Core Polarization Research Articles

Shell Model Investigation of Some p and sd-Shell Nuclei with Harmonic Oscillator and Skyrme Interactions

In this study, the longitudinal charge and form factors for the nuclei 9Be and 28Si lying in the p and sd shells are studied by employing the Harmonic Oscillator potential (HO) and Skyrme effective interaction (Sk35−Skzs∗). The C0 and C2 from factors calculated for the ground state 3/2-, the 5/2- (2.429 MeV) and 7/2- (6.380 MeV) for 9Be, while the ground state 0+ and 2+ (1.779 MeV) state for 28Si nucleus. Calculations of microscopic perturbations that involve intermediate one-particle, one-hole excitation from the core and MS orbits into all upper orbits with excitations are utilized to generate the effective charges necessary to account for the “core polarization effect”. The shell model calculations are utilized on the extended model space to include all 1s, 1p, 2s–1d, 2p‑1f orbits with truncation. Bohr-Mottelson collective model and Tassie model with properly estimated effective neutron and proton charges are taken into account to consider the effect of the core contribution. The estimated form factors were compared with the measured available data and they were in good agreement for most of the studied states. A conclusion can be drawn that truncation is very good choice to study the longitudinal form factors.
 
 The choice of Harmonic Oscillator potential (HO) and Skyrme effective interaction (Sk35−Skzs∗) is adequate for form estimation of longitudinal form factors.
 The estimation of the effective charges based on microscopic perturbations that involve intermediate one-particle, one-hole excitation from the core and MS orbits into all upper orbits with excitations is adequate.
 The truncation proves to be very successful to perform the study.

The Magnetic Form Factors for Some Nuclei 51V, 59Co, 93Nb, 115In by using Valence with and Without Core Polarization Effects Models

The magnetic electron scattering form factor with glekpn, d3f7, ho models space for 51V , 59Co, 93Nb, and 115In nuclei are discussed with and without core polarization effects(CP). The calculations are done with the help of NuShellX@MUS code. The radial wave function for the single-particle matrix elements have been calculated with the SKyrme-Hartree Fock (SKX), Wood-Saxon(WS), and harmonic oscillator (HO) potentials. valence model(Vm) used in these calculation to calculate form factors with core-polarization effects. The results give a good agreement with available experimental data.

Revised and Extended Analysis of Ar vi

This paper analyzes the emission spectrum of Ar vi and adds new information about this ion. We use a capillary light source to study the Ar vi spectrum, presenting 39 line classifications for the first time, including one line in the ultraviolet region. A total of nine possible Ar vi lines in the ultraviolet between 3288 and 3440 Å are analyzed. We revised the wavelengths of the lines at 1284.01 and 1307.42 Å previously used to identify Ar vi in astronomical objects. The lifetimes, weighted transition rates (gA) and their estimated uncertainties, and cancellation factors are obtained using a Hartree–Fock calculation with energy parameters adjusted to fit the values of the experimental levels and modified to include core polarization effects. We analyze all the experimentally known transitions of the Ar vi spectrum, with particular attention to conflicting information. Isoelectronic sequences of energy levels and transitions, for which the trend is not a smooth curve, are analyzed. We revise previous studies where the information needed to support line classifications and level designations is incomplete.

A Method for Suppressing Error of Fiber Optic Current Transformer Caused by Temperature Based on λ/4 Wave Plate Fabricated With Polarization-Maintaining Photonic Crystal Fiber

The beat length of λ/4 wave plate of fiber optic current transformer (FOCT) will change with the temperature fluctuation of environment, which will result in additional phase error, reducing the accuracy of current measurement. In the paper, we presented a FOCT based on λ/4 wave plate fabricated with polarization maintaining photonic crystal fiber (PCF). Combined with error model caused by λ/4 wave plate in FOCT, we analyzed the specific mechanism of temperature influence on λ/4 wave plate. Aiming at the problem of fusing PCF to panda polarization maintaining fiber, we optimized the related parameters of fiber fusion splicer to reduce the fusion loss of the fiber. It was experimentally verified that the beat length of PCF is less sensitive to temperature than that to elliptical core polarization maintaining fiber. Finally, we measured current of FOCT utilizing two kinds of λ/4 wave plates in full temperature range from -40 °C to 70 °C. It was verified that it is insensitive to temperature for FOCT when utilizing PCF λ/4 wave plate, with the corresponding system current measurement accuracy 0.5S level.

