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

2019 ◽  
Vol 12 (24) ◽  
pp. 87-99
Author(s):  
Sara. H. Ibrahim
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Electric Quadrupole ◽  
Transition Strength ◽  
Matrix Elements ◽  
Core Polarization ◽  
Model Calculations ◽  
Polarization Effects ◽  
The Core ◽  
Effective Charges

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.

scholarly journals Study of the Electric Quadrupole Moments for some Scandium Isotopes Using Shell Model Calculations with Different Interactions

2018 ◽  
Vol 15 (3) ◽  
pp. 304-309
Author(s):  
Baghdad Science Journal
Keyword(s):  
Shell Model ◽  
Theoretical Calculations ◽  
Microscopic Theory ◽  
Model Space ◽  
Electric Quadrupole ◽  
Quadrupole Moments ◽  
Core Polarization ◽  
Model Calculations ◽  
Major Shell ◽  
Experimental Values

The electric quadrupole moments for some scandium isotopes (41, 43, 44, 45, 46, 47Sc) have been calculated using the shell model in the proton-neutron formalism. Excitations out of major shell model space were taken into account through a microscopic theory which is called core polarization effectives. The set of effective charges adopted in the theoretical calculations emerging about the core polarization effect. NushellX@MSU code was used to calculate one body density matrix (OBDM). The simple harmonic oscillator potential has been used to generate the single particle matrix elements. Our theoretical calculations for the quadrupole moments used the two types of effective interactions to obtain the best interaction compared with the experimental data. The theoretical results of the quadrupole moments for some scandium isotopes performed with FPD6 interaction and Bohr-Mottelson effective charge agree with experimental values.

Schalenmodellrechnungen beim Kern O18 mit geschwindigkeitsabhängigen Zwei-Teilchen-Potentialen

1967 ◽  
Vol 22 (4) ◽  
pp. 415-421
Author(s):  
Hans Grote
Keyword(s):  
Experimental Data ◽  
Harmonic Oscillator ◽  
Shell Model ◽  
Interaction Potential ◽  
Ground State ◽  
Wave Functions ◽  
Absolute Position ◽  
Model Calculations ◽  
The Core ◽  
Free Parameters

The energies of the low lying levels and the absolute position of the ground state of the nucleus O18 are calculated using five velocity-dependent potentials. The calculation is based on the shell model with two outer neutrons in the potential of the Ο16 core. The interaction potential as well as the core potential are fitted to experimental data, leaving no free parameters in the final result.The wave functions of the harmonic oscillator are used in each case of the five velocity-dependent potentials. An additional computation is carried out using one of these potentials and taking into account the perturbation of the wave functions. It turns out that, for satisfactory application of the velocity-dependent potentials in shell model calculations, this perturbation should be considered.

Microscopic Large Scale psd Shell Model with M3Y Residual Interaction to Calculate Electron Scattering Form Factors

2017 ◽  
Vol 6 (1) ◽  
pp. 56-61
Author(s):  
Khalid S. Jassim ◽  
Rawaa A. Abdul-Nabe
Keyword(s):  
Shell Model ◽  
Electron Scattering ◽  
Large Scale ◽  
Theoretical Calculations ◽  
Form Factors ◽  
Scale Model ◽  
Core Polarization ◽  
Model Calculations ◽  
Polarization Effects ◽  
Realistic Interaction

The longitudinal and the transverse electron scattering form factors for 6Li, 9Be, 11B and 12C nuclei have been studied with and without core polarization effects using shell model calculations. The psdmwk is used as effective interaction for psd-shells. The core-polarization effects are calculated in the first-order perturbation theory including excitations up to 4ħω using the Michigan three-range Yakawa M3Y as a realistic interaction. The wave functions of radial single particle matrix elements have been calculated with harmonic oscillator potential. For all nuclei under studying, Comparison between experimental and theoretical calculations show that the form factors with core-polarization effect calculations give good consistency with experiment data. So we concluded that the large scale model space enhanced the results to become closed to the experimental data.

scholarly journals Investigation of the Quadrupole Moment and Form Factors of Some Ca Isotopes

2020 ◽  
Vol 17 (2) ◽  
pp. 0502 ◽  
Author(s):  
Ahmed H Ali
Keyword(s):  
Effective Interaction ◽  
Form Factors ◽  
Electric Quadrupole ◽  
Quadrupole Moments ◽  
Matrix Elements ◽  
Calcium Isotopes ◽  
The Core ◽  
Effective Charges ◽  
The One ◽  
Nuclear Shell

Nuclear shell model is adopted to calculate the electric quadrupole moments for some Calcium isotopes 20Ca (N = 21, 23, 25, and 27) in the fp shell. The wave function is generated using a two body effective interaction fpd6 and fp space model. The one body density matrix elements (OBDM) are calculated for these isotopes using the NuShellX@MSU code. The effect of the core-polarizations was taken through the theory microscopic by taking the set of the effective charges. The results for the quadrupole moments by using Bohr-Mottelson (B-M) effective charges are the best. The behavior of the form factors of some Calcium isotopes was studied by using Bohr-Mottelson (B-M) effective charges.

