancer and bone metastases. Production activities result in the environmental release of airborne radioactive emissions, which are governed by Clean Air Act regulations described in 40 CFR Part 61, Subpart H. Stack 3039, the source that emits radioactive effluents from 227 Ac production, is subject to additional requirements outlined in American National Standards Institute (ANSI) N13.1-1969 due to its grandfathered status. Radioactive emissions are limited to levels below those that would cause annual compliance dose standards for members of the public to be exceeded and stack 3039 to lose its grandfathered status. To allow for maximum production of 227 Ac without exceeding relevant dose limits, monthly tracking of project emissions and resulting CAP88-PC modeled effective doses to a maximally exposed individual have been implemented. Four years of tracking data were compiled and analyzed to identify additional methods that could be used to estimate project doses more frequently, potentially further optimizing 227 Ac production while maintaining compliance with applicable regulations.

atmospheric emissions↗

DOE OSTI2026

Fault-tolerant resource comparison of qudit and qubit encodings for diagonal quadratic operators

Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings, but their fault-tolerant advantage over qubit encodings remains unclear. We compare the non-Clifford cost of implementing quadratic diagonal evolutions, exemplified by 𝑈 = 𝑒$^{−𝑖⁢𝑡⁢𝜙^2_𝑥}$ in a uniform field-amplitude discretization of a real scalar field, using either one logical 𝑑-level qudit or 𝑛 𝑏 = ⌈log 2⁡ 𝑑⌉ logical qubits. We analyze two standard settings: product-formula simulation and linear combination of unitaries (LCU) per block encoding, taking the resource metric to be the number of non-Clifford gates after synthesis into a discrete logical gate set. Because tight synthesis bounds for general single-qudit rotations are not known, we express the qudit constructions in terms of embedded two-level SU⁡(2) rotations and derive explicit finite-𝑑 break-even conditions for their synthesis cost; these serve as compiler targets for when qudit encodings can outperform the qubit baseline. Within the constructive models studied here, product-formula implementations would require an exponentially stronger per-primitive synthesis advantage for qudits to win asymptotically, while in the LCU setting the qubit encoding is asymptotically cheaper in 𝑑. Nevertheless, the finite-𝑑 threshold analysis identifies low-dimensional regions in which qudits can yield meaningful constant-factor savings, particularly for LCU-based implementations. As a secondary analysis of the LCU construction, we use an idealized negligible-overhead qubit-qudit code-switching model to give an absolute 𝑇-count comparison and reinterpret the savings as an allowable per-switch overhead budget.

Godwood, Samuel [Univ. of Liverpool (United Kingdo↗

DOE OSTI2025

Synthesis of single-qutrit circuits from Clifford+𝑅 gates

Here, we present two deterministic compilation algorithms for single-qutrit unitaries with O ( log 1 / ɛ ) gate depth. Each algorithm selects a nearby approximation to the target unitary and then exactly synthesizes the approximation over the Clifford + R basis. The first algorithm exhaustively searches over the group; while the second algorithm searches only for Householder reflections. The exhaustive search algorithm yields an average R count of 2.193 ( 11 ) + 8.621 ( 7 ) log 10 ( 1 / ɛ ) , albeit with a time complexity of O ( ɛ − 4.4 ) . The Householder search algorithm results in a larger average R count of 3.20 ( 13 ) + 10.77 ( 3 ) log 10 ( 1 / ɛ ) at a reduced time complexity of O ( ɛ − 0.42 ) , greatly extending the reach in ɛ . These costs correspond asymptotically to 35% and 69% more non-Clifford gates compared with synthesizing the same unitary with two qubits. Such initial results are encouraging for using the R gate as the nontransversal gate for qutrit-based computation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Logical error rates for the surface code under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions

With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical errors in plausible hardware implementations of quantum error-correcting codes. Detailed error modeling of computational instructions on particular FTQC architectures will enable the better prediction of error propagation in FT-encoded quantum circuits while revealing where greater attention is needed in hardware design. In this work, we consider logical error rates for the surface code implemented on a hypothetical grid-based trapped-ion quantum charge-coupled device architecture. Specifically, we construct logical channels for the idling surface code and examine its diamond error under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions. We include the coherent dephasing noise that is known to accumulate during physical qubit idling and transport in these systems, determining idling and transport durations using the time-resolved output of an open-source trapped-ion surface code compiler. To estimate expectation values of logical Pauli observables following hardware circuits containing non-Clifford sources of noise, we utilize a Monte Carlo technique to sample from an underlying quasiprobability distribution of Clifford circuits that we independently simulate in a phase-sensitive fashion. We verify error suppression up to code distance 𝑑 = 11 at coherent dephasing rates near and below those of current-generation trapped-ion quantum computers and find that logical error rates align with those of analogous fully stochastic simulations in this regime. Exploring higher dephasing rates at 𝑑 = 3−5, we find evidence for growing coherent rotations about all three logical Pauli axes, increased diagonal logical error process matrix elements relative to those of stochastic simulations, and a reduced dephasing rate threshold. Overall, our work paves a way toward realistic hardware emulation of small fault-tolerant quantum processes, e.g., members of an FTQC instruction set.

