Shell Model Research Articles

On a Study of Photoionization of Atoms and Ions from Endohedral Anions

We study the relationship between the results of two qualitatively different semi-empirical models for photoionization cross sections, σnℓ, of neutral atoms (A) and their cations (A+) centrally encapsulated inside a fullerene anion, CNq, where q represents the negative excess charge on the shell. One of the semi-empirical models, broadly employed in previous studies, assumes a uniform excess negative charge distribution over the entire fullerene cage, by analogy with a charged metallic sphere. The other model, presented here, considers the quantum states of the excess electrons on the shell, determined by specific n and ℓ values of their quantum numbers. Remarkably, both models yield similar photoionization cross sections for the encapsulated species. Consequently, we find that the photoionization of the encapsulated atoms or cations inside the CNq anion is influenced only slightly by the quantum states of the excess electrons on the fullerene cage. Furthermore, we demonstrate that the influence decreases even further as the size of the fullerene cage increases. All this holds true at least under the assumption that the encapsulated atom or cation is compact, i.e., its electron density remains primarily within itself rather than being drawn into the fullerene shell. This remarkable finding results from Hartree–Fock calculations combined with a popular modeling of the fullerene shell which is simulated by an attractive spherical annular potential.

Extraction of Spectra in the Shell Model Monte Carlo Method Using Imaginary-Time Correlation Matrices

Extraction of Spectra in the Shell Model Monte Carlo Method Using Imaginary-Time Correlation Matrices

Numerical approximation of the solution of Koiter’s model for an elliptic membrane shell in absence of friction subjected to an obstacle via the penalty method

Numerical approximation of the solution of Koiter’s model for an elliptic membrane shell in absence of friction subjected to an obstacle via the penalty method

Quantum-enhanced Green's function Monte Carlo algorithm for excited states of the nuclear shell model

Quantum-enhanced Green's function Monte Carlo algorithm for excited states of the nuclear shell model

Modal analysis of key components of crusher based on digital simulation technology

The modal characteristics of the crusher rotor and shell constitute the crucial factors influencing vibration and noise. Based on the principle of simplification, the rotor component model was established. Through mesh optimization, the model accuracy and calculation efficiency can be ensured, and the calculation of natural frequency and modal shapes was completed based on ANSYS. To verify the accuracy of the finite element model, the modal test was carried out by the hammering method. Sensors were set in three different directions to obtain the frequency response function and the modal assurance criterion matrix mode confidence criterion. Using the same research method, the modal characteristics of the shell model were simulated and analyzed. The research results show that the modal parameters identified by the modal test are basically consistent with the simulation model. The natural frequencies of the rotor and the shell are quite different from the excitation frequency of the motor, and resonance problems will not occur when the crusher is proper functioning.

Theoretical analysis and predictions for the two-neutrino double electron capture of 124Xe

Abstract We provide a complete theoretical description of the two-neutrino electron capture in 124Xe improving both the nuclear and the atomic structure calculations. We improve the general formalism through the use of the Taylor expansion method, leading to higher order terms in the decay rate of the process. The nuclear part is treated with pn-QRPA and interacting shell model (ISM) methods. The nuclear matrix elements (NMEs) are calculated with the pn-QRPA method with isospin restoration by fixing the input parameters so that the experimental decay rate is reproduced, resulting in values significantly lower than in previous calculations. The validity of the pn-QRPA NMEs is tested by showing their values to be comparable with the ones for double-beta decay with emission of two electrons of 128,130Te, which have similar pairing features. Within the ISM, we reproduce the total experimental half-life within a factor of two and predict the capture fraction to the KK channel of about 74%. We also predict the capture fractions to other decay channels and show that for the cumulative decay to the KL1-KO1 channels, a capture fraction of about 24% could be observed experimentally. On the atomic side, calculations are improved by accounting for the Pauli blocking of the decay of innermost nucleon states and by considering all s-wave electrons available for capture, expanding beyond the K and L1 orbitals considered in previous studies. We also provide improved atomic relaxation energies of the final atomic states of 124Te, which may be used as input for background modeling in liquid Xenon experiments.

Analysis of the cylindrical shell model using a new four node quadrilateral element compared to ABAQUS elements

Shell models and loadings are very complicated in practice, especially in civil and mechanical engineering, due to their lightweight properties and ability to resist loads. Then; numerical tests are very important for this type of structure. In this work, numerical investigations of a cylindrical shell under concentrated loads are presented. Two finite elements used for this study, the new element ACM-Q4SBE1 and the S4R element of the code “ABAQUS”. The results obtained by the two elements, ACM-Q4SBE1 and S4R ABAQUS, are in agreement. The superiority and efficiency of the flat shell element approach for thin shell structures has been confirmed.

