Analytical Derivations of Single-Particle Matrix Elements in Nuclear Shell Model

2016 ◽  
Vol 66 (1) ◽  
pp. 104-114
Author(s):  
Aziz H. Fatah ◽  
R.A. Radhi ◽  
Nzar R. Abdullah
Keyword(s):  
Shell Model ◽  
Single Particle ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Nuclear Shell

scholarly journals Neutrinoless double beta nuclear matrix elements around mass 80 in the nuclear shell-model

2015 ◽  
Vol 93 ◽  
pp. 01055
Author(s):  
N. Yoshinaga ◽  
K. Higashiyama ◽  
D. Taguchi ◽  
E. Teruya
Keyword(s):  
Shell Model ◽  
Nuclear Matrix ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Nuclear Shell

Collective motion in the nuclear shell model III. The calculation of spectra

1963 ◽  
Vol 272 (1351) ◽  
pp. 557-577 ◽  
Keyword(s):  
Shell Model ◽  
Collective Motion ◽  
Mass Region ◽  
Wave Functions ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
One Dimensional ◽  
The One ◽  
Nuclear Shell ◽  
Main Pattern

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

scholarly journals SHELL MODEL DESCRIPTION OF 102–108Sn ISOTOPES

2012 ◽  
Vol 21 (04) ◽  
pp. 1250049
Author(s):  
T. TRIVEDI ◽  
P. C. SRIVASTAVA ◽  
D. NEGI ◽  
I. MEHROTRA
Keyword(s):  
Shell Model ◽  
Single Particle ◽  
State Of The Art ◽  
Model Space ◽  
Model Description ◽  
Nuclear Shell Model ◽  
Model Calculations ◽  
Particle Orbits ◽  
Recent Experimental Work ◽  
Nuclear Shell

We have performed shell model calculations for neutron deficient even 102-108 Sn and odd 103-107 Sn isotopes in sdg7/2h11/2 model space using two different interactions. The first set of interaction is due to Brown et al. and second is due to Hoska et al. The calculations have been performed using doubly magic 100 Sn as core and valence neutrons are distributed over the single particle orbits 1g7/2, 2d5/2, 2d3/2, 3s1/2 and 1h11/2. In more recent experimental work for 101 Sn [I. G. Darby et al., Phys. Rev. Lett.105 (2010) 162502], the g.s. is predicted as 5/2+ with excited 7/2+ at 172 keV. We have also performed another two set of calculations by taking difference in single particle energies of 2d5/2 and 1g7/2 orbitals by 172 keV. The present state-of-the-art shell model calculations predict fair agreement with the experimental data. These calculations serve as a test of nuclear shell model in the region far from stability for unstable Sn isotopes near the doubly magic 100 Sn core.

scholarly journals Application of single particle model to determine the spin and parity of levels of 59Fe nucleus

2015 ◽  
Vol 18 (1) ◽  
pp. 92-101
Author(s):  
Son An Nguyen ◽  
Lanh Dang
Keyword(s):  
Experimental Data ◽  
Excited State ◽  
Shell Model ◽  
Single Particle ◽  
Ground State ◽  
Particle Model ◽  
Nuclear Shell Model ◽  
Average Mass ◽  
Single Particle Model ◽  
Nuclear Shell

The spin and parity of the excited state and the ground state of nuclei are two of important properties of the nuclei quantum. However, up to now we do not have appropriate equipments to directly detetmine the spin and parity of nuclei. This paper shows the application of nuclear shell model to study the spin and parity of intermediate levels and ground state of 59Fe nucleus. Comparing to previously experimental data, this nucleus singleparticle model is suitable of the average mass and odd A nuclei.

scholarly journals Nuclear Shell Model And Quantum Phase Transitions

2019 ◽  
Vol 26 ◽  
pp. 88
Author(s):  
S. Karampagia ◽  
V. Zelevinsky
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Shell Model ◽  
Quantum Phase Transitions ◽  
Mean Field ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Model Hamiltonian ◽  
Orbital Space ◽  
Nuclear Shell

The usual nuclear shell model defines nuclear properties through an effective mean-field plus a two-body interaction Hamiltonian in a finite orbital space. In this study we try to understand the correlation between the various parts of the shell model Hamiltonian and the nuclear observables and collectivity in nuclei. By varying specific groups of matrix elements we find signs of a phase transition in nuclei between a non-collective and a collective phase. In all cases studied the collective phase is attained when the single-particle transfer matrix elements are dominant in the shell model Hamiltonian, giving collective characteristics to nuclei.

CORRELATION BETWEEN EIGENVALUES AND SORTED DIAGONAL MATRIX ELEMENTS OF A LARGE DIMENSIONAL MATRIX

2008 ◽  
Vol 17 (supp01) ◽  
pp. 334-341
Author(s):  
AKITO ARIMA
Keyword(s):  
Shell Model ◽  
Uniform Distribution ◽  
Diagonal Matrix ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Extrapolation Methods ◽  
Dimensional Matrix ◽  
Nuclear Shell

Functional dependences of eigenvalues as functions of sorted diagonal elements are given for realistic nuclear shell model (NSM) hamiltonian, the uniform distribution hamiltonian and the GOE hamiltonian. In the NSM case, the dependence is found to be linear. We discuss extrapolation methods for more accurate predictions for low-lying states.

AN IDENTITY INVOLVING 9-j COEFFICIENTS

1964 ◽  
Vol 42 (6) ◽  
pp. 1081-1086 ◽  
Author(s):  
James D. Talman ◽  
William W. True
Keyword(s):  
Shell Model ◽  
Model Theory ◽  
The Other ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Nuclear Shell ◽  
Tensor Operators

An identity involving 9-j coefficients which may be of some value in spectroscopic calculations is obtained. Two proofs of the identity are described. In one proof the recoupling of matrix elements of tensor operators is considered; in the other the general methods of Yutsis, Levinsonas, and Vanagas are used. Two applications of the identity to nuclear shell-model theory are described.

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