Core Polarization Effects Research Articles

Magnetic Dipole Moments, Occupation Numbers and Magnetic Form Factors of Some Neutron Rich Nuclei in sdpf-shell

In the sdpf shell model, static and dynamic characteristics of certain neutron-rich nuclei are measured by using the SDPF interactions: Magnetic dipole moments (𝜇), occupation numbers (occ#) and magnetic electron scattering form factors for the ground state, they are presented for some Vanadium (23V) and Manganese (25Mn) isotopes using radial wave functions for the single-particle matrix elements of harmonic-oscillator potential (HO). These isotopes are 48V (4 1+), 49V (7/2- 3/2), 50V (6+ 2), 53Mn (7/2- 3/2), 54Mn (3+ 2) and 56Mn (3+ 3). The calculations introduced with model space (MS) and core-polarization CP effects are included through effective g factors. In model space and with core-polarization effects, the magnetic transition probability B(M1) is also calculated. The calculations of one-body density matrix OBDM together with the interaction SDPFK are carried out in the sdpf-model space using the OXBASH code. The theoretical results of the 𝜇 moments agree with recent experimental data.

Coulomb C2 and C4 Form Factors of 18O, 20,22Ne Nuclei Using Bohr−Mottelson Collective Model

Coulomb C2 and C4 form factors with core-polarization effects to 2+ and 4+ states in 18O and 20,22Ne have been studied using shell model calculations. The two-body effective Wildenthal interaction and universal sd-shell interaction A (USDA) are used for sd-shell orbits. Corepolarization effects are calculated using the Coulomb valance Tassie model (CVTM) and Bohr–Mottelson (BM) collective model. Some wave functions of the radial single-particle matrix elements have been calculated with harmonic oscillator (HO), Wood–Saxon (WS), and SKX potentials. The inclusions of core-polarization effects give good agreements with experimental data as comparing with model space calculations. The results for different potentials are compared.

Inelastic Electron Scattering Form Factor of Isoscalar (T = 0) and Isovector (T = 1) Particle-hole States in 12C and 16O

Inelastic longitudinal and transverse electron scattering form factors of low-lying T = 0, T = 1 particle-hole states of 12C and 16O are studied in the framework of the Tamm–Dancoff approximation (TDA). The Hamiltonian with the Michigan-three-Yukawa (M3Y) potential is diagonalized. To obtain a good agreement with the experimental data, the ground state is corrected by including the admixture from higher orbits with regard for the core polarization effects.

Experimental and Theoretical Radiative Parameters of Highly Excited Levels in Re ii

Abstract Natural radiative lifetimes of 22 odd-parity levels of Re ii in the energy range between 43,937.7 and 65,572.3 cm−1 were measured by the time-resolved laser-induced fluorescence method. To our knowledge, the lifetimes for 18 out of 22 levels were measured for the first time. The theoretical radiative lifetimes and branching fractions (BFs) for these levels were obtained from pseudorelativistic Hartree–Fock calculations including core-polarization effects. By combining the experimental lifetimes and calculated BFs, a set of semiempirical transition probabilities and oscillator strengths for 232 Re ii lines were determined. The radiative parameters obtained in the present work will greatly enrich the atomic database of Re ii and hence are expected to be helpful for astrophysicists in Re abundance evaluation of stars.

Electromagnetic Form Factors for 7,9,11Be Isotopes with Exact Center of Mass Correction

The shell model calculations with Cohen-Kurath (C-K) interaction were carried out to investigate form factors of elastic transverse electron scattering, and magnetic dipole-moments of odd 7,9,11Be isotopes. The effect of the exact value of center of mass correction was adopted to generate the magnetic form factors in Born approximation picture. The contribution of the higher 2p-shell configuration was included to reproduce the experimental data. A significant improvement was obtained in the present results with core-polarization (CP) effect through the effective g-factors. The occupancies percentage with respect to the valence nucleons was also calculated.