Glucose hydrochar consists of linked phenol, furan, arene, alkyl, and ketone structures revealed by advanced solid-state nuclear magnetic resonance

The molecular structure of hydrochars produced from 13C-enriched glucose under various conditions has been elucidated based on advanced one- and two-dimensional (2D) 1H-13C and 13C–13C solid-state nuclear magnetic resonance (NMR) with spectral editing. Regardless of synthesis conditions, hydrochars consist mostly of oxygen-substituted arene rings (including diphenols) and furans connected by alkyl linkers rich in ketones. Cross-linking nonprotonated and methyne (C-H) alkyl carbons have been identified through spectrally edited 2D NMR. Alkenes and ‘quaternary’ C-O are observed only at low synthesis temperature, while some clusters of fused arene rings are generated at high temperature. Hydrochar composition is nearly independent of reaction time in the range from 1 to 5 h. Equilibration of 13C magnetization within 1 s shows that the materials are homogeneous on the 5-nm scale, refuting core–shell models of hydrochar microspheres. While furan C-O carbons bonded to alkyl groups or ketones show distinctive cross peaks in 2D NMR, phenolic C-OH is observed unambiguously by hydroxyl-proton selection. While methylene-linked furan rings are fairly common, the signal previously assigned to furan Cα-Cα linkages is shown to arise from abundant, stable catecholic ortho-diphenols, whose HO-C=C-OH structure is proved by 2D13C–13C NMR after hydroxyl-proton selection. Quantitative 13C NMR spectra of low- and high-temperature hydrochars have been matched by chemical-shift simulations for representative structural models. Mixed phenol and furan rings connected by ketones and alkyl linkers provide good fits of the experimental spectra, while literature models dominated by large clusters of fused rings and with few phenols or alkyl-linked ketones do not.

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

Abstract We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6Li and 12C using the ab initio symmetry-adapted no-core shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3-6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

The Electro-Excitation Form Factors for Low-Lying States of 7Li Nucleus

The transverse electron scattering form factors have been studied for low –lying excited states of 7Li nucleus. These states are specified by J? T= (0.478MeV), (4.63MeV) and (6.68MeV). The transitions to these states are taking place by both isoscalar and isovector components. These form factors have been analyzed in the framework of the multi-nucleon configuration mixing of harmonic oscillator shell model with size parameter brms=1.74fm. The universal two-body of Cohen-Kurath is used to generate the 1p-shell wave functions. The core polarization effects are included in the calculations through effective g-factors and resolved many discrepancies with experiments. A higher configuration effect outside the 1p-shell model space, such as the 2p-shell, enhances the form factors for q-values and reproduces the data. The present results are compared with other theoretical models. PACS: 25.30.Bf Elastic electron scattering - 25.30.Dh Inelastic electron scattering to specific states – 21.60.Cs Shell model – 27.20. +n 5? A ?19

On the applicability limits of the structurally orthotropic shell model in problems of calculating the buckling under axial compression of waffle cylindrical shells

The article considers the solution of the buckling problem of a waffle cylindrical shell under axial compression using the Euler (bifurcation) approach. Two models are used: a model based on the numerical integration method and a model based on the finite element method. The first model assumes that the stiffeners are structurally an orthotropic shell obeying the Kirchhoff-Love hypotheses, with the assumption of "smearing". The second model uses a tetrahedron element with ten nodes. The study is based on experimental data from tests of one of the waffle cylindrical shell samples under axial compression. The research results show that with an increase in the waffle shell rib thickness, a discrepancy between the calculation results of the two models is observed. With the optimal value of the k parameter, characterizing the ratio of the rib thickness to the rib pitch, equal to 0.035, such a discrepancy is estimated to be about 5%. At the same time, the calculation using the model of a structurally orthotropic shell leads to an underestimation of the critical load compared to the finite element model. This provides an estimate of the loss of stability of a waffle cylindrical shell with a safety margin. For parameter k between 0.02 and 0.05, the difference between the results from the two computational models for critical loads does not exceed 11%.

