Decay of ${}^{10}\mathrm{C}$ excited states above the $2p+2\alpha$ threshold and the contribution from “democratic” two-proton emission

The decay of ${}^{10}\mathrm{C}$ excited states to the $2p+2\alpha$ exit channel has been studied using an $E/A=10.7$ MeV ${}^{10}\mathrm{C}$ beam inelastically scattered from a ${}^9\mathrm{Be}$ target. Levels associated with two-proton decay to the ground state of ${}^8\mathrm{Be}$ have been observed. These include states at 5.18 and 6.54 MeV which decay by sequential two-proton emission through the long-lived ground state of ${}^9\mathrm{B}$. In addition, states at 5.3 and 6.57 MeV were found in which there is no long-lived intermediate state between the two proton emissions. For the 6.57 MeV state, the two protons are preferably emitted on the same side of the decaying ${}^{10}\mathrm{C}$ fragment.

Figure 1

The level scheme of ${}^{10}\mathrm{C}$ and other nuclei of interest in its particle decay. Arrows indicate known transitions and those established in this work. The thick arrows indicate democratic two-proton emission.

Figure 2

The ${}^{12}\mathrm{C}$ excitation-energy distribution from $3\alpha$ events. The histogram shows the experimental distribution, while the curve gives the predictions of the Monte Carlo simulations. An additional exponential background was added to the simulated results to aid in the comparison with the data.

Figure 3

Experimental distribution of reconstructed excitation energy: (a) All detected $2p+2\alpha$ events. (b)–(e) Event groups one to four. As reference, the vertical dashed lines indicate the centroids of the two prominent peaks in panel (c) associated with the second group. In (b), the simulated efficiency for detecting events initiated by a $p+{}^9{\mathrm{B}}_{\mathrm{g}.\mathrm{s}.}$ decay is indicated by the dashed curve.

Figure 4

Experimental distributions of reconstructed excitation energy: (a) for ${}^8\mathrm{Be}$ fragments from $\alpha \text{−}\alpha$ pairs. (b) ${}^9\mathrm{B}$