Measurements of the ${}^2\mathrm{H}({}^{16}\mathrm{C},{}^{16}\mathrm{C}^{*}\to {}^4\mathrm{He}+{}^{12}\mathrm{Be}$ oder ${}^6\mathrm{He}+{}^{10}\mathrm{Be}){}^2\mathrm{H}$ inelastic excitation and cluster-decay reactions have been carried out at a beam energy of about 23.5 MeV/u. A specially designed detection system, including one multilayer silicon-strip telescope at around zero degrees, has allowed the high-efficiency threefold coincident detection and therefore the event-by-event determination of the energy of the unstable nucleus beam. The decay paths from the ${}^{16}\mathrm{C}$ resonances to various states of the final ${}^{10}\mathrm{Be}$ oder ${}^{12}\mathrm{Be}$ nucleus are recognized thanks to the well-resolved $Q$-value spectra. The reconstructed resonances at 16.5(1), 17.3(2), 19.4(1), and 21.6(2) MeV are assigned as the $0^{+}, 2^{+}, 4^{+}$, and $6^{+}$ members, respectively, of the positive-parity ${(3/2_{\pi }^{-})}^2{(1/2_{\sigma }^{-})}^2$-bond linear-chain molecular band in ${}^{16}\mathrm{C}$, based on the angular-correlation analysis for the 16.5 MeV state and the excellent agreement of decay patterns between the measurements and theoretical predictions. Moreover, another intriguing high-lying state was observed at 27.2(1) MeV which decays almost exclusively to the $\approx 6$ MeV states of ${}^{10}\mathrm{Be}$, in line with the newly predicted pure $\sigma$-bond linear-chain configuration.

• Received 29 August 2021
• Revised 28 November 2021
• Accepted 22 March 2022

DOI:https://doi.org/10.1103/PhysRevC.105.044302