Study the Nuclear Structure of Some Even-Even Ca Isotopes Using the Microscopic Theory

The root-mean square-radius of proton, neutron, matter and charge radii, energy level, inelastic longitudinal form factors, reduced transition probability from the ground state to first-excited 2+ state of even-even isotopes, quadrupole moments, quadrupole deformation parameter, and the occupation numbers for some calcium isotopes for A=42,44,46,48,50 are computed using fp-model space and FPBM interaction. 40Ca nucleus is regarded as the inert core for all isotopes under this model space with valence nucleons are moving throughout the fp-shell model space involving 1f7/2, 2p3/2, 1f5/2, and 2p1/2 orbits. Model space is used to present calculations using FPBM interaction, and with the effects of core-polarization are obtained by the first order core polarization through a microscopic theory is called modified surface delta interaction which allows all higher orbits are excited by particle-hole excitation from the core and model space orbits. Also, each isotope's effective charge is determined by using the collective model by Bohr and Mottelson formula. The current result corresponds to the experimental data by taking into account core polarization effects.

The Effective M3Y Residual Interaction In 41Ca As a Nuclear Diffraction Grating of Electrons

The total and individual multipole moments of magnetic electron scattering form factors in 41Ca have been investigated using a widely successful model which is the nuclear shell model configurations keeping in mind of 1f7/2 subshell as an L-S shell and Millinar, Baymann, Zamick as L-S shell (F7MBZ) to give the model space wave vector. Also, harmonic oscillator wave functions have been used as wave function of a single particle in 1f7/2 shell. Nucleus 40Ca as core closed and Core polarization effects have been used as a corrective with first order correction concept to basic computation of L-S shell and the excitement energy has been implemented with 2ћω. The core polarizability effect has been utilized to incorporate the rejected space (core + higher arrangement) via L-S shell with a realism interaction of effective M3Y P2 interaction to connect the model space particles in motion with the spouse (p-h). The two body M3Y interactions have been utilized as an interaction residue to calculate the core polarizability matrix elements. Finally, the theoretical result of the form factor has been compared with the experimental results.

Study the Nuclear Structure of Some Cobalt Isotopes

The nuclear structure of some cobalt (Co) isotopes with mass number A=56-60 has been studied depending on the effect of some physical properties such as the electromagnetic properties effects, such as, elastic longitudinal form factors, electric quadrupole moments, and magnetic dipole moments. The fp model space is used to present calculations using GXFP1 interaction by adopting the single particle wave functions of the harmonic oscillator. For all isotopes under consideration, the 40Ca nucleus is regarded as an inert core in fp model-space, while valence nucleons are moving through 1f7/2, 2p3/2, 1f5/2, and 2p1/2 orbits. The effects of core-polarization are obtained by the first order core polarization through a microscopic theory. In addition, the core polarization was added using the effective charge and effective g factors to calculate quadrupole and magnetic moments, respectively. The results obtained are compared to experimental data that is accessible.

Radiative lifetimes, branching fractions, and oscillator strengths for highly excited levels in singly ionized tantalum (Ta ii)

ABSTRACT Radiative lifetimes of 28 levels of Ta ii in the energy range 29256.907–55128.389 cm−1 were measured by time-resolved laser-induced fluorescence (TR-LIF) spectroscopy in laser-ablation plasma. Among the results, to our knowledge, 24 lifetimes are reported for the first time. These lifetimes, ranging from 2.7 to 111 ns, were combined with theoretical branching fractions obtained from pseudo-relativistic Hartree–Fock calculations including core-polarization effects to deduce semi-empirical transition probabilities and oscillator strengths for 284 Ta ii spectral lines.

