Single-particle Matrix Elements Research Articles

Core-polarization effects on electron scattering in 10B, 19F and 39K nuclei

In the study of NN interactions, calculations are performed from the longitudinal shape factor through inelastic scattering of electrons. The determination of the longitudinal shape factor in the inelastic scattering of electrons is based on the transfer momentum and angular momentum. We delve into the analysis of electron scattering shape factors as well as CP — standing for nuclear polarization — in longitudinal inelastic shell models. This is done using NuShellX, where we employ a sum potential HO to look at 10B, 39K, and 19F nuclei. Among the computations carried out include those of Single Particle Matrix Elements and Inelastic Electron Scattering Shape Factors which are then pitted against experimental data. The outcomes depict a scenario where the model space provides a full explanation on NushellX shape factor compared to nuclear polarization; this thereby implies less contribution from certain quarters towards shaping this factor. On another front, the comparison shows that results from longitudinal form factor polarization for NuShellX core find resonance with what is already available experimentally— a pointer towards reliability if not outright correctness.

Calculations of The Shell Model for 27Mg Isotope

Using shell-model calculations, the nuclear structure (energy levels and reduced transition probability) of 27Mg isotope has been studied. Shell-model codes, Oxbash for Windows operating system, were utilized to calculate the outcomes. Using a harmonic oscillator, the wave functions of radial single-particle matrix elements have been calculated. The calculated energy levels and available experimental data up to 5 MeV for 27Mg are compared. Core-polarization effects on reduced transition probability are introduced via first-order perturbation theory, which permits higher energy configurations via nucleon excitations from core orbits to those outside model space up to 9ℏω. The core-polarization effects have improved the agreement between B(E2) and their corresponding experimental data, but have no effect on B(M1), B(M2), and B(E1).

Electroexcitation Form Factors and Deformation of 20,22Ne Isotopes Based on the Shell Model and Hartree-Fock plus BCS Calculations

Nuclear structure of 20,22Ne isotopes has been studied via the shell model with Skyrme-Hartree-Fock calculations. In particular, the transitions to the low-lying positive and negative parity excited states have been investigated within three shell model spaces; sd for positive parity states, spsdpf large-basis (no-core), and zbme model spaces for negative parity states. Excitation energies, reduced transition probabilities, and elastic and inelastic form factors were estimated and compared to the available experimental data. Skyrme interaction was used to generate a one-body potential in the Hartree-Fock calculations for each selected excited states, which is then used to calculate the single-particle matrix elements. Skyrme interaction was used to calculate the radial wave functions of the single-particle matrix elements, from which a one-body potential in Hartree-Fock theory with SLy4 parametrization can be generated. Furthermore, we have explored the interplays among neutron and proton density profiles in two dimensions, along with the deformations of 20,22Ne using Hartree-Fock plus BCS calculations.

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.

Hamiltonian sensitivity in calculating the electromagnetic moments and electroexcitation form factor for the sd nuclei using shell model with Skyrme–Hartree–Fock

In this work, the nuclear electromagnetic moments for the ground and low-lying excited states for sd shell nuclei have been calculated, resulting in a revised database with 56 magnetic dipole moments and 41 electric quadrupole moments. The shell model calculations are performed for each sd isotope chain, considering the sensitivity of changing the sd two-body effective interactions USDA, USDE, CWH and HBMUSD in the calculation of the one-body transition density matrix elements. The calculations incorporate the single-particle wave functions of the Skyrme interaction to generate a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. For most sd shell nuclei, the experimental data are well reproduced, except for those spans near the island of inversion. In order to interpret the structure of low-lying excited states, the electric quadrupole and magnetic dipole transition form factors and the corresponding reduced transition probabilities in the sd shell nuclei have also been calculated, for which the experimental data are available. The present results demonstrate the nuclear electromagnetic moments’ sensitivity to many forms of the understanding of nucleon–nucleon interactions and provide a crucial baseline for future improvements in conceptual calculations.

Nuclear matrix elements calculation for K-forbidden β-decays

A certain interest in the experimental nuclear physic community has been expressed for the precise detection of the β-shape of low Q-value decays, such as 9Tc →99 Ru+e −+, tied to the search for the absolute mass of the neutrino. The necessity of a reliable way to compute the single-particle matrix elements for second forbidden operators has driven the implementation of a general algorithm to obtain the nuclear matrix elements for any given transition of generic forbiddenness K. Particular attention is then placed on the accuracy of the approximations commonly used in this context.

