Search for in-band transitions in the candidate superdeformed band in ${}^{28}\mathrm{Si}$

Background: Superdeformed (SD) bands are suggested by theory around ${}^{40}\mathrm{Ca}$ and in lighter alpha-conjugate nuclei such as ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, and ${}^{32}\mathrm{S}$. Such predictions originate from a number of theoretical models including mean-field models and antisymmetrized molecular dynamics (AMD) calculations. While SD bands have been identified in ${}^{40}\mathrm{Ca}$ and its near neighbors, evidence of their existence in the lighter, midshell nuclei is circumstantial at best. The key evidence of superdeformation would be the observation of transitions with high $B$($E2)$ transition strengths connecting states in a rotational sequence. This is challenging information to obtain since the bands lie at a high excitation energy and competition from out-of-band decay is dominant.

Purpose: The purpose of the present study is to establish a new methodology to circumvent the difficulties in identifying and quantifying in-band transitions through directly populating candidate states in the SD band in ${}^{28}\mathrm{Si}$ through inelastic alpha scattering, selecting such states with a spectrometer, and measuring their gamma-ray decay with a large array of high-purity germanium detectors, allowing direct access to electromagnetic transition strengths.

Methods: Excited states in ${}^{28}\mathrm{Si}$ were populated in the ${}^{28}\mathrm{Si}(\alpha ,{\alpha }^{\prime })$ reaction using a 130-MeV ${}^4\mathrm{He}$ beam from the K140 AVF cyclotron at the Research Center for Nuclear Physics. Outgoing alpha particles were analyzed using the Grand Raiden spectrometer positioned at an angle of $9.1^{\circ }$ to favor the population of states with $J\approx 4$. Coincident gamma rays were detected with the CAGRA array of 12 HPGe clover detectors augmented by a set of four large ${\mathrm{LaBr}}_3$ detectors.

Results: Data analysis showed that it was possible to identify additional low-energy transitions in competition with high-energy decays from excited states in ${}^{28}\mathrm{Si}$ in the vicinity of 10 MeV. However, while the candidate $4^{+}$ SD state at 10.944 MeV was populated, a 1148-keV transition to the candidate $2^{+}$ SD state at 9.796 MeV was not observed, and only an upper limit for its transition strength of $B\left(E2\right)<43$ W.u. could be established. This contradicts AMD predictions of $\approx 200$ W.u. for such a transition.

Conclusion: The present study strongly rejects the hypothesis that the candidate set of states identified in ${}^{28}\mathrm{Si}$ represents an SD band, which demonstrates the potential of the methodology devised here.

Figure 1

Key elements of the band structure of ${}^{28}\mathrm{Si}$ relevant to the present work. The ground-state band is oblate deformed and coexists with an excited prolate band. Candidate states for a superdeformed (SD) band are indicated. Transition strengths, i.e., $B\left(E2\right)$ in W.u., are indicated where known, including limits. Transition strengths shown in red are those derived in the present work, as presented in Table 1.

Figure 2

Calibrated focal-plane spectrum. Peaks in the spectrum associated with the population of known excited states in ${}^{28,29,30}\mathrm{Si}$ are identified with a letter. Peaks corresponding to excited states in rotational bands in ${}^{28}\mathrm{Si}$ are shown in red (see Fig. 3).

Figure 3

Subset of the excited states and rotational bands in ${}^{28}\mathrm{Si}$. The rotational bands are labeled with the $K^{\pi }$ assigned to them in the literature. The rotational sequence labeled “SD” is the candidate superdeformed band. States shown in red were populated in the present study; they are labeled with a letter which corresponds to the peaks observed in the focal-plane spectrum (see Fig. 2).

Figure 4

Background-subtracted coincidence matrix of gamma rays in prompt coincidence with detection of alpha particles in the focal plane corresponding to the population of excited states in ${}^{28}\mathrm{Si}$. The red line indicates the locus corresponding to transitions to the ground state; the yellow line, to the $2_1^{+}$ state; and the black line, to the $4_1^{+}$ state in ${}^{28}\mathrm{Si}$.

Figure 5

Sample gamma-ray spectrum obtained by gating on the $3_1^{+}$ state at 6276 keV in the focal-plane data. Single- and double-escape peaks are labeled “s” and “d,” respectively. Contaminant peaks from other silicon isotopes, ${}^{29}\mathrm{Si}$ and ${}^{30}\mathrm{Si}$, are labeled “c.”

Figure 6

Gamma-ray spectrum obtained by gating on the 10 182/10 190-keV doublet. Single- and double-escape peaks are labeled “s” and “d,” respectively. Inset: Expanded view of the gamma-ray spectrum between 700 and 950 keV, where two new transitions with energies of $\approx 800$ and $\approx 865$ keV are identified.

Figure 7

High-energy portion of the gamma-ray spectrum gated by the 10 944-keV state. Each transition is labeled and the positions of single- and double-escape peaks with respect to the photopeak are indicated by dotted lines. A previously unreported transition with an energy of 11 007 keV is marked.

Figure 8

Midenergy portion of the gamma-ray spectrum gated by the 10 944-keV state. Transitions are labeled and the locations of single- and double-escape peaks relative to the photopeak are indicated by dotted lines. Inset: Expanded view of the region between 3500 and 3700 keV where three transitions of interest are located. For reasons of clarity, only the key transitions relevant to the present analysis are marked. The remaining peaks are all associated with known transitions in ${}^{28}\mathrm{Si}$ with the exception of the peak labeled “c,” which is a known transition in ${}^{30}\mathrm{Si}$ associated with weak selection of the state labeled “u” in Fig. 3, which sits on the shoulder of the state of interest, “t.”

Figure 9

Low-energy portion of the gamma-ray spectrum gated by the 10 944-keV state. The single-escape peak corresponding to the intense 1778-keV $2^{+}\to 0^{+}$ transition is labeled “s” and the $\left(3_6^{-}\right)\to 2_6^{+}$ transition is marked.