Cross-Sections of Neutral-Current Neutrino Scattering on 94,96Mo Isotopes

In our recent publications, we presented neutral-current ν–nucleus cross-sections for the coherent and incoherent channels for some stable Mo isotopes, assuming a Mo detector medium, within the context of the deformed shell model. In these predictions, however, we have not included the contributions in the cross-sections stemming from the stable 94,96Mo isotopes (abundance of 94Mo 9.12% and of 96Mo 16.50%). The purpose of the present work is to perform detailed calculations of ν–94,96Mo scattering cross-sections, for a given energy Eν of the incoming neutrino, for coherent and incoherent processes. In many situations, the Eν values range from 15 to 30 MeV, and in the present work, we used Eν = 15 MeV. Mo as a detector material has been employed by the MOON neutrino and double-beta decay experiments and also from the NEMO neutrinoless double-beta decay experiment. For our cross-section calculations, we utilize the Donnelly–Walecka multipole decomposition method in which the ν–nucleus cross-sections are given as a function of the excitation energy of the target nucleus. Because only the coherent cross-section is measured by current experiments, it is worth estimating what portion of the total cross-section represents the measured coherent rate. This requires the knowledge of the incoherent cross-section, which is also calculated in the present work.

Buckling analysis of PMMA hemispherical pressure shells with thickness variation

The buckling behaviour of polymethyl methacrylate (PMMA) hemispherical pressure shells under uniform external pressure was investigated experimentally and numerically. Six PMMA hemispherical pressure shells were prepared via the free blow-forming process. The geometry and wall thickness of each hemispherical shell were measured. The collapse loads and final failure modes of all shells were obtained via a hydrostatic pressure device. In addition, through optical 3D scanning, a numerical model of the hemispherical shell that reflects the actual geometric imperfection was established and used in the finite element buckling analysis. The numerical results were in agreement with the test results. These findings provide a reference for evaluating the buckling load of PMMA hemispherical shells prepared via the free blow-forming process.

Three-dimensional fracture mechanics model of conch shells with hierarchical crossed-lamellar structures

Three-dimensional fracture mechanics model of conch shells with hierarchical crossed-lamellar structures

Strain redistribution in stochastically perturbed single and dual-phase cellular materials under quasistatic compression

Inspired by the stochastic and dual-phase nature of spongy bone, this work examines the effect of the perturbation on the strain distribution in a single and dual-phase, surface-based cellular structure subjected to quasistatic compression. Each effect (perturbation and the introduction of a second phase) is studied in isolation, as well as in combination, using Digital Image Correlation (DIC) for the analysis of the resulting strain fields. Starting from a periodic, single-phase surface-based cellular structure, aperiodicity was introduced at three different levels, and specimens were designed with a second-phase introduced using a core–shell modeling approach. All designs were fabricated using multi-material extrusion, with ABS and TPU as the two materials used. The specimens were subjected to quasi-static compression until densification, with results showing that the addition of a second phase and aperiodicity were each found to delocalize strain, mitigate sympathetic cell collapse in continuous failure bands, thereby decreasing undulations in the stress plateau region. The dual-phase cellular structure was found to absorb more energy per unit mass and volume when normalized by the Maximum Transmitted Stress (MTS) but this trend was arrested at high levels of aperiodicity. While aperiodicity had a significant, and occasionally detrimental, effect on the behavior of the single-phase cellular structure, its effect on dual-phase cellular structures was far more muted, suggesting the benefits of adding a second-phase to aperiodic structures to improve isotropy without large sensitivities on account of local variations in the degree and nature of aperiodicity.

Nonlinear Finite Element Formulation for Thin-Walled Conical Shells

This study presents a novel finite element formulation to predict the geometrically nonlinear response of conical shells under a wide range of practical loading conditions. The formulation expresses the discretized equilibrium equations in terms of the first Piola-Kirchhoff stress tensor and its conjugate gradient of the virtual displacements, is based on the kinematics of Love-Kirchhoff thin shell theory and the Saint-Venant-Kirchhoff constitutive model, and captures the follower effect of pressure loading. The formulation takes advantage of the axisymmetric nature of the shell geometries by adopting a Fourier series to characterize the displacement distributions along the circumferential direction while using Hermitian interpolation along the meridional direction. Comparisons with general shell models show the accuracy of the formulation under various loading conditions with a minimal number of degrees of freedom, resulting in a significant computational efficiency compared to conventional general-purpose shell solutions.

