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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Triaxiality and shape dynamics in 70 Ge

The electromagnetic properties of low-lying states in 70 Ge were investigated via multi-step Coulomb excitation of a 70 Ge beam impinging on a 208 Pb target at the ATLAS facility of the Argonne National Laboratory. A total of 27 transitional elements and six diagonal matrix elements coupling 11 low-lying states, were extracted from the measured cross sections. These were used to calculate reduced transition probabilities, spectroscopic quadrupole moments, and rotational invariant shape parameters, providing enhanced precision and expanding on previous studies. The experimental data were compared within several theoretical frameworks, including the generalized triaxial rotor model, configuration interaction shell-model calculations, and computations within the combined frameworks of relativistic density functional theory and the five-dimensional collective Hamiltonian. The results demonstrate a good agreement with the experimental data and, in conjunction with calculations using a two-state mixing model, support significant triaxiality and strong mixing between the 0$^{+}_{1}$ and 0$^{+}_{2}$ states. This results in the magnitudes of their respective quadrupole deformations [β rms (0$^{+}_{1}$) = 0.228 (3), β rms (0$^{+}_{2}$) = 0.273 (1)] being more similar than previously observed. Furthermore, the implications of these results for understanding the complex shape coexistence phenomena, the role of triaxiality, and shape evolution along the Ge isotopic chain are discussed.

59 ≤ A ≤ 89↗
DOE OSTI2025

Attosecond X-Ray Core-Level Chronoscopy of Aromatic Molecules

Attosecond photoemission or photoionization delays are a unique probe of the structure and the electronic dynamics of matter. However, the spectral congestion of valence photoelectron spectra sets fundamental limits to the complexity of systems that can be studied, and the delocalization of valence electron wave functions blurs the spatial origin of the photoelectron wave packet. Using attosecond x-ray pulses from LCLS, we demonstrate the key advantages of measuring core-level delays: The photoelectron spectra remain atomlike, the measurements become element specific, and the observed scattering dynamics originate from a pointlike source when multicenter interference effects are negligible. We exploit these unique features to reveal the effects of changing functional groups (C-H vs N) and symmetry on attosecond scattering dynamics by measuring and calculating the photoionization delays between N−1⁢𝑠 and C−1⁢𝑠 core shells of a series of aromatic azabenzene molecules. Remarkably, the delays increase with the number of nitrogen atoms in the molecule and reveal multiple resonances. We identify two previously unknown mechanisms regulating the associated attosecond dynamics, namely the enhanced confinement of the trapped wave function with the replacement of C-H groups by N atoms and the decrease of the coupling strength among the photoemitted partial waves with increasing symmetry. This study demonstrates the unique opportunities opened by measurements of core-level photoionization delays for unraveling attosecond electron dynamics in complex matter.

Ji, Jia-Bao [Eidgenoessische Technische Hochschule↗
DOE OSTI2025

Signatures of Selection for Resistance/Tolerance to Perkinsus olseni in Grooved Carpet Shell Clam ( Ruditapes decussatus ) Using a Population Genomics Approach

ABSTRACT The grooved carpet shell clam ( Ruditapes decussatus ) is a bivalve of high commercial value distributed throughout the European coast. Its production has suffered a decline caused by different factors, especially by the parasite Perkinsus olsenii . Improving production of R . decussatus requires genomic resources to ascertain the genetic factors underlying resistance/tolerance to P. olseni i . In this study, the first reference genome of R . decussatus was assembled through long‐ and short‐read sequencing (1677 contigs; 1.386 Mb) and further scaffolded at chromosome level with Hi‐C (19 superscaffolds; 95.4% of assembly). Repetitive elements were identified (32%) and masked for annotation of 38,276 coding‐ and 13,056 non‐coding genes. This genome was used as a reference to develop a 2bRAD‐Seq 13,438 SNP panel for a genomic screening on six shellfish beds distributed across the Atlantic Ocean and Mediterranean Sea. Beds were selected by perkinsosis prevalence and the infection level was individually evaluated in all the samples. Genetic diversity was significantly higher in the Mediterranean than in the Atlantic region. The main genetic breakage was detected between those regions (F ST = 0.224), being the Mediterranean more heterogeneous than the Atlantic. Several loci under divergent selection (394 outliers; 261 genomic windows) were detected across shellfish beds. Samples were also inspected to detect signals of selection for resistance/tolerance to P. olseni i by using infection‐level and population‐genomics approaches, and 90 common divergent outliers for resistance/tolerance to perkinsosis were identified and used for gene mining. Candidate genes and markers identified provide invaluable information for controlling perkinsosis and for improving production of the grooved carpet shell clam.

