Core and/or No-Core Shell Model Calculations of the Nuclear Structure for the 6Li, 32S, 92Mo, and 90Zr Nuclei

Abstract

The present paper calculates the energy levels and electron scattering form factors of several medium and light nuclei. This calculation involves many components that need to be taken into account to ensure both feasibility and accuracy, including mathematics methods, quantum mechanical theory, and the theoretical framework and formulas of the nuclear shell model. In this study, the energy levels of ⁶Li nuclei were calculated using the no-core shell model with WBT, WBM, and WBP effective residual interactions. The core shell model was employed to calculate the energy levels for the ³²S and ⁹²Mo nuclei. Based on the no-core shell model energy level calculations, the theoretical elastic (C0) electron scattering form factors of 6Li were obtained, while the core shell model was used to calculate the longitudinal C2 electron scattering form factor for the ³²S, ⁹²Mo, and ⁹⁰Zr nuclei using the Tassie Model (TM). Potentials of the SKX(Skyrm Interaction\ force) and HO (Harmonic Oscillator) were utilized calculate the radial single-particle matrix elements’ wave functions. The Shell model code NuShell-X@MSU was utilized in this present work. The energy level calculations of the ⁶Li nuclei with wbm and wbt interactions show good agreement with experimental data compared to the wbp interaction. The core shell model calculations for the energy levels of ³²S and ⁹²Mo nuclei show reasonable agreement with the experimental data. In addition, the longitudinal C2 inelastic electron scattering form factors of ⁹²Mo, ⁹⁰Zr, and ³²S nuclei exhibit good agreement with experimental results.