<b>Study of Nuclear Deformations for Some Nuclei located Near the Nuclear Island of Inversion Region</b>

In this work, we have carried out a detailed theoretical analysis of the nuclear deformations of some of the nuclei situated in the vicinity and within the nuclear Island of Inversion. The properties that were studied included the calculation of the magnetic moment and the electric quadrupole moment to gather with reduced quadrupole deformation parameter for even-even isotopes of Ne, Mg, and Si nuclei, to explain the behavior of the nuclei in question, and how much they deviate from the spherical shape in this critical region. All theoretical computations were conducted utilizing the NushellX@MSU shell model code within the sd space with the effective two-body interaction USDC. The comparative analysis with available experimental data revealed that certain theoretical parameterizations produced results in good agreement with experimental values. For instance, the theoretical magnetic moment of 29Si was found to be −0.522, closely matching the experimental value of −0.555, indicating reasonable consistency. Furthermore, noticeable variations were observed in the calculated moments and deformations of the studied nuclei. For example,31Mg exhibited a theoretical magnetic moment of 1.348 compared to the experimental value of −0.883. Additionally, some isotopes displayed very large deformations, which confirms the presence of intricate shell effects due to the increased number of neutrons and the resulting modifications in the internal structure of the nucleus