Shell Model Calculations for Some Properties of 29-34Mg Isotopes

The calculations of the shell model, based on the large basis, were carried out for studying the nuclear 29-34Mg structure. Binding energy, single neutron separation energy, neutron shell gap, two neutron separation energy, and reduced transition probability, are explained with the consideration of the contributions of the high-energy conﬁgurations beyond the model space of sd-shell. The wave functions for these nuclei are used from the model of the shell with the use of the USDA 2-body effective interaction. The OBDM elements are computed with the use of NuShellX@MSU shell model code that utilizes the formalism of proton-neutron.

Download Full-text

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

Ukrainian Journal of Physics ◽

10.15407/ujpe66.4.293 ◽

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.

Download Full-text

Shell-model calculations for upper pf-shell nuclei with an effective interaction

EPJ Web of Conferences ◽

10.1051/epjconf/201819401006 ◽

2018 ◽

Vol 194 ◽

pp. 01006

Author(s):

Kalin Drumev

Keyword(s):

Shell Model ◽

Effective Interaction ◽

Model Space ◽

Model Calculations ◽

Energy Eigenstates ◽

Mixed Symmetry ◽

Symmetry Approach ◽

Oscillator Shell ◽

Single Oscillator ◽

Pf Shell

Results obtained for the energy spectra and the low-lying positive-parity energy eigenstates of the upper p f -shell nuclei 64Ge and 68Se with the use of the effective interaction JUN45 are reported. We address the question of how appropriate is the possibility to construct a symmetry-adapted shell model in a single oscillator shell using a Pairing-plus-Quadrupole Hamiltonian. Specifically, we study the goodness of the symmetries pseudo SU(3) and O(6) in the structure of the energy eigenstates. Finally, we relate our results to a proposed mixed-symmetry approach which is able to simultaneously account for the presence of both the pairing and the quadrupole modes as the most important ingredients in the effective interaction while using a restricted part of the full model space.

Download Full-text

Shell model calculations in the A=80-100 mass region and study of double β transitions

HNPS Proceedings ◽

10.12681/hnps.2834 ◽

2020 ◽

Vol 1 ◽

pp. 156

Author(s):

J. Sinatkas ◽

L. D. Skouras ◽

D. Strottman ◽

J. D. Vergados

Keyword(s):

Shell Model ◽

Satisfactory Agreement ◽

Effective Interaction ◽

Model Space ◽

Mass Region ◽

Least Square ◽

Matrix Elements ◽

Model Calculations ◽

Least Square Fit ◽

The One

The structure of the Ζ,Ν < 50 nuclei is examined in a model space consisting of the 0g9/2, 1p1/2, 1p3/2 and the 0f5/2 hole orbitals outside the doubly closed 100Sn core. The effective interaction for this model space is derived by introducing second order corrections to the Sussex matrix elements, while the one-hole energies are deduced by a least square fit to the observed levels. The results of the calculation are found to be in very satisfactory agreement with experiment for all nuclei with 38<Ζ<46 but for Ζ<38 this agreement begins to deteriorate. Such a feature possibly indicates the appearance of deformation and the breaking of the Ν=50 core. The wavefunctions of the calculation are used to determine double β matrix elements in the Ge, Se, Sr and Kr isotopes.

Download Full-text

Shell model calculations in the A ~ 100 mass region

HNPS Proceedings ◽

10.12681/hnps.2931 ◽

2020 ◽

Vol 6 ◽

pp. 225

Author(s):

P. Divari ◽

L. D. Skouras

Keyword(s):

Shell Model ◽

Large Scale ◽

Model Space ◽

Mass Region ◽

Matrix Elements ◽

Model Calculations ◽

Single Neutron ◽

Least Squares Fit ◽

The Matrix ◽

Inert Core

The properties of nuclei with 39≤Ζ≤47 and Ν=51-52 are investigated in large scale shell-model calculations. The doubly closed nucleus 100Sn is selected as the reference state and the nuclei under examination are described in terms of proton holes and one up two neutrons outside the inert core. The proton holes are distributed in a model space consisting of the orbitals g9/2, p1/2, p3/2 while f5/2 is sometimes also considerd. Similary the model space for the neutron particles in cludes the orbitals g7/2, d5/2, d3/2, s1/2 and in certain cases h11/2. The effective two-body interaction and the matrix elements of the effective operators were deter mined by introducing second-order corrections to the Sussex matrix elements. The single proton holes as well as the single-neutron energies were treated as parameters which were determined by least-squares fit to the observed levels of 39≤Ζ≤47, Ν=50 and Ν=51 respectively. The results of the calculation were found to be in satisfactory agreement with experimental data and this enable us to make predictions about the properties of some exotic nuclei in the vicinity of 100Sn.