Sambade, Inés M. [Department of Zoology, Genetics ↗
DOE OSTI2024

Mesh Computing Remote Automatic Workflow

The software suite uses a microservice architecture using Docker and `docker-compose`. The microservices are as follows: 1. User interface. This interface is written in JavaScript using the Svelte framework. It exposes form elements and a 3D visualizer to prompt the user through the definition of microstructure parameters, and setting parameters for mesh generation and refinement. 2. Mesh generator. This is a container running the Python package for DREAM3D to generate a voxelized mesh that represents a microstructure defined by the user in the interface. 3. Cubit runner. This is a secure shell protocol tool that makes the submitting the DREAM mesh to an HPC instance and starts to run Cubit shell commands to smooth the grain boundaries with its `sculpt` library, applies user-defined boundary node sets, and bundles and returns the simulation-ready meshes and input files as a zipped directory.

Harris, BrennanKay↗
DOE OSTI2025

Harvesting Reactor Pressure Vessel Beltline Material from the Decommissioned Zion Nuclear Power Plant Unit 1

The decommissioning of the Zion Nuclear Power Plant (NPP) provided a unique opportunity to harvest and study service-aged reactor pressure vessel (RPV) beltline materials. This work, conducted through the U.S. Department of Energy’s Light Water Reactor Sustainability (LWRS) Program, aims to improve the understanding of radiation-induced embrittlement to support extended nuclear plant operations. Material segments containing the Linde 80 flux, wire heat 72105 (WF-70) beltline weld and the A533B Heat B7835-1 base metal, obtained from the intermediate shell region with a peak fluence of 0.7 × 10 19 n/cm 2 (E > 1.0 MeV), were extracted, cut into blocks, and machined into test specimens for mechanical and microstructural characterization. The segmentation process involved oxy-propane torch-cutting, followed by precision machining using wire saws and electrical discharge machining (EDM). A chemical composition analysis confirmed the expected variations in alloying elements, with copper levels being notably higher in the weld metal. The harvested specimens enable a detailed evaluation of through-wall embrittlement gradients, a comparison with the existing surveillance data, and the validation of predictive embrittlement models. This study provides critical data for assessing long-term reactor vessel integrity, informing aging-management strategies, and supporting regulatory decisions to extend the life of nuclear plants. This article is a revised and expanded version of a paper entitled, “Current Status of the Characterization of RPV Materials Harvested from the Decommissioned Zion Unit 1 Nuclear Power Plant”, PVP2017-65090, which was accepted and presented at the ASME 2017 Pressure Vessels and Piping Conference, Waikoloa, HI, USA, 16–20 July 2017.

harvesting beltline material↗
DOE OSTI2025

QM Investigation of Rare Earth Ion Interactions with First Hydration Shell Waters and Protein-Based Coordination Models

Here, conventional methods for extracting rare earth metals (REMs) from mined mineral ores are inefficient, expensive, and environmentally damaging. Recent discovery of lanmodulin (LanM), a protein that coordinates REMs with high-affinity and selectivity over competing ions, provides inspiration for new REM refinement methods. Here, we used quantum mechanical (QM) methods to investigate trivalent lanthanide cation (Ln 3+ ) interactions with coordination systems representing bulk solvent water and protein binding sites. Energy decomposition analysis (EDA) showed differences in the energetic components of Ln 3+ interaction with representatives of solvent (water, H 2 O) and protein binding sites (acetate, CH 3 COO – ), highlighting the importance of accurate description of electrostatics and polarization in computational modeling of REM interactions with biological and bioinspired molecules. Relative binding free energies were obtained for Ln 3+ with coordination complexes originating from binding sites in PDB structures of a lanthanum binding peptide (PDB entry 7CCO) and LanM, with explicit consideration of the first hydration shell waters, according to quasi-chemical theory (QCT). Beyond the first shell, the bulk solvent environment was represented with an implicit continuum model. Ln 3+ interactions with (H 2 O) 9 and both binding site models became more favorable, moving down the periodic series. This trend was more pronounced with the protein binding site models than with water, resulting in affinity increasing with periodic number, except for the last REM, Lu 3+ , which bound less favorably than the preceding element, Yb 3+ . Using the truncated 7CCO binding site model, the magnitude and trend of the experimental Ln 3+ relative binding free energies for the whole 7CCO peptide were reproduced. Conversely, the previously reported experimental data for LanM show a preference for the earlier lanthanides; this is likely due to longer-range interactions and cooperative effects, which are not represented by the reduced models. Using the truncated 7CCO binding site model, the magnitude and trend of the experimental Ln 3+ relative binding free energies for the whole 7CCO peptide were reproduced. In contrast to the previously reported experimental data for LanM, the peptide preferentially binds the earlier lanthanides. This difference likely arises due to longer-range interactions and cooperative effects not represented by the peptide. Further investigation of Ln 3+ interactions with whole proteins using polarizable molecular mechanics models with explicit solvent is warranted to understand the influence of longer-ranged interactions, cooperativity, and bulk solvent. Nevertheless, the present work provides new insights into Ln 3+ interactions with biomolecules and presents an effective computational platform for designing specific single-site REM binding peptides more efficiently.