Quenching of the quantum p-strength in light exotic nuclei

One-nucleon spectroscopic overlaps, their strength or spectroscopic factors (SFs), and nucleon removal cross sections for light nuclei in the mass range A≤12 were evaluated using the fully correlated Quantum Monte Carlo (QMC) wave functions (WFs). Harder (AV18+UX) and softer (NV2+3) bare interactions were used providing consistent results. The SFs were also taken from simple Shell Model (SM) calculations. This structure information was incorporated in the standard three-body Faddeev/Alt-Grassberger-Sandhas reaction formalism to evaluate the (p,pN) cross sections. The results further our understanding of the quenching of the quantum p-shell strength obtained from structure and reactions. We have found the ratios of the total QMC sums of SFs to the SM ones to be uniform and ∼ 3/4. The corresponding ratios of the sums Below Particle Threshold (BPT) of SFs, as well as of total cross sections, deviate strikingly from the uniform trend in some special cases. We find these ratios to be close to unit for Li9→8Li+n and C9→8B+p. In contrast, they are strongly reduced for C11→10C+n and B11→10Be+p mirror transitions, resulting from the quenching of the strength for low-lying 2+ final state transitions. The QMC theoretical cross section BPT for C11(p,pn) is about two times smaller than the experimental data.

High-precision measurements of the atomic mass and electron-capture decay Q value of 95Tc

A direct measurement of the ground-state-to-ground-state electron-capture decay Q value of 95Tc has been performed utilizing the double Penning trap mass spectrometer JYFLTRAP. The Q value was determined to be 1695.92(13) keV by taking advantage of the high resolving power of the phase-imaging ion-cyclotron-resonance technique to resolve the low-lying isomeric state of 95Tc (excitation energy of 38.910(40) keV) from the ground state. The mass excess of 95Tc was measured to be −86015.95(18) keV/c2, exhibiting a precision of about 28 times higher and in agreement with the value from the newest Atomic Mass Evaluation (AME2020). Combined with the nuclear energy-level data for the decay-daughter 95Mo, two potential ultra-low Q-value transitions are identified for future long-term neutrino-mass determination experiments. The atomic self-consistent many-electron Dirac–Hartree–Fock–Slater method and the nuclear shell model have been used to predict the partial half-lives and energy-release distributions for the two transitions. The dominant correction terms related to those processes are considered, including the exchange and overlap corrections, and the shake-up and shake-off effects. The normalized distribution of the released energy in the electron-capture decay of 95Tc to excited states of 95Mo is compared to that of 163Ho currently being used for electron-neutrino-mass determination.

Snap-through eversion of axisymmetric shells under contact indentation

In this paper, we systematically investigate the stability of an axisymmetric shell and the snap-through eversion induced by indentation through a discrete numerical approach. To capture the intricate interplay between the geometric and boundary nonlinearities during contact actuation, we employ the discrete axisymmetric shell model accompanied by the incremental potential formulation for our analysis. Our results reveal that the indentation response of a spherical shell can be classified into three groups, i.e. monotonous, monostable and bistable behaviours, whose boundaries can be characterized by a simple scaling law. We further discover that, for bistable shells, the snap-through eversion happens at a critical state where the configurations are universal, which is independent of the indenter size and can be captured by a simple geometric model. One interesting prediction of our model is that, with increasing indenter size, the contact state between the shell and indenter changes from conformal contact to partial separation, which is validated by a finite element method simulation. Our findings may provide explanations for some biophysical phenomena (e.g. cell fusion) and can also guide optimal designs of intelligent structures (e.g. soft actuators and soft robots).

ECONOMIC EFFICIENCY OF APPLICATION OF OPTIMIZED MILL BED

This paper presents the selection of optimization parameters for the bed geometry of a long metal cutting machine (MCM), the design problem and boundary conditions were given. Five different geometries were designed for further mathematical analysis to meet the requirements of the problem. Static analysis of the mathematical model of the bed shells was performed by finite element method (FEM) using BETA CAE System tool, ABAQUS, which showed that by using stiffeners in the form of two variable pitch spirals and three hollow tubes, as well as changing the design at the connection point of the beam support to the bollards of the long bed of the metal cutting machine, the stresses that occurred in these places at an angle of 90° were reduced. The geometries were chosen in such a way that it was possible to reduce the stresses occurring at the point of cutting, to reduce the deflection, to increase the rigidity of the structure. The economic calculation aimed at determining the cost of a long metal-cutting machine tool with the proposed geometry has been carried out. The analysis of the unit cost of the product (long bed of the metal-cutting machine tool made of polymer concrete with optimized geometry) has been carried out, the calculation of the annual economic effect from the use of the proposed method of manufacturing has been carried out. Keywords: MCM, FEM, statistical analysis, product cost, economic calculation.