Calculation of the electromagnetic moments and electroexcitation form factors for some boron isotopes using shell model with skyrme interaction

The magnetic dipole and electric quadrupole moments for some Boron isotopes were calculated using the shell model taking into account the effect of the two-body effective interactions and the single-particle potentials. These isotopes are; (8 5)B(2 +), (1 50)B(3 +), (1 51)B((3/2)−), ( 1 52)B(1 +) and (1 53)B((3/2)−). Also, the elastic and inelastic longitudinal and transverse electron scattering form factors are calculated for 10B and 11B, for which there are available experimental data. The one-body transition density matrix elements (OBDM) were calculated using the two-body effective interactions; PWT, PEWT, PKUO and CKIHE, which are carried out in the p-shell model space. Skyrme interaction was implemented to generate the single-particle matrix elements with Hartree-Fock approximation and compared with those of harmonic-oscillator and Wood-Saxon potentials. All the evaluated results were compared with available experimental data. The present work has led us to conclude that the shell model calculations with Skyrme type interaction give a good tool for nuclear structure studies. All signs for the experimental electromagnetic moments data are reproduced correctly. The longitudinal and transverse form factors for positive and negative parity states are fairly well reproduced when using a suitable model space.

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.

Calculation of the Magnetic Dipole and Electric Quadrupole Moments of some Sodium Isotopes using Shell Model with Skyrme Interaction

In the present work, the magnetic dipole and electric quadrupole moments for some sodium isotopes have been calculated using the shell model, considering the effect of the two-body effective interactions and the single-particle potentials. These isotopes are; 21Na (3/2+), 23Na (3/2+), 25Na (5/2+), 26Na (3+), 27Na (5/2+), 28Na (1+) and, 29Na (3/2+). The one-body transition density matrix elements (OBDM) have been calculated using the (USDA, USDB, HBUMSD and W) two-body effective interactions carried out in the sd-shell model space. The sd shell model space consists of the active 2s1/2, 1d5/2, and1d1/2 valence orbits above the inert 16O nucleus core, which remains closed. Skyrme interaction was implemented to generate the single-particle matrix elements with Hartree-Fock approximation and compared with those of harmonic oscillator and Wood-Saxon potentials. From the outcome of our investigation, it is possible to conclude that the shell model calculations with Skyrme-type interaction give a reasonable description for most of the selected Na isotopes. No significant difference was noticed for the magnetic dipole moments and electric quadrupole moments with experimental data, where all signs for the experimental data are reproduced correctly.

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.

Interpretation of enhanced electric dipole transitions in Br73 by the reflection-asymmetric triaxial particle rotor model

The recently observed positive and negative parity bands in $^{73}\mathrm{Br}$ are investigated by the reflection-asymmetric triaxial particle rotor model. The experimental energy spectra as well as the electric transition probabilities $B(E1), B(E2)$, and the ratio $B(E1)/B(E2)$ are well reproduced by the theoretical calculations. It is found that the enhanced interband $E1$ transitions between the opposite-parity bands, a crucial evidence for octupole correlations, are mainly contributed by the intrinsic single-particle electric dipole matrix elements.

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.

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.

Study of the Electric Quadrupole Transitions in 50-51Mn Isotopes by Using F742pn and F7cdpn Interactions

The nuclear shell-model has been used to compute excitation levels of ground band and electric quadrupole transitions for 50-51Mn isotopes in f-shell. In the present study, f742pn and f7cdpn effective interactions have been carried out in full f-shell by using Oxbash Code. The radial wave functions of the single-particle matrix elements have been calculated in terms of the harmonic oscillator (Ho) and Skyrme20 potentials. The predicted theoretical results have been compared with the available experimental data; it has been seen that the predicted results are in agreement with the experimental data. From the current results of the calculations, many predictions of angular momentum and parities of experimental states have been made, and the energy spectra predictions of the ground band and B(E2; ↓) electric quadrupole transitions in 50-51Mn isotopes of the experimental data are not known yet. In the nuclear shell-model calculations framework, energy levels have been determined for 50-51Mn isotopes; new values of electric quadrupole transitions have been predicted in the studied results. This investigation increases the theoretical knowledge of all isotopes with respect to the energy levels and reduced transition probabilities.

Coulomb form factors of 25Mg nuclei using Bohr–Mottelson collective model with Skyrme interaction potential

Coulomb [Formula: see text] and C4 form factors to the 5/2[Formula: see text], 7/2[Formula: see text], 9/2[Formula: see text], 9/2[Formula: see text] and 11/2[Formula: see text] states in [Formula: see text]Mg nuclei have been studied using shell model calculations. The universal sd-shell interaction A (USDA) is used for sd-shell orbits. Two models have been used to calculate core-polarization (CP) effects. These models are Coulomb Valance Tassie model (CVTM) and Bohr–Mottelson (BM) collective model. The wave functions of radial single particle matrix elements have been calculated with Skyrme interaction potential (SKX). Electron scattering factors results showed good agreement using the BM collective model comparing with the experimental data.

