Positive-Parity Linear-Chain Molecular Band in ${}^{16}\mathrm{C}$

An inelastic excitation and cluster-decay experiment ${}^2\mathrm{H}({}^{16}\mathrm{C},{}^4\mathrm{He}+{}^{12}\mathrm{Be}\text{or}{}^6\mathrm{He}+{}^{10}\mathrm{Be}){}^2\mathrm{H}$ was carried out to investigate the linear-chain clustering structure in neutron-rich ${}^{16}\mathrm{C}$. For the first time, decay paths from the ${}^{16}\mathrm{C}$ resonances to various states of the final nuclei were determined, thanks to the well-resolved $Q$-value spectra obtained from the threefold coincident measurement. The close-threshold resonance at 16.5 MeV is assigned as the $J^{\pi }=0^{+}$ band head of the predicted positive-parity linear-chain molecular band with $(3/2_{\pi }^{-}{)}^2(1/2_{\sigma }^{-}{)}^2$ configuration, according to the associated angular correlation and decay analysis. Other members of this band were found at 17.3, 19.4, and 21.6 MeV based on their selective decay properties, being consistent with the theoretical predictions. Another intriguing high-lying state was observed at 27.2 MeV which decays almost exclusively to ${}^6\mathrm{He}+{}^{10}\mathrm{Be}(\sim 6\mathrm{MeV})$ final channel, corresponding well to another predicted linear-chain structure with the pure $\sigma$-bond configuration.

Figure 1

A schematic view of the experimental setup. $\mathrm{x}$ in ${\mathrm{T}}_{1\mathrm{x}}$ and ${\mathrm{T}}_{2\mathrm{x}}$ stands for up and down.

Figure 2

Excitation energy spectra of ${}^{16}\mathrm{C}$ reconstructed from two final channels (${}^4\mathrm{He}+{}^{12}\mathrm{Be}+{}^2\mathrm{H}$ and ${}^6\mathrm{He}+{}^{10}\mathrm{Be}+{}^2\mathrm{H}$) and gated on $Q$-value peaks for decaying into ${}^{12}\mathrm{Be}(0_1^{+})$ (a), ${}^{12}\text{Be}(2_1^{+})$ (b), ${}^{10}\mathrm{Be}(0_1^{+})$ (d), ${}^{10}\mathrm{Be}(2_1^{+})$ (e), and ${}^{10}\mathrm{Be}(\sim 6\mathrm{MeV})$ (f). Each spectrum is fitted by the sum (red solid line) of several resonant peaks (blue solid line). The black dashed lines stand for the detection efficiencies as a function of excitation energy, for each of which the maximum is indicated by the percentage value. The vertical black dotted lines are plotted to guide the eyes for the corresponding states. The $Q$-value spectra in (c) and (g) are described in the text.

Figure 3

Angular correlation between ${}^4\text{He}$ and ${}^{12}\text{Be}$ fragments decaying from the 16.5 MeV resonance in ${}^{16}\mathrm{C}$. Experimental results are compared with theoretical distributions corrected by the detection efficiency. The corresponding reduced ${\chi }^2$ values are also presented accordingly.

Figure 4

Relative cluster decay widths from the resonant states in ${}^{16}\mathrm{C}$ to the ${}^4\text{He}+{}^{12}\text{Be}$ and ${}^6\text{He}+{}^{10}\text{Be}$ final channels, extracted from presently observed spectra in Fig. 2 (left panel) and AMD calculations [21] (right panel). The upward hatched, filled, plane hatched, downward hatched, and cross hatched column bars represent decays to ${}^{12}\mathrm{Be}(\mathrm{g}.\mathrm{s}.)$, ${}^{12}\mathrm{Be}(2_1^{+})$, ${}^{10}\mathrm{Be}(\mathrm{g}.\mathrm{s}.)$, ${}^{10}\mathrm{Be}(2_1^{+})$, and ${}^{10}\mathrm{Be}(\sim 6\mathrm{MeV})$ final states, respectively. Colors are used to differentiate the various excited states. Each partial cluster decay width is normalized to the sum of the widths from the same mother resonance.