Search for in-band transitions in the candidate superdeformed band in Si28

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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 $^{28}\mathrm{Si}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$ 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 $9.{1}^{\ensuremath{\circ}}$ to favor the population of states with $J\ensuremath{\approx}4$. 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 $B(E2)<43$ W.u. could be established. This contradicts AMD predictions of $\ensuremath{\approx}200$ 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.

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