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

2019 ◽  
Vol 12 (24) ◽  
pp. 110-121
Author(s):  
Wael A. Saeed A. Saeed
Keyword(s):  
Theoretical Data ◽  
Microscopic Theory ◽  
Quadrupole Moments ◽  
Matrix Elements ◽  
Oscillator Potential ◽  
Core Polarization ◽  
Model Calculations ◽  
Harmonic Oscillator Potential ◽  
Polarization Effects ◽  
Major Shell

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.

scholarly journals Nuclear structure study of [22,24]Ne and [24]Mg nuclei

2019 ◽  
Vol 65 (2) ◽  
pp. 159
Author(s):  
Fouad A. Majeed ◽  
And Sarah M. Obaid
Keyword(s):  
Experimental Data ◽  
Shell Model ◽  
Nuclear Structure ◽  
Transition Probabilities ◽  
Form Factors ◽  
Model Space ◽  
High Energy ◽  
Core Polarization ◽  
Model Calculations ◽  
The Core

Shell model calculations based on large basis has been conducted to study the nuclear structure of $^{20}Ne$, $^{22}Ne$ and $^{24}Mg$ nuclei. The energy levels, inelastic electron scattering form factors and transition probabilities are discussed by considering the contribution of  configurations with high-energy beyond the model space of sd-shell model space which is denoted as the core polarization (CP) effects.~The Core polarization is considered by taking the excitations of nucleus from the $1s$ and $1p$ core orbits and also from the valence $2s$ $1d$ shell orbit in to higher shells with $4\hbar\omega$. The effective interactions $USDA$ and $USDB$ are employed with $sd$ shell model space to perform the calculation and the core polarization are calculated with $MSDI$ as residual interaction.~The calculated energy level schemes,  form factors and transition probabilities were compared with the corresponding experimental data. The effect of core polarization is found very important for the calculation of $B(C2)$, $B(C4)$ and form factors, and gives excellent results in comparison with the experimental data without including any adjustable parameters.

scholarly journals Large Scale Shell Model Calculations of the Negative-Parity States Structure in 24Mg Nucleus

2021 ◽  
Vol 66 (4) ◽  
pp. 293
Author(s):  
A.A. Al-Sammarraie ◽  
F.A. Ahmed ◽  
A.A. Okhunov
Keyword(s):  
Shell Model ◽  
Large Scale ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Energy Levels ◽  
Form Factors ◽  
Model Space ◽  
Negative Parity ◽  
Matrix Elements ◽  
Model Calculations

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

scholarly journals O2 State in 18 O by using Core – Polarization effects

2008 ◽  
pp. 66-72
Keyword(s):  
Perturbation Theory ◽  
Experimental Studies ◽  
Form Factors ◽  
Wave Model ◽  
Collective Model ◽  
Core Polarization ◽  
Polarization Effects ◽  
The Core ◽  
The Subject ◽  
Space Wave

Coulomb form factors for E0 transition in 18O are discussed taking into account core-polarization effects. These effects are taken into account through the collective model of Tassie and also through a microscopic perturbation theory including excitations up to 2p1f shell. Space wave model functions defined for the orbits 1 and 2125O nucleus has been the subject of extensive theoretical and experimental studies, which received much attention in last decade [Alex Brown et.al.2005]. The 18O system contains two neutrons in addition to the16O core distributed in the sd – shell. d1 are obtained from the diagonalization of the interaction Hamilonian of Wildenthal. The calculations include the 0 2state with excitation energies3.6337MeV. The core – polarization effects which incorporate the ollective model of Tassei describe the data very well for this state.

scholarly journals ββ DECAY AND NUCLEAR STRUCTURE

2007 ◽  
Vol 16 (02) ◽  
pp. 552-560 ◽  
Author(s):  
E. CAURIER ◽  
F. NOWACKI ◽  
A. POVES
Keyword(s):  
Shell Model ◽  
Nuclear Matrix ◽  
Large Scale ◽  
Predictive Power ◽  
Strong Impact ◽  
Matrix Elements ◽  
Model Calculations ◽  
Mode Stability ◽  
Recent Developments

The determination of accurate nuclear matrix elements for ββ decay processes is a challenge for nuclear theory and can have a strong impact in neutrino physics. Large Scale Shell Model (LSSM) calculations are among the best tools for such determination and recent developments have allowed to extend its application domains. In particular, systematic studies of nuclear matrix elements calculations have been now undertaken in this framework for most of the ββ emitters. These calculations are crucial in the determination of the most favorable emitters in the forthcoming generation of ββ experiments. The present paper focuses on the recent advances and remaining difficulties of shell model calculations for the neutrinoless mode. Stability and predictive power of the results will be discussed.

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