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 $\gamma$-ray detectors. High-spin states of the nucleus are populated using ${}^{18}\mathrm{O}$(${}^{16}\mathrm{O},\alpha n$) and ${}^{18}\mathrm{O}$(${}^{13}\mathrm{C},2n$) reactions at $E_{\mathrm{lab}}=30$–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 $\gamma$ 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.

Figure 1

Top: Level lifetimes of the 1274-keV ($J^{\pi }=3/2^{+}$) state in the ${}^{29}\mathrm{Si}$ nucleus from earlier measurements. Results from the present measurement are also included (see text for details). Bottom: Angular distribution coefficients for the 1596-keV ($7/2^{-}\to 5/2^{+}$) transition in the ${}^{29}\mathrm{Si}$ nucleus from the earlier and the present work (see text for details).

Figure 2

Coincidence spectrum with gates on the 1274- and the 2028-keV transitions in ${}^{29}\mathrm{Si}$. Transitions belonging to the ${}^{29}\mathrm{Si}$ nucleus are labeled with the respective energies, while contaminant peaks are labeled with a pound sign (#). Inset: Higher energy transitions ($E_{\gamma }>2.0$ MeV).

Figure 3

Experimental $R_{\mathrm{anisotropy}}$ values for transitions in ${}^{29}\mathrm{Si}$ from the present work. The new transition is followed by an asterisk.

Figure 4

Top: Plot of polarization asymmetry for transitions in ${}^{29}\mathrm{Si}$ from the present measurements. Transitions with an established electromagnetic nature in ${}^{41}\mathrm{Ca}$ and ${}^{38}\mathrm{Ar}$ are included for reference. These nuclei were populated following the interaction of the beam halo with the aluminum target frame. Bottom: Corresponding polarization ($P$) values. The new transition identified in the present work is followed by an asterisk.

Figure 5

Level scheme of the ${}^{29}\mathrm{Si}$ nucleus from the present work. The new level and the de-exciting transition are followed by an asterisk. Levels and transitions that are known from previous studies but could not be conclusively confirmed in the present work are indicated by dotted lines.

Figure 6

Angular distribution fit for the 1596-keV ($7/2_1^{-}\to 5/2_1^{+}$) transition in the ${}^{29}\mathrm{Si}$ nucleus and corresponding ${\chi }^2$ analysis for obtaining the mixing ratio.

Figure 7

Representative fits to the Doppler shapes observed for the 1596- and 2028-keV transitions in the ${}^{29}\mathrm{Si}$ nucleus.

Figure 8

Comparison of the $B\left(E2\right)$ transition probabilities (in Wu) in ${}^{28}\mathrm{Si}$ as reported by Jenkins et al. [20] with those from the present calculations (numbers in blue: USDA).

Figure 9

Comparison of the experimental level energies of the ${}^{30}\mathrm{Si}$ nucleus from Ref. [7] with the shell model calculations in the present work. These calculations for ${}^{30}\mathrm{Si}$ were carried out using the SDPFMW interaction with purely $sd$ configurations for positive-parity states and $1\hslash \omega$ excitations for negative-parity states.