Download Full-text

Shell model calculations in the A=90-98 mass region. A study of the N=51. nuclei

HNPS Proceedings ◽

10.12681/hnps.2895 ◽

2020 ◽

Vol 5 ◽

pp. 90

Author(s):

P. Divari ◽

L. D. Skouras

Keyword(s):

Shell Model ◽

Large Scale ◽

Model Space ◽

Mass Region ◽

Matrix Elements ◽

Model Calculations ◽

Single Neutron ◽

Least Squares Fit ◽

The Matrix ◽

Inert Core

The properties of nuclei with 39 < Ζ < 47 and N=51 are investigated in large scale shell-model calculations. The doubly closed nucleus 100Sn is selected as the reference state and the nuclei under examination are described in terms of proton holes and a single neutron outside the inert core. The proton holes are distributed in a model space consisting of the orbitals g9/2, p1/2, p3/2 while f5/2 is sometimes also considerd. Similary the model space for the single neutron includes the orbitals g7/2, d5/2, d3/2, s1/2 and in certain cases h11/2. The effective two-body interaction and the matrix elements of the effective operators were determined by introducing second-order correctios to the Sussex matrix elements. The single proton holes as well as the single-neutron energies were treated as parameters which were determined by least-squares fit to the observed levels of 39 < Ζ < 47, N=50 and Ν=51 respectively. The results of the calculation were found to be in satisfactory agreement with experimental data and this enable us to make predictions about the properties of some exotic nuclei in the vicinity of 100Sn.

Download Full-text

Investigation of the level structure of 90Nb nucleus using the shell model

Nukleonika ◽

10.2478/nuka-2019-0014 ◽

2019 ◽

Vol 64 (4) ◽

pp. 113-116

Author(s):

Wu Yi-Heng ◽

Yang Dong ◽

Ma Ke-Yan ◽

Luo Peng-Wei

Keyword(s):

Shell Model ◽

Level Structure ◽

Model Space ◽

Negative Parity ◽

Spin States ◽

Shell Closure ◽

Model Calculations ◽

High Spin States ◽

Single Neutron ◽

Subshell Closure

Abstract Shell model calculations have been carried out for 90Nb nucleus with the model space in which the valence protons occupy the f5/2, p3/2, p1/2, and g9/2 orbitals and the valence neutrons occupy the p1/2, g9/2, d5/2, and g7/2 orbitals. According to the calculated results, the negative parity is from the contribution of the proton of the f5/2, p3/2, and p1/2 orbits. The moderate spin states of 90Nb are mainly due to the excitation of protons from the f5/2 and p3/2 orbits to the p1/2 and g9/2 orbits across the Z = 38 subshell closure, and the high spin states arise from the excitation of a single neutron from the g9/2 orbit into the d5/2 orbit across the N = 50 shell closure.

Download Full-text

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

Revista Mexicana de Física ◽

10.31349/revmexfis.65.159 ◽

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.

Download Full-text

Chaotic features of energy spectrum in 68Ge Nucleus Using the Nuclear Shell Model

Iraqi Journal of Physics (IJP) ◽

10.30723/ijp.v18i44.514 ◽

2020 ◽

Vol 18 (44) ◽

pp. 109-115

Author(s):

Hayder Ali Abd ALabas ◽

Adel Khalaf Hamoudi

Keyword(s):

Energy Spectrum ◽

Shell Model ◽

Level Density ◽

Effective Interaction ◽

Model Space ◽

Nuclear Shell Model ◽

Nuclear Level Density ◽

Gaussian Form ◽

Model Calculations ◽

Nuclear Shell

Chaotic features of nuclear energy spectrum in 68Ge nucleus are investigated by nuclear shell model. The energies are calculated through doing shell model calculations employing the OXBASH computer code with effective interaction of F5PVH. The 68Ge nucleus is supposed to have an inert core of 56Ni with 12 nucleons (4 protons and 8 neutrons) move in the f5p-model space ( and ). The nuclear level density of considered classes of states is seen to have a Gaussian form, which is in accord with the prediction of other theoretical studies. The statistical fluctuations of the energy spectrum (the level spacing P(s) and the Dyson-Mehta (or statistics) are well described by the Gaussian orthogonal ensemble (GOE). Furthermore, these fluctuations are independent on the spin J.

Download Full-text

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

Baghdad Science Journal ◽

10.21123/bsj.15.3.304-309 ◽

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.

Download Full-text