Quantum benchmarking↗

DOE OSTI2024

Dynamics of qudit gates and effects of spectator modes on optimal control pulses

Qudit gates for high-dimensional quantum computing can be synthesized with high precision using numerical quantum optimal control techniques. Large circuits are broken down into modules and the tailored pulses for each module can be used as primitives for a qudit compiler. Application of the pulses of each module in the presence of extra modes may decrease their effectiveness due to crosstalk. In this paper, we address this problem by simulating qudit dynamics for circuit quantum electrodynamics systems. As a test case, we take pulses for single-qudit swap gates optimized in isolation and then apply them in the presence of spectator modes each of which are in Fock states. We provide an experimentally relevant scaling formula that can be used as a bound on the fidelity decay. Our results show that frequency shift from spectator mode populations has to be ≲ 0.1 % of the qudit's nonlinearity in order for high-fidelity single-qudit gates to be useful in the presence of occupied spectator modes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Energy dependence of polarized 𝛾⁢𝛾 → 𝑒 + ⁢ 𝑒− in peripheral Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 and 200 GeV with the STAR experiment at RHIC

We report the differential yields at mid-rapidity of the Breit-Wheeler process (𝛾⁢𝛾 → 𝑒 + ⁢𝑒 − ) in peripheral Au+Aucollisions at $\sqrt{s_{NN}}$ = 54.4 and 200 GeV with the STAR experiment at the Relativistic Heavy Ion Collider (RHIC), as a function of energy $\sqrt{s_{NN}}$, 𝑒 + ⁢𝑒 − transverse momentum 𝑝 T , 𝑝$^{2}_{T}$, invariant mass 𝑀 𝑒⁢𝑒 , and azimuthal angle. In the invariant mass range of 0.4 < 𝑀 𝑒⁢𝑒 < 2.6GeV/𝑐 2 at low transverse momentum (𝑝 T < 0.15GeV/𝑐), the yields increase while the pair √⟨𝑝$^{2}_{T}$⟩ decreases with increasing $\sqrt{s_{NN}}$, a feature that is correctly predicted by the QED calculation. Here, the energy dependencies of the measured quantities are sensitive to the nuclear form factor, infrared divergence and photon polarization. The data are compiled and used to extract the charge radius of the Au nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Primitive quantum gates for an S U ( 3 ) discrete subgroup: Σ ( 36 × 3 )

We construct the primitive gate set for the digital quantum simulation of the 108-element Σ ( 36 × 3 ) group. This is the first time a non-Abelian crystal-like subgroup of S U ( 3 ) has been constructed for quantum simulation. The gauge link registers and necessary primitives—the inversion gate, the group multiplication gate, the trace gate, and the Σ ( 36 × 3 ) Fourier transform—are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Mixing effects on spectroscopy and partonic observables of heavy mesons with logarithmic confining potential in a light-front quark model

Using the variational principle, we systematically investigate the mass spectra and wave functions of both 1⁢𝑆 and 2⁢𝑆 state heavy pseudoscalar (𝑃) and vector (𝑉) mesons within the light-front quark model. This approach incorporates a Coulomb plus logarithmic confinement potential to accurately describe the constituent quark and antiquark dynamics. Additionally, spin hyperfine interactions are introduced perturbatively to compute the masses of pseudoscalar and vector mesons. The present analyses of the 1⁢𝑆 and 2⁢𝑆 states require the consideration of mixing between them to account for empirical constraints. These constraints include the mass gap Δ⁢𝑀 𝑃 >Δ⁢𝑀 𝑉 , where Δ⁢𝑀 𝑃⁡(𝑉) =𝑀$^{2⁢𝑆}_{𝑃⁡(𝑉)}$−𝑀$^{1⁢𝑆}_{𝑃⁡(𝑉)}$ and the hierarchy of the decay constants 𝑓 1⁢𝑆 >𝑓 2⁢𝑆 . We find the optimal value of the mixing angle to be 𝜃 =1⁢8°, significantly enhancing the consistency between our spectroscopic predictions and the experimental data compiled by the Particle Data Group. Furthermore, based on the predicted mass, the newly observed resonance 𝐵 𝐽⁡ (5840) could be assigned as a 2 1⁢ 𝑆 0 state in the 𝐵 meson family. The study also reports various pertinent observables, including twist-two distribution amplitudes, electromagnetic form factors, charge radii, 𝜉 moments, and transition form factors that are found to be consistent with both available lattice simulations and experimental data. In addition, our predicted branching ratios for the channels of 𝐵 + →𝜏 + ⁢𝜈 𝜏 as well as rare decays of 𝐵 0 and 𝐵$^0_𝑠$ appear in accordance with experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Quantum algorithm to simulate Lindblad master equations