Open quantum dynamics induced by light scalar fields

We consider the impact of a weakly coupled environment comprising a light scalar field on the open dynamics of a quantum probe field, resulting in a master equation for the probe field that features corrections to the coherent dynamics, as well as decoherence and momentum diffusion. The light scalar is assumed to couple to matter either through a nonminimal coupling to gravity or, equivalently, through a Higgs portal. Motivated by applications to experiments such as atom interferometry, we assume that the probe field can be initialized, by means of external driving, in a state that is not an eigenstate of the light scalar-field--probe system, and we derive the master equation for single-particle matrix elements of the reduced density operator of a toy model. We comment on the possibilities for experimental detection and the related challenges, and highlight possible pathways for further improvements. This derivation of the master equation requires techniques of non-equilibrium quantum field theory, including the Feynman-Vernon influence functional and thermo field dynamics, used to motivate a method of Lehmann-Symanzik-Zimmermann-like reduction. In order to obtain cutoff-independent results for the probe-field dynamics, we find that it is necessary to use a time-dependent renormalization procedure. Specifically, we show that non-Markovian effects following a quench, namely the violation of time-translational invariance due to finite-time effects, lead to a time-dependent modulation of the usual vacuum counterterms.

Microscopic calculations of the electric Quadrupole transition strengths of Be isotopes (9, 10, 12, 14)

Electric Quadrupole transitions are calculated for beryllium isotopes (9, 10, 12 and 14). Calculations with configuration mixing shell model usually under estimate the measured E2 transition strength. Although the consideration of a large basis no core shell model with 2ℏtruncations for 9,10,12 and14 where all major shells s, p, sd are used, fail to describe the measured reduced transition strength without normalizing the matrix elements with effective charges to compensate for the discarded space. Instead of using constant effective charges, excitations out of major shell space are taken into account through a microscopic theory which allows particle–hole excitations from the core and model space orbits to all higher orbits with 2ℏw excitations which are called core-polarization effects. The two body Michigan sum of three ranges Yukawa potential (M3Y) is used for the core-polarization matrix element. The simple harmonic oscillator potential is used to generate the single particle matrix elements of all isotopes considered in this work. The b value of each isotope is adjusted to reproduce the experimental matter radius, These size parameters of the harmonic oscillator almost reproduce all the root mean square (rms) matter radii for 9,10,12,14Be isotopes within the experimental errors. Almost same effective charges are obtained for the neutron- rich Be isotopes which are smaller than the standard values. The major contribution to the transition strength comes from the core polarization effects. The present calculations of the neutron-rich 12,14Beisotopes show a deviation from the general trends in accordance with experimental and other theoretical studies. The configurations arises from the shell model calculations with core-polarization effects reproduce the experimental B(E2) values.

Quadrupole moments of exotic carbon isotopes (9C, 11C, 17C and 19C) including core polarization effect

Quadrupole Q moments and effective charges are calculated for 9C, 11C, 17C and 19C exotic nuclei using shell model calculations. Excitations out of major shell space are taken into account through a microscopic theory which are called core-polarization effects. The simple harmonic oscillator potential is used to generate the single particle matrix elements of 9,11,17,19C. The present calculations with core-polarization effects reproduced the experimental and theoretical data very well.

The effects of core polarisation on some even–even sd-shell nuclei using Michigan three-range Yukawa and modified surface delta interactions

Elastic and inelastic electron scattering from even–even \(Z=N\) sd-shell (\(^{28}\hbox {Si}, {}^{32}\hbox {S}\) and \(^{36}\hbox {Ar}\)) nuclei has been studied using the nuclear shell-model configurations. The transition rates \(B\left( {C2\uparrow } \right) \) from the ground 0\(^{+}\) state to the first excited \(2_{1}^{+}\) state, the electric quadrupole moments Q, the elastic longitudinal C0 and inelastic longitudinal C2 form factors are calculated. SDBA and USDA model spaces have been used. The radial wave functions of the single-particle matrix elements have been calculated in terms of the harmonic oscillator (HO) and Skyrme–Hartree–Fock (SHF) potentials. The configurations higher than the core and the model space are taken into account within a microscopic theory that includes one particle–one hole excitations from the core and model space orbits to higher allowed orbits with 2\(\hbar \omega \) excitations. These effects are defined as core polarisation (CP) effects. Two-body Michigan three-range Yukawa (M3Y) effective nucleon–nucleon interaction and the modified surface delta interaction (MSDI) have been used as residual interactions for the CP matrix elements. The calculations are performed using the shell-model code Nushell@MSU, where the deduced results, including CP, are more compatible with the available experimental and theoretical results.

Shell model and Hartree-Fock calculations of electron scattering form factors for 25Mg nucleus

Shell model and Hartree-Fock calculations have been adopted to study the elastic and inelastic electron scattering form factors for 25Mg nucleus. The wave functions for this nucleus have been utilized from the shell model using USDA two-body effective interaction for this nucleus with the sd shell model space. On the other hand, the SkXcsb Skyrme parameterization has been used within the Hartree-Fock method to get the single-particle potential which is used to calculate the single-particle matrix elements. The calculated form factors have been compared with available experimental data.