Calculating some nuclear properties of chromium isotopes in the shell model

Abstract

The present study provides an in-depth theoretical examination of the shell model for a range of even-even Chromium (Z = 24) isotopes, encompassing neutron numbers both 22 and 36. The shell model calculations relied on assumptions about the disregarded core-polarization effects and the utilization of effective charges. We performed extensive theoretical calculations to determine the probability of reduced electric quadrupole transition, B(E2;0_g.s⁺ → 2⁺), the intrinsic quadrupole moments (Q₀), the deformation parameters (β₂,δ), and the inclusion of effective interactions such as fpd6, fpv, fpbm, and kb3. Using the NuShellX@MSU algorithm, the one-body density matrix elements (OBDM) were computed for these isotopes. Various effective charges were utilized in these computations, including NU-E effective charges obtained from the Nushellx@MSU software, ST-E standard effective charges, and BM-E effective charges calculated using Bohr and Mottelson’s method. Comparative analysis was conducted between the theoretical values of transition rate B(E2), intrinsic quadrupole moments, deformation parameters and the available experimental data. The gained theoretical conclusions were subsequently contrasted with prior experimental data, which had similarly demonstrated the collapse of the magical property of the Cr isotope. The intrinsic quadrupole moment was optimal when employing the kb3 interaction, but the deformation parameter appeared optimal when using two interactions, fpbm and kb3. Furthermore, it has been demonstrated that the magical characteristic of the ⁵²Cr (N = 28) isotope undergoes collapse.