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

Production of Radioactive 22 Na in Core-collapse Supernovae: The Ne-E(L) Component in Presolar Grains and Its Possible Consequences on Supernova Observations

Presolar graphite grains carry the isotopic signatures of their parent stars. A significant fraction of presolar graphites show isotopic abundance anomalies relative to solar for elements such as O, Si, Mg, and Ca, which are compatible with nucleosynthesis in core-collapse supernovae (CCSNe). Therefore, they must have condensed from CCSN ejecta before the formation of the Sun. Their most puzzling abundance signature is the 22 Ne-enriched component Ne-E(L), interpreted as the effect of the radioactive decay of 22 Na (T 1/2 = 2.6 yr). Previous works have shown that if H is ingested into the He shell and not fully destroyed before the explosion, the CCSN shock in the He-shell material produces large amounts of 22 Na. Here we focus on such CCSN models, showing a radioactive 26 Al production compatible with grain measurements, and analyze the conditions of 22Na nucleosynthesis. In these models, 22 Na is mostly made in the He shell, with a total ejected mass varying between 2.6 × 10 −3 M ⊙ and 1.9 × 10 −6 M ⊙ . We show that such 22 Na may already impact the CCSN light curve 500 days after the explosion, and at later stages it can be the main source powering the CCSN light curve for up to a few years before 44 Ti decay becomes dominant. Based on the CCSN yields above, the 1274.53 keV γ-ray flux due to 22 Na decay could be observable for years after the first CCSN light is detected, depending on the distance. This makes CCSNe possible sites to detect a 22 Na γ-ray signature consistently with the Ne-E(L) component found in presolar graphites. Finally, we discuss the potential contribution from 22 Na decay to the Galactic positron annihilation rate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Structural Analysis of Curium, Promethium, and Early Lanthanides Using 2,2′:6′,2″-Terpyridine in the Presence of Acid

Trivalent lanthanides and actinides are difficult to separate, often relying on subtle differences in bonding between the 4f– and 5f–orbitals. However, trivalent Cm poses additional complexity owing to its half-filled 5f 7 shell. This configuration causes Cm to have very similar properties to several of the early lanthanides, more specifically, similarly sized Pm. In this study, similarities were probed through isolating an isostructural series between the early lanthanides (La–Eu) and Cm with the oligoamine 2,2′:6′2″-terpyridine in the presence of acid. Single-crystal X-ray diffraction studies highlighted the similarities of Pm and Cm under these conditions and further demonstrated the difficulty in separating these elements. Despite the similarities, differences exist between interactions of Pm and Cm with terpyridine in the solid state. Interestingly, Cm appears to be more similar to Sm than to Pm. Furthermore, this study continues to probe the fundamental chemistry of Pm and Cm with respect to slight differences that can be leveraged in their separation from each other.

Vogt, Trenton B. [Michigan State Univ., East Lansi↗
DOE OSTI2025

Robust ab initio predictions for dimensionless ratios of 𝐸⁢2 and radius observables. I. Electric quadrupole moments and deformation

We report that converged results for 𝐸⁢2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction approaches. Matrix elements of the 𝐸⁢2 operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. However, we exploit systematic correlations between the calculated 𝐸⁢2 and radius observables to yield meaningful predictions for relations among these observables. In particular, we examine ab initio predictions for dimensionless ratios of the form 𝑄/𝑟 2 for nuclei throughout the 𝑝 shell. Meaningful predictions for electric quadrupole moments may then be made by calibrating to the ground-state charge radius, if experimentally known, or vice versa. Moreover, these dimensionless ratios provide ab initio insight into the nuclear quadrupole deformation.

ab initio calculations↗
DOE OSTI2025

Robust ab initio predictions for dimensionless ratios of 𝐸⁢2 and radius observables. II. Estimation of 𝐸⁢2 transition strengths by calibration to the charge radius

