Abstract
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.
Highlights
The shell structure of single-particle levels in a spherical potential can be affected by the nuclear deformation (1)
The nuclear electric quadrupole moment depends on a deflection of nuclear charge distribution from spherical symmetry which gives a useful measure of the core polarization especially if the valence nucleons are neutrons which do not directly participate to the electric quadrupole moment (3)
The characteristics of the quadrupole collectivity that develops N ≥20 are discussed by comparing the experimental values of the quadrupole moments with the shell model calculations
Summary
The shell structure of single-particle levels in a spherical potential can be affected by the nuclear deformation (1). The outer-nucleons can move in a certain configuration space which interact with the core and each other by a residual interaction such particle–particle and particle–core interactions (2) These interactions depend on the selected model space and residual interactions; one can investigate this by comparing several experimental parameters such as spin/parity, excitation energy, the magnetic moment and the quadrupole moment and parametrization of the residual interaction and validity of the model space. Shell model calculations; adopt fixed measurement of the effective charges. Ogawa et al (4) adopted the B-M which contain both the universal dependence (N-Z)/A and the overcome effects for bound particles which showed that the experimental data of the quadrupole moments were in agreement (5). The calculated ground-state electric quadrupole moments for the fpd[6] and fpm[13] interactions are compared with experimental values (for nuclei 41,43,44,45Sc, 41,43,45,47,49Ca, 45Ti). Numbered k and is axial symmetric about the z-axis
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