Be optical lattice clocks with the fractional Stark shift up to the level of 10−19

The energy levels and electric dipole () matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic , magnetic dipole () and electric quadrupole () polarizabilities as well as the hyperpolarizabilities of the and states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity I is in the range of 14.3–15.9 kW cm−2 and the detuning δ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7–40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 × 10−18. While, when I is in the range of 15.01–15.46 kW cm−2 and δ is in the range of 40.73–40.76 MHz, the fractional Stark shifts are lower than 1.0 × 10−19.

Study of the one-neutron transfer reaction in 18O + 76Se collision at 275 MeV in the context of the NUMEN project

Heavy-ion one-nucleon transfer reactions are promising tools to investigate single-particle configurations in nuclear states, with and without the excitation of the core degrees of freedom. An accurate determination of the spectroscopic amplitudes of these configurations is essential for the study of other direct reactions as well as beta-decays. In this context, the 76Se(18O,17O)77Se one-neutron transfer reaction gives a quantitative access to the relevant single particle orbitals and core polarization transitions built on 76Se. This is particularly relevant, since it provides data-driven information to constrain nuclear structure models for the 76Se nucleus.The excitation energy spectrum and the differential cross section angular distributions of this nucleon transfer reaction was measured at 275 MeV incident energy for the first time using the MAGNEX large acceptance magnetic spectrometer. The data are compared with calculations based on distorted wave Born approximation and coupled channel Born approximation adopting spectroscopic amplitudes for the projectile and target overlaps derived by large-scale shell model calculations and interacting boson-fermion model.These reactions are studied in the frame of the NUMEN project. The NUMEN (NUclear Matrix Elements for Neutrinoless double beta decay) project was conceived at the Istituto Nazionale di Fisica Nucleare–Laboratori Nazionali del Sud (INFN-LNS) in Catania, Italy, aiming at accessing information about the nuclear matrix elements (NME) of neutrinoless double beta decay (0νββ) through the study of the heavy-ion induced double charge exchange (DCE) reactions on various 0νββ decay candidate targets. Among these, the 76Se nucleus is under investigation since it is the daughter nucleus of 76Ge in the 0νββ decay process.

Magic wavelengths for 6s1/2 → 5d3/2,5/2 transitions of Yb+ ions

The wave functions, energy levels and matrix elements of Yb+ ions are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined. Then, the magic wavelengths of the magnetic sublevel 6s1/2,m = 1/2 → 5d3/2,m = ±3/2,±1/2 and 6s1/2,m = 1/2 → 5d5/2,m = ±5/2,±3/2,±1/2 transitions in the linearly, right-handed, and left-handed polarized light are further determined. The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.

Longitudinal Form Factors and Quadrupole Moments of 22,26Na Isotopes with Different Interactions

The longitudinal electron scattering form factors and the electric quadrupole moments are calculated for the states with Jπ T= 3+0 (ground state) and 1+ 0 (583keV excited state) of 22Na and Jπ T= 3+2 (ground state) of 26Na. Shell model calculations are based on USDA, USDB and Wildenthal interactions. The exact center of mass correction is included in Born approximation picture to generate the longitudinal form factors. The core polarization (CP) effect with the values of effective nucleon charges ep=1.35, en= 0.35, with Bohr Mottelson formula gave a good agreement with the measured electric quadrupole moments. The structure of the nuclei under consideration shows that the 1d5/2 orbit is dominant configuration for 22Na, and 2s1/2 orbit for 26Na.