Converged results for 𝐸⁢2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction approaches. Matrix elements of the 𝐸⁢2 operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. However, we exploit systematic correlations between the calculated 𝐸⁢2 and radius observables to yield meaningful predictions for relations among these observables. In particular, we examine ab initio predictions for dimensionless ratios of the form 𝐵⁡(𝐸⁢2)/(𝑒 2 ⁢𝑟 4 ) for nuclei throughout the 𝑝 shell. Finally, meaningful predictions for 𝐸⁢2 transition strengths may then be made by calibrating to the ground-state charge radius if experimentally known.

ab initio calculations↗
DOE OSTI2025

Direct reactions for astrophysical p-capture rates with ORRUBA and GODDESS

Understanding the nucleosynthesis and energy generation in quiescent and explosive stellar burning requires a detailed understanding of reaction rates on many unstable nuclides. Such reaction rates are often governed by the properties of low-lying, isolated proton resonances. Though direct measurements of resonance strengths are ultimately desired, and are a focus of rare isotope beam facilities worldwide, such tour-de-force experiments must be guided by indirect techniques, in order to know resonance energies, J π assignments, and estimated widths, to inform targeted measurements. Furthermore, some important low-lying resonances may be too weak for direct measurements with radioactive beams, and indirect techniques provide the only practical constraints. Additionally, there has been growing interest in the astrophysical role of isomeric states, which can influence the reaction flow in nucleosynthetic reaction networks, and hence impact the quantitative interpretation of astronomical observables, such as γ-ray signatures, and elemental and isotopic ratios. Properties of single-proton resonances can be obtained by exploiting the selectivity of direct reactions, such as single-nucleon transfer and charge-exchange reactions. Constraining proton-capture rates via direct reactions has been a focus of the astrophysics program at ORNL for over two decades, spurring the development of the ORRUBA and GODDESS detector systems. Herein, a review of recent developments in instrumentation and radioactive beam delivery (including isomeric beam experiments) is presented, along with some specific examples of astrophysically interesting sd-shell nuclides, which have been a target of recent ORRUBA and GODDESS experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Surface Nanostructure Control and Thermodynamic Stability Analysis of Femtosecond Laser-Ablated CuCoMn 1.75 NiFe 0.25 Nanoparticles

Surface nanostructure control is the key to functionalizing nanomaterials. This paper presents a characterization with thermodynamic stability analysis of CuCoMn 1.75 NiFe 0.25 high-entropy alloy (HEA) nanoparticles synthesized by femtosecond laser ablation in ethanol and liquid nitrogen (LN2). Using multimodal electron microscopy and spectroscopy, we examine phase, particle size, defect structure, chemical distribution, and surface composition and relate them to HEA stability. Elemental distributions are uniform in both media, but LN2 produces smaller particles with a narrower size distribution and mainly single- or few-domain interiors, whereas ethanol yields larger particles built from 2–4 nm crystallites with domain aggregation. Edge defects appear in both but energy-dispersive X-ray spectroscopy (EDS) is broadly uniform with local fluctuations in ethanol. X-ray photoelectron spectroscopy (XPS), supported by an attenuation model, indicates an ∼1 nm oxide overlayer that suppresses Mn 2p intensity; correcting for it returns Mn toward the bulk value. UV–NIR and photoluminescent spectra independently support a thin oxide shell. Composition-based thermodynamic descriptors place LN2 closer to bulk mixing parameters, while ethanol raises ΔH_mix and lowers Ω. Cooling simulations are consistent (LN2 ∼ 0.1 μs quench, ethanol ∼1 μs). In conclusion, these results connect solvent-controlled kinetics and thermodynamics to crystalline state and surface chemistry, informing surface control of HEA nanoparticles.

Femtosecond Laser Ablation↗
DOE OSTI2025

Determination of proton and neutron contributions to the 0$^+_{𝑔⁡𝑠}$ → 2$^+_{1}$ excitations in 42 Si and 44 S using inelastic proton scattering in inverse kinematics and intermediate-energy Coulomb excitation

