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

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Ghofran W. Harby
Ali. A. Alzubadi


         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.

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Harby GW, Alzubadi AA. Calculation of the Magnetic Dipole and Electric Quadrupole Moments of some Sodium Isotopes using Shell Model with Skyrme Interaction. IJP [Internet]. 2022 Sep. 1 [cited 2023 Feb. 6];20(3):40-9. Available from:


Ali A.H. and Alzubadi A.A., Calculation Magnetic Dipole Moments, Electric Quadrupole Moments and Form Factors for Some Ti Isotopes. Physica Scripta, 2020. 95(10): pp. 105306.

Maison D.E., Skripnikov L.V., and Flambaum V.V., Theoretical Study of 173YbOH to Search for the Nuclear Magnetic Quadrupole Moment. Physical Review A, 2019. 100(3): pp. 032514(1-5).

Keim M., Georg U., Klein A., Neugart R., Neuroth M., Wilbert S., Lievens P., Vermeeren L., and Brown B., Measurement of the Electric Quadrupole Moments of 26–29Na. The European Physical Journal A, 2000. 8(1): pp. 31-40.

Brown B.A., The Nuclear Shell Model towards the Drip Lines. Progress in Particle Nuclear Physics, 2001. 47(2): pp. 517-599.

Hadyńska-Klȩk K., Napiorkowski P.J., Zielińska M., Srebrny J., Maj A., Azaiez F., Dobón J.V., Kicińska-Habior M., Nowacki F., and Naïdja H., Quadrupole Collectivity in 42Ca from Low-Energy Coulomb Excitation with AGATA. Physical Review C, 2018. 97(2): pp. 024326(1-20).

Lawson R., Theory of the Nuclear Shell Model. 1980, New York Oxford University Press.

Faessler A., IBA and the Bohr-Mottelson Model. Nuclear Physics A, 1983. 396: pp. 291-305.

Evans R.D. and Evans R., The Atomic Nucleus. Vol. 582. 1955: McGraw-Hill New York.

Neyens G., Nuclear Magnetic and Quadrupole Moments for Nuclear Structure Research on Exotic Nuclei. Reports on Progress in Physics, 2003. 66(4): pp. 633-689.

Rainwater J., Nuclear Energy Level Argument for a Spheroidal Nuclear Model. Physical Review, 1950. 79(3): pp. 432-434.

Safronova M., Safronova U., Radnaev A., Campbell C., and Kuzmich A., Magnetic Dipole and Electric Quadrupole Moments of the 229 Th Nucleus. Physical Review A, 2013. 88(6): pp. 060501(1-5).

Radhi R., Alzubadi A.A., and Ali A., Magnetic Dipole Moments, Electric Quadrupole Moments, and Electron Scattering Form Factors of Neutron-Rich s d− p f Cross-Shell Nuclei. Physical Review C, 2018. 97(6): pp. 064312(1-13).

Brussaard P.J. and Glaudemans P.W.M., Shell Model Applications In Nuclear Spectroscopy. 1977, Amsterdam: North Holland.

Brink D. and Stancu F., Evolution of Nuclear Shells with the Skyrme Density Dependent Interaction. Physical Review C, 2007. 75(6): pp. 064311(1-14).

Brown B. and Rae W., The Shell-Model Code [email protected] MSU. Nuclear Data Sheets

120: pp. 115-118.

National Nuclear Data Center;:

Stone N., Table of Nuclear Magnetic Dipole and Electric Quadrupole Moments. Atomic Data Nuclear Data Tables, 2005. 90(1): pp. 75-176.