Screening-induced phase transitions in core-shell ferroic nanoparticles

Using the Landau-Ginzburg-Devonshire approach, we study screening-induced phase transitions in core-shell ferroic nanoparticles for three different shapes: an oblate disk, a sphere, and a prolate needle. The nanoparticle is made of a ferroic ${\mathrm{CuInP}}_{2}{\mathrm{S}}_{6}$ core and covered by a tunable screening shell made of a phase-change material with a conductivity that varies as the material changes between semiconductor and metallic phases. We reveal a critical influence of the shell screening length on the phase transitions and spontaneous polarization of the nanoparticle core. Since the tunable screening shell allows the control of the polar state and phase diagrams of core-shell ferroic nanoparticles, the obtained results can be of particular interest for applications in nonvolatile memory cells.

Longitudinal and transverse form factors from 65Cu and 71Ga nuclei

In the present work, the inelastic electron scattering for longitudinal and transverse form factors of 65Cu and 71Ga nuclei lies in the fp-shell region are studied in the framework of the shell model. The calculation is performed in the (1f5/2, 2p3/2, 2p1/2, 1g9/2) model space using jun45 effective interaction. The wavefunctions employed to conduct the shell model calculations are extracted from the jun45 effective interaction for these nuclei with the jj44 shell model space and (Sk35−Skzs ∗) residual interaction to evaluate the interactions matrix element between initial and final states. The effective charges used to account for the core-polarization (CP) effect are created using calculations of microscopic perturbations that include intermediate one-particle, one-hole excitation from the core and the model space (MS) orbits into all upper orbits with \(n\hslash \omega\) excitations following the same approach done in [Radhi et al. in Euro. Phys. J. A 50:1–9, 2014]. To account for the (CP) effects contribution, the inelastic form factor is obtained by employing the shape of Tassie and Bohr–Mottelson models with appropriate proton and neutron effective charges. The calculated form factors were compared with available experimental data.

Global Full-Dimensional Potential Energy Surface for the Reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 and the Formation Rate and Lifetime of the 23Na287Rb2 Collision Complex.

A full-dimensional global potential energy surface (PES) for the reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 was constructed based on high-level ab initio calculations. The short-range part was expressed as a permutation invariant polynomial-neural network (PIP-NN) fit of 22 003 ab initio points calculated using a coupled cluster method with the one-electron basis 5s5p5d2f plus effective core potentials and core polarizability potentials, while the long-range part was represented in an asymptotically correct form based on multipole expansion. The formation rate of the 23Na287Rb2 complex calculated using a quantum statistical method is in good agreement with experiment, while the estimated 19.20 μs lifetime of the complex from Rice-Ramsperger-Kassel-Marcus (RRKM) theory is significantly shorter than the measured millisecond decay rate, signaling either the inadequacy of RRKM theory or a yet unresolved loss mechanism.

Re-Evaluation of the Nuclear Magnetic Octupole Moment of 209Bi

We modified the Hfs92 code of the GRASP package in order to describe the magnetic octupole hyperfine interaction. To illustrate the utility of the modified code, we carried out state-of-the-art calculations of the electronic factors of the magnetic octupole hyperfine interaction constants for levels in the ground configuration of the Bi atom. The nuclear magnetic octupole moment of the 209Bi isotope was extracted by combining old measurements of the hyperfine structures of 6p34S3/2o [Hull, R.; Brink, G. Phys. Rev. A 1970, 1, 685] and 2P3/2o [Landman, D.A.; Lurio, A. Phys. Rev. A 1970, 1, 1330] using the atomic-beam magnetic-resonance technique with our theoretical electronic factors. The present extracted octupole moment was consistent with all the available values but the one obtained in the single-particle nuclear shell model approximation. This observation supports the previous finding that nuclear many-body effects, such as the core polarization, significantly contribute to the nuclear magnetic octupole moment in the case of 209Bi.

