A theoretical comparison has been made for some calcium isotopes ( $_{20}$ $_{20}$ Ca) which are even–even nuclei and have the atomic mass (Z = 20) with its previous experimental data. Theoretical calculations of some $_{20}$ $_{20}$ Ca isotopes (A = 42, 44, 46, 48, 50, 52) adopted by the shell model theory were performed to calculate the transition rate B(E2), theoretical intrinsic quadruple moments ( $Q_{0 Th})$ $Q_{0 Th})$ and theoretical deformation parameters ( $β_{2}$ $β_{2}$ , $δ)_{Th}$ $δ)_{Th}$ were calculated by two methods by using different effective interactions for each isotope such as, su3fp, fpbm, fprkb, fpd6, kb3. Through code NuShellX@MSU, the single-body density matrix was calculated. The effects of the core polarization were neglected by adopting various effective charges that were employed, effective charges of conventional (Con-E), effective charges of standard (St-E) and effective charges of Bohr and Mottelson (B-M-E) which were calculated. The theoretical values of the B(E2)_Th, the $Q_{0 Th}$ $Q_{0 Th}$ and the ( $β_{2}$ $β_{2}$ , $δ)_{Th}$ $δ)_{Th}$ were then compared with the previous experimental data where values of the transition rate B(E2)_Th, theoretical intrinsic quadrupole moments $Q_{0 Th}$ $Q_{0 Th}$ and theoretical deformation parameter ( $β_{2}$ $β_{2}$ , $δ)_{Th}$ $δ)_{Th}$ , using the fpbm, the fpd6 and the kb3 interactions were the best.

Keywords:

PACS: 21.60 Cs

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