Shell Model Investigation of Some p and sd-Shell Nuclei with Harmonic Oscillator and Skyrme Interactions

Abstract

In this study, the longitudinal charge and form factors for the nuclei 9Be and 28Si lying in the p and sd shells are studied by employing the Harmonic Oscillator potential (HO) and Skyrme effective interaction (Sk35−Skzs∗). The C0 and C2 from factors calculated for the ground state 3/2-, the 5/2- (2.429 MeV) and 7/2- (6.380 MeV) for 9Be, while the ground state 0+ and 2+ (1.779 MeV) state for 28Si nucleus. Calculations of microscopic perturbations that involve intermediate one-particle, one-hole excitation from the core and MS orbits into all upper orbits with excitations are utilized to generate the effective charges necessary to account for the “core polarization effect”. The shell model calculations are utilized on the extended model space to include all 1s, 1p, 2s–1d, 2p‑1f orbits with truncation. Bohr-Mottelson collective model and Tassie model with properly estimated effective neutron and proton charges are taken into account to consider the effect of the core contribution. The estimated form factors were compared with the measured available data and they were in good agreement for most of the studied states. A conclusion can be drawn that truncation is very good choice to study the longitudinal form factors.
 
 The choice of Harmonic Oscillator potential (HO) and Skyrme effective interaction (Sk35−Skzs∗) is adequate for form estimation of longitudinal form factors.
 The estimation of the effective charges based on microscopic perturbations that involve intermediate one-particle, one-hole excitation from the core and MS orbits into all upper orbits with excitations is adequate.
 The truncation proves to be very successful to perform the study.