CALCULATION OF THE INELASTIC LONGITUDINAL ELECTRON SCATTERING OF 20Ne AND 24Mg NUCLEI

The inelastic longitudinal electron scattering form factors F(q)'s, an expression for the transition charge density are studied where the deformation in nuclear collective modes is taken into consideration besides the shell model transition density. The core polarization transition density is evaluated by adopting the shape of Tassie model together with form of the ground state two-body charge density distributions which included the effect of short range correlation(SRC). It is noticed that the core polarization effects which represent the collective modes are essential in obtaining a good agreement between the calculated inelastic longitudinal F(q)'s and those of experimental data for 20Ne and 24Mg nuclei.

Electromagnetic moments and magnetic form factors of the ground states of odd-A nuclei in the vicinity of Z = 20 closure

Magnetic dipole and electric quadrupole moments are calculated for odd-[Formula: see text] nuclei in the vicinity of [Formula: see text] closure. Also, elastic magnetic electron scattering form factors are calculated for some of these nuclei, for which there are available experimental data. Excitation out of major shell space is taken into account through a microscopic theory which allows particle–hole excitation from the core and model-space orbits to all higher orbits with [Formula: see text] excitations, with [Formula: see text] as the number of shells that gives convergence to core-polarization matrix elements. Effective charges are obtained for each isotope. Core polarization (CP) is essential for obtaining a reasonable description of the electric quadrupole moments, but has no effect on the magnetic dipole moments but squeezes the magnetic form factors, and describes the data very well. For nuclei where there are data for large momentum transfer values, Skyrme–Hartree–Fock (SHF) method is used to generate from it a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. Those with high momentum transfer data which give evidence of the structure of the different multipoles, are more well described using SHF formalism than the harmonic oscillator (HO) single-particle matrix elements.

Correlation Consistent Basis Sets and Core Polarization Potentials for Al-Ar with ccECP Pseudopotentials.

New correlation consistent basis sets for the second-row atoms (Al–Ar) to be used with the neon-core correlation consistent effective core potentials (ccECPs) have been developed. The basis sets, denoted cc-pV(n+d)Z-ccECP (n = D, T, Q), include the “tight”-d functions that are known to be important for second-row elements. Sets augmented with additional diffuse functions are also reported. Effective core polarization potentials (CPPs) to account for the effect of core–valence correlation have been adjusted for the same elements, and two different forms of the CPP cutoff function have been analyzed. The accuracy of both the basis sets and the CPPs is assessed through benchmark calculations at the coupled-cluster level of theory for atomic and molecular properties. Agreement with all-electron results is much improved relative to the basis sets that originally accompanied the ccECPs; moreover, the combination of cc-pV(n+d)Z-ccECP and CPPs is found to be a computationally efficient and accurate alternative to including core electrons in the correlation treatment.

Energy levels, absorption oscillator strengths, transition probabilities, polarizabilities, and g factors of Ar13+ ions

An accurate determination of various parameters of ${\mathrm{Ar}}^{13+}$ is presented in this work. The wave functions and energy levels of the low-lying states within the configurations of $2{s}^{2}2p$ and $2s2{p}^{2}$ are calculated using the fully relativistic multiconfiguration Dirac-Hartree-Fock method, while the wave functions of higher excited states with the configurations $2{s}^{2}nl\phantom{\rule{4pt}{0ex}}(n\ensuremath{\ge}3$, $l=s,p,d)$ are obtained using the relativistic configuration interaction plus core polarization method. Then, the absorption oscillator strengths, transition probabilities, polarizabilities, and $g$ factors are determined. The contributions of electron correlation effects, Breit interaction, and quantum electrodynamics effects are also investigated. The present results agree well with the available theoretical and experimental results. The $g$ factors of the $2{s}^{2}2p\phantom{\rule{4pt}{0ex}}^{2}P_{1/2,3/2}$ states agree with the experimental measurements on a level of ${10}^{\ensuremath{-}6}$.