We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for the Lindblad master equation, achieved by decomposing the dynamics into dissipative and Hamiltonian components and replacing the dissipative segments with randomly compiled, easily implementable elements. The sampling approach eliminates the need for ancillary qubits to simulate the dissipation process and reduces the gate complexity in terms of the number of jump operators. We provide a rigorous performance analysis of the algorithm. We also extend the algorithm to time-dependent Lindblad equations, generalize the family of Markovian master equations it can be applied to, and explore applications beyond the Markovian noise model. A new error bound, in terms of the diamond norm, for second-order product formulas for time-dependent Liouvillians is provided that might be of independent interest. Published by the American Physical Society 2025

Borras, Evan (ORCID:000900017709037X)↗

DOE OSTI2024

Native Two-Qubit Gates in Fixed-Coupling, Fixed-Frequency Transmons Beyond Cross-Resonance Interaction

Fixed-frequency superconducting qubits demonstrate remarkable success as platforms for stable and scalable quantum computing. Cross-resonance gates have been the workhorse of fixed-coupling, fixed-frequency superconducting processors, leveraging the entanglement generated by driving one qubit resonantly with a neighbor’s frequency to achieve high-fidelity, universal controlled- () gates. Here, we use on-resonant and off-resonant microwave drives to go beyond cross-resonance, realizing natively interesting two-qubit gates that are not equivalent to gates. In particular, we implement and benchmark native i , , i SWAP , and b gates; in fact, any SU ( 4 ) unitary can be achieved using these techniques. Furthermore, we apply these techniques for an efficient construction of the B gate: a perfect entangler from which any two-qubit gate can be reached in only two applications. We show that these native two-qubit gates are better than their counterparts compiled from cross-resonance gates. We elucidate the resonance conditions required to drive each two-qubit gate and provide a novel frame tracking technique to implement them in Qiskit. Published by the American Physical Society 2024

Physics↗

DOE OSTI2024

Quantum Tensor-Product Decomposition from Choi-State Tomography

The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt or tensor-product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here, we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor-product decomposition of a unitary the effect of which on the small subsystem is captured in classical memory, while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator nonlocality and effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions. Published by the American Physical Society 2024

Mansuroglu, Refik (ORCID:000000017352513X)↗

DOE OSTI2024

Circuit-Based Leakage-to-Erasure Conversion in a Neutral-Atom Quantum Processor

Atom-loss errors are a major limitation of current state-of-the-art neutral-atom quantum computers and pose a significant challenge for scalable systems. In a quantum processor with cesium atoms, we demonstrate proof-of-principle circuit-based conversion of this form of leakage error to erasure errors via leakage-detection units (LDUs), which nondestructively map information about the presence or absence of the qubit onto the state of an ancilla. We benchmark the performance of the LDU using a three-outcome low-loss state-detection method and find that the LDU detects atom-loss errors with approximately 93.4% accuracy, limited by technical imperfections of our apparatus. We further compile and execute a SWAP LDU, wherein the roles of the original data atom and ancilla atom are exchanged under the action of the LDU, providing “free refilling” of atoms in the case of atom loss. This circuit-based leakage-to-erasure error conversion is a critical component of a neutral-atom quantum processor where the quantum information may significantly outlive the lifetime of any individual atom in the quantum register. Finally, we demonstrate that LDUs may also be used to handle other forms of leakage errors where population moves to states outside of the computational subspace.

Chow, Matthew N. H. [Sandia National Laboratories ↗

DOE OSTI2026

Observing the effects of numbers of valence nucleons on 0$^{+}_{𝑔⁡𝑠}$ → 2$^{+}_{1}$ transitions in deformed nuclei by comparing proton and neutron transition matrix elements

We examined the ratios of neutron and proton transition matrix elements, 𝑀 𝑛 /𝑀 𝑝 , for the 0$^{+}_{𝑔⁡𝑠}$ → 2$^{+}_{1}$ transitions in 48 even-even stable nuclei with 𝑁 > 20 for which electromagnetic matrix elements were compiled by Pritychenko et al. and for which high-quality inelastic proton-scattering data were available. Several deformed rare-earth nuclei have (𝑀 𝑛 /𝑀 𝑝 )/(𝑁/𝑍) values significantly below 1.0, which is not consistent with a simple liquid-drop picture. However, this phenomenon can be explained using a schematic picture in which 𝑀 𝑝 reaches a maximum at proton midshell (𝑍 = 66) and 𝑀𝑛 reaches its maximum at neutron midshell (𝑁 = 104). Several midmass vibrational nuclei have 𝑀 𝑛 /𝑀 𝑝 values significantly below 𝑁/𝑍, which is not consistent with the expectation that 𝑀 𝑛 /𝑀 𝑝 = 𝑁/𝑍 in such nuclei. As a result, a shell-model investigation of these observations might yield insights about this behavior.

Collective levels↗