Here, we have measured the 0$^+_{𝑔⁡𝑠}$ → 2$^+_1$ transition in the neutron-rich 𝑁 = 28 isotope 42 Si using the probes of intermediate-energy Coulomb excitation and inelastic proton scattering in inverse kinematics at the Facility for Rare Isotope Beams with beam particle rates of ≈ 5 particles/s. The results of these two measurements allowed us to determine 𝑀 𝑛 /𝑀 𝑝 , the ratio of the neutron and proton transition matrix elements for the 0$^+_{𝑔⁡𝑠}$ → 2$^+_1$ transition. In addition, we have measured the 0$^+_{𝑔⁡𝑠}$ → 2$^+_1$ transition in the isotone 44 S using inverse kinematics inelastic proton scattering. By comparing the 44 S proton-scattering result with a recent intermediate-energy Coulomb excitation result on the same transition, we were able to determine 𝑀 𝑛 /𝑀 𝑝 for the 0$^+_{𝑔⁡𝑠}$ → 2$^+_1$ transition in this nucleus as well. This work strengthens the evidence that 42 Si has a stable quadrupole deformation in its ground state and that 44 S does not. Both conclusions are further supported by shell-model calculations carried out with the FSU interaction.

39 ≤ A ≤ 58↗
DOE OSTI2024

Evidence of short chains in liquid sulfur

High energy x-ray pair distribution function measurements show the average coordination number of the first shell in liquid sulfur is 1.86 ± 0.04 across the λ-transition, not precisely 2.0 as widely accepted. This indicates that upon melting, liquid sulfur does not comprise solely of S 8 rings but also possesses a significant number of short chains. Intensities of the pre-peak and first diffraction peak of the x-ray structure factor and third peak height of the pair distribution function all show deviations at the λ-transition temperature T λ , associated with the break-up of S 8 rings and the start of oligomer polymerization. A significant number of non-bonded or loosely bonded “interstitial atoms,” with an average coordination number of 0.20 ± 0.005, are also observed in the so-called “forbidden zone” between the first and second shells upon melting. The number of interstitial atoms is found to decrease to a minimum at the λ-transition, but the majority persist into the high temperature polymerized liquid. Furthermore, the existence of short chains and nearby interstitial atoms represent the two main factors required to initiate the S 8 -ring to chain transition, as proposed by recent molecular dynamics simulations.

Chemical bonding↗
DOE OSTI2024

R-matrix calculations for opacities: I. Methodology and computations

Abstract An extended version of the R -matrix methodology is presented for calculation of radiative parameters for improved plasma opacities. Contrast and comparisons with existing methods primarily relying on the distorted wave approximation are discussed to verify accuracy and resolve outstanding issues, particularly with reference to the opacity project (OP). Among the improvements incorporated are: (i) large-scale Breit–Pauli R -matrix calculations for complex atomic systems including fine structure, (ii) convergent close coupling wave function expansions for the ( e + ion) system to compute oscillator strengths and photoionization cross sections, (iii) open and closed shell iron ions of interest in astrophysics and experiments, (iv) a treatment for plasma broadening of autoionizing resonances as function of energy-temperature-density dependent cross sections, (v) a ‘top-up’ procedure to compare convergence with R -matrix calculations for highly excited levels, and (vi) spectroscopic identification of resonances and bound ( e + ion) levels. The present R -matrix monochromatic opacity spectra are fundamentally different from OP and lead to enhanced Rosseland and Planck mean opacities. An outline of the work reported in other papers in this series and those in progress is presented. Based on the present re-examination of the OP work, opacities of heavy elements might require revisions in high temperature-density plasma sources.

Pradhan, A. K. (ORCID:0000000187753643)↗
DOE OSTI2024

Distilling the Essential Elements of Nuclear Binding via Neural-Network Quantum States

To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. Furthermore, we address this challenge by leveraging a variational Monte Carlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to 𝐴 = 20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.

Binding energy & masses↗
DOE OSTI2025

Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets

We present a model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm produces DFBSs suitable for accurate robust DF approximation of 2-particle interactions in mean-field and correlated electronic structures. The algorithm is designed to (a) saturate the OBS product space by a large regularized set of primitive solid-harmonic Gaussian shells with nonuniform distribution of exponents, followed by (b) pruning of the shells according to their contributions to the 2- body energy of a correlated atomic ensemble. Building the DFBS generator model almost exclusively on mathematical and physical principles allows one to limit the number of parameters that control the density fitting error to three, with a single set of parameters sufficient for computations with all basis cardinal numbers, with and without correlation of core electrons, with and without scalar and spin-dependent relativistic effects, spanning almost all of the Periodic Table. Performance assessment included basis sets up to quadruple-ζ quality from several major basis set families, using molecules composed of main-group, d-block, and f-block elements. The resulting DF errors in Hartree−Fock and second-order MP2 energies (with relativistic all-electron treatments, when appropriate) were on the order of 20 and 10 μE h per electron, respectively.

Approximation↗
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↗