Coordination of Ethylamine on Small Silver Clusters: Structural and Topological (ELF, QTAIM) Analyses.

Amine ligands are expected to drive the organization of metallic centers as well as the chemical reactivity of silver clusters early growing during the very first steps of the synthesis of silver nanoparticles via an organometallic route. Density functional theory (DFT) computational studies have been performed to characterize the structure, the atomic charge distribution, and the planar two-dimensional (2D)/three-dimensional (3D) relative stability of small-size silver clusters (Agn, 2 ≤ n ≤ 7), with or without an ethylamine (EA) ligand coordinated to the Ag clusters. The transition from 2D to 3D structures is shifted from n = 7 to 6 in the presence of one EA coordinating ligand, and it is explained from the analysis of the Ag-N and Ag-Ag bond energies. For fully EA saturated silver clusters (Agn-EAn), the effect on the 2D/3D transition is even more pronounced with a shift between n = 4 and 5. Subsequent electron localization function (ELF) and quantum theory of atoms in molecules (QTAIM) topological analyses allow for the fine characterization of the dative Ag-N and metallic Ag-Ag bonds, both in nature and in strength. Electron transfer from ethylamine to the coordinated silver atoms induces an increase of the polarization of the metallic core.

Longitudinal form Factors of 25Mg with Bohr-Mottelson Model Using Large-scale Shell Model

The longitudinal electron scattering form factors in large scale SDPF-shell for 25Mg with SDPF now as effective interaction have been discussed using Bohr-Mottelson model to computation core polarization (CP). The calculation are done with the help of NuShell code. To determine the single-particle wave function, the SKyrme-Hartree Fock potential was used to compute the matrix elements' radial wave function containing a single particle. Bohr-Mottelson model is used in these calculation. The result show good agreement with experimental data for 25Mg nucleus.

Effects of poling direction and imperfection of interfaces on a pre-stressed system with a piezoelectric core bonded to elastic faces

This paper models the resonance behavior of an initially stressed sandwich plate-strip consisting of a piezoelectric core and elastic faces, based on a rigid foundation, exposed to a time-harmonic force. Our research is conducted according to the linearized theory of electro-elasticity for solids under initial stress. This model assumes that there is a spring-type imperfectness at interfaces between the piezoelectric core and the face materials, both in the normal and tangential directions, and the core layer is poling in various directions. A mathematical model is created for the current problem, and then the finite element method (FEM) is used to solve it. Further, attention is focused on the influence of the mentioned imperfectness and the poling directions on the frequency response of plate-strip, in addition to the effects of the most important parameters on this response. The results show that as the imperfectness at the interface planes has the greatest effect on the horizontal polarization of the piezoelectric core, the mentioned polling direction inhibits the resonance mode of the system.

Commensurate vortex-core switching in magnetic nanodisks at gigahertz frequencies

The development of future spintronic applications requires a thorough and fundamental understanding of the magnetisation dynamics. Of particular interest are magnetic nanodisks, in which the vortex state emerges as a stable spin configuration. Here, we focus on how the vortex core polarisation can be reversed periodically by an oscillating magnetic field, applied perpendicularly to the disk's surface. By means of micromagnetic simulations, we demonstrate the presence of several subharmonic switching modes, i.e., the commensurate ratio between the switching frequency of the core and the driving frequency. The underlying mechanism of this periodic behaviour depends on the disk thickness. For thin disks, the core switches periodically due to resonant excitation of radial spin wave modes, while it is due to the breathing mode in the case of thick disks. However, overlap of both modes impedes periodic vortex core switching. For thin disks, the threshold field amplitude required for periodic switching can be lowered to about 30~mT by increasing the disk diameter. For thick disks, in contrast, the minimal field is largely unaffected by the disk diameter, as only the energy density of a central region around the vortex core is relevant to excite the breathing mode. Our results contribute to the understanding of the switching mechanisms in magnetic nanodisks, which are of technological interest due to their potential in non-volatile memory devices.