Cross-shell excitations in ${}^{31}\mathbf{Si}$

The ${}^{31}\mathrm{Si}$ nucleus was produced through the ${}^{18}\mathrm{O}({}^{18}\mathrm{O}, \alpha n$) fusion-evaporation reaction at $E_{\mathrm{lab}}=24\mathrm{MeV}$. Evaporated $\alpha$ particles from the reaction were detected and identified in the Microball detector array for channel selection. Multiple $\gamma$-ray coincidence events were detected in Gammasphere. The energy and angle information for the $\alpha$ particles was used to determine the ${}^{31}\mathrm{Si}$ recoil kinematics on an event-by-event basis for a more accurate Doppler correction. A total of 22 new states and 52 new $\gamma$ transitions were observed, including 14 from states above the neutron separation energy. The positive-parity states predicted by the shell-model calculations in the $sd$ model space agree well with experiment. The negative-parity states were compared with shell-model calculations in the $psdpf$ model space with some variations in the $N=20$ shell gap. The best agreement was found with a shell gap intermediate between that originally used for $A\approx 20$ nuclei and that previously adapted for ${}^{32,34}\mathrm{P}$. This variation suggests the need for a more universal cross-shell interaction.

Figure 1

Portions of the $\gamma$ spectra in coincidence with $\alpha$ particles and 1695-keV $\gamma$ rays. All of the $\gamma$ lines in these regions are labeled with their energies in red color to indicate that they are newly reported.

Figure 2

Portions of the $\gamma$ spectra in coincidence with $\alpha$ particles and 1439-keV $\gamma$ rays. All of the $\gamma$ lines in these regions are labeled with their energies in red color to indicate that they are newly reported.

Figure 3

Energy level scheme of likely positive-parity states in ${}^{31}\mathrm{Si}$ from this work. The newly observed states and transitions are shown in red and the widths of the decay lines are proportional to their intensities.

Figure 4

Energy level scheme of likely negative-parity states in ${}^{31}\mathrm{Si}$ from this work. See the caption of Fig. 3 for more information.

Figure 5

A comparison of selected negative-parity experimental states with 1p1h states calculated with three versions of the WBP interaction. The theory level lines are color coded by the calculated occupancies of the neutron $0f_{7/2}, 1p_{3/2}$, and $1p_{1/2}$ orbitals.

Figure 6

A comparison of experimental energies of the lowest negative-parity states in ${}^{29,31,33}\mathrm{Si}$ along with the calculated positions using the WBP-b interaction.

Figure 7

Graph of neutron resonances on ${}^{30}\mathrm{Si}$ from Ref. [8] with locations of the states seen in the present experiment indicated by vertical arrows. The 6888-keV state observed in the present work is not likely to be the $3/2^{-}$ one reported in the $n$ resonance experiment, as discussed in the text.