Relativistic Configuration-Interaction and Perturbation Theory Calculations of the Sn XV Emission Spectrum

Recently, there has been increased interest in developing advanced bright sources for lithography. Sn ions are particularly promising due to their bright emission spectrum in the required wavelength range. Cowan’s code has been used to model the emission; however, it has adjustable parameters, which limit its predictive power, and it has limited relativistic treatment. Here, we present calculations based on ab initio relativistic configuration-interaction many-body perturbation theory (CI-MBPT), with relativistic corrections included at the Dirac-Fock level and core-polarization effects with the second-order MBPT. As a proof of principle that the theory is generally applicable to other Sn ions with proper development, we focused on one ion where direct comparison with experimental observations is possible. The theory can also be used for ions of other elements to predict emissions for optimization of plasma-based bright sources.

Electromagnetic multipoles of positive parity states in 27Al by elastic and inelastic electron scattering

Nuclear structure of 27Al nucleus has been investigated using shell model with self-consistent Hartree–Fock calculations. Shell model calculations are performed with full sd model space for positive parity states. For all selected excited states, Skyrme interactions are adopted to generate from them a one-body potential in Hartrre-Fock theory to calculate the single-particle matrix elements and compared with those of the harmonic oscillator. The deduced results are discussed for the longitudinal and transverse form factors and compared with the available experimental data. It has been found that the core-polarization effects are essential in obtaining a reasonable description of the data.

Elastic and inelastic form factors including 2-body short-range correlation effect

The charge distributions and elastic electron form factors for 18O, 42,44Ca, 58Ni, and 118Sn nuclei were considered using the cluster expansion of the 1- and 2-body terms. Inelastic electron form factors to 2+ states with core-polarization effects were studied, where the nuclear collective modes were considered alongside the shell model transition density. The influence of short-range correlations (SRCs) was calculated by the parameter β, which was introduced into the ground-state charge distribution and concluded the Jastrow-type function. It is found that the inclusion of 2-body correlations is necessary to describe the observed data of elastic and inelastic form factors at high momentum transfer q > 3 fm–1.

New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV)

A capillary pulsed-discharge and a theta-pinch were used to record Kr spectra in the region of 330–4800 Å. A set of 168 transitions of these spectra were classified for the first time. We extended the analysis to twenty-five new energy levels belonging to 3s23p24d, 3s23p25d even configurations. We calculated weighted transition probabilities (gA) for all of the experimentally observed lines and lifetimes for new energy levels using a relativistic Hartree–Fock method, including core-polarization effects.

Dynamic Core Polarization in High Harmonic Generation from Solids: The Example of MgO Crystals.

Previously, the strong field processes in solids have always been explained by the single-active-electron (SAE) model with a frozen core excluding the fluctuation of background electrons. In this work, we demonstrate the strong field induced dynamic core polarization effect and propose a model for revealing its role in high harmonic generation (HHG) from solids. We show that the polarized core induces an additional polarization current beyond the SAE model based on the frozen cores. It gives a new mechanism for HHG and leads to new anisotropic structures, which are experimentally observed with MgO. Our experiments indicate that the influences of dynamic core polarization on HHG are obvious for both linearly and elliptically polarized laser fields. Our work establishes the bridge between the HHG and the dynamic changes of the effective many-electron interaction in solids, which paves the way to probe the ultrafast electron dynamics.

Weak-field asymptotic theory of tunneling ionization of the hydrogen molecule including core polarization, spectator nucleus, and internuclear motion effects

We present a state-of-the-art theory of tunneling ionization of the hydrogen molecule in a static electric field. The theory is based on the leading-order many-electron weak-field asymptotic theory and successively incorporates core polarization, spectator nucleus, and internuclear motion effects. The predictions of the theory are compared with ab initio calculations of the ionization rate of ${\mathrm{H}}_{2}$ with frozen nuclei and experimental results on the anisotropy of strong-field ionization of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$. The comparison reveals the relative role of the different effects. We show that all the effects should be taken into account in order to achieve good agreement with the ab initio and experimental results.

