Spectroscopy and shell model calculations in Si isotopes

The $^{29}\mathrm{Si}$ nucleus has been studied using heavy-ion-induced fusion-evaporation reactions and, for the first time, using a large array of high-resolution $\ensuremath{\gamma}$-ray detectors. High-spin states of the nucleus are populated using $^{18}\mathrm{O}$($^{16}\mathrm{O},\ensuremath{\alpha}n$) and $^{18}\mathrm{O}$($^{13}\mathrm{C},2n$) reactions at ${E}_{\mathrm{lab}}=30$\char21{}34 MeV. Previously reported levels are confirmed and a new level is identified in the present study. Spin-parity assignments are carried out based on the anisotropy and polarization measurements of the observed $\ensuremath{\gamma}$ transitions. Level lifetimes are measured using the Doppler shift attenuation method, with modified analysis techniques for the thick molecular target (${\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$) used in the present setup. The lifetime of the lowest negative-parity state at ${E}_{x}=3624$ keV is substantially modified from the previously reported value. Large-basis shell model calculations are carried out for the nucleus using updated interactions and the results corroborate the experimental findings. The calculations are also carried out for the neighboring $^{28,30}\mathrm{Si}$ isotopes. In the case of the $^{28}\mathrm{Si}$ nucleus, the calculations adequately reproduce most of the deformed structures, as represented by the quadrupole moments extracted therefrom. In the $^{30}\mathrm{Si}$ nucleus, the negative-parity states are reproduced for the first time without any ad hoc lowering of the single-particle energies. It can be generally stated that the shell model calculations adequately describe the experimental observations in these nuclei.