Studying Inelastic Electron Scattering of Magnetic Form Factors M1 for 48Ca Nucleus Using Skyrme Interaction

The M1 inelastic scattering form factors from 48Ca nucleus have been investigated through nuclear shell theory. The nuclear effective two body interaction fpbm of Richter has been utilized to generate the two body wave vectors with Harmonic oscillator wave function as a single particle wave function in Fp shell model space. Core polarization effect has been used to include the discarded space (core+ higher configuration) via model space with realistic interaction of Skyrme Sly5 to couple the model space active particles with the pair (particle-hole) excited in energy of 2ћω. Calculated results has been compared to available experimental data.

Effect of the Exact Center of Mass Correction on the Longitudinal Form Factors for Neutron Rich 12,14,18N Isotopes

The nuclear structure of the ground state for even 12,14,18N isotopes are studied within the shell model framework through the longitudinal elastic electron scattering. The generate wave functions from two-body interaction of Cohen and Kurath in the p-shell for 12,14N, and psdsu3 interaction for 18N nucleus. The exact value of the center of mass correction in the translation invariant shell model (TISM) are re-examined for longitudinal form factors. The contribution of a higher 2p-shell configuration resolves some discrepancies with the experiments for the form factors at q-values. The inclusion of the core polarization effects through an effective nucleon charge gives a reasonable agreement for the present results with available data. The occupancy percentage with respect to the valance nucleons is also calculated.

GaN bandgap bias caused by semi-core treatment in pseudopotentials analyzed by the diffusion Monte Carlo method

This study investigates how the prediction of the gallium nitride (GaN) bandgap is affected by treating semi-core d-electrons as either valence or core states in the pseudopotentials, which correspond to small-core and large-core approximations, respectively. To distinguish the effect of semi-core treatment from another bandgap problem recognized in density functional theory (DFT), that is, the underestimation related to the self-interaction problem, we perform diffusion Monte Carlo (DMC) evaluations under the fixed-node approximation and the optical gap scheme (where the evaluation uses N-electron many-body wavefunctions). A comparison to experimental measurements of bandgap energies indicates that DMC predictions are overestimated, whereas DFT simulations, which are used as a guiding function (DFT → DMC), are typically underestimated. This agrees with the trend reported in previous DMC studies on bandgap estimates. The large-core approximation results in a greater overestimation than the small-core treatment in both DFT and DMC. The bias in the overestimation is ∼30% for the DFT → DMC operation. Several possible causes of this bias are considered, such as pd-hybridization, core-polarization, and electronic screening effects. However, although these factors could qualitatively account for the overestimation caused by the large-core treatment, the estimated magnitude of the bias is too small to explain the evaluated difference between small-core and large-core approximations of the bandgap.

Calculation magnetic dipole moments, electric quadrupole moments and form factors for some Ti isotopes

This paper presents calculations of the magnetic moments, the quadrupole moments, and the form factors of a number of titanium isotopes as determined using the shell model space. The calculations of the shell model have adopted the model space (MS) with core-polarization effects, which were included for two types of effective g factors and different effective charges. The wave functions are generated using the harmonic oscillator potential (HO) with size parameters b, which for these isotopes are calculated. The one body density matrices (OBDM) for these isotopes were obtained using the NuShellX@MSU code, which used an adopted fpd6 interaction and fp model space. Reasonable results are obtained that show the collapse of the magicity property at neutron number N = 28.

Elastic and Inelastic Electron-Nucleus Scattering Form Factors for Be9 Nucleus

The computations of the elastic and inelastic Coulomb form factors for the electron-nucleus scattering of Beryllium nucleus Be9 have performed with Core Polarization (CP) effects including the realistic Michigan sum of Three Range Yukawa (M3Y) Interaction, and the other residual interaction which is Modified Surface Delta Interaction (MSDI). In addition to mean square root charge density and charge radii for the ground state. The perturbation theory was adopted to compute the Core Polarization by using the Harmonic Oscillators (HO) potential to calculate single-particle radial wave functions.
 In the comparison between the theoretical calculations of Coulomb form factors by (MSDI) interaction, realistic (M3Y) interaction, and the experimental results that measured before, it noticed that the Coulomb form factors for the (M3Y) interaction gave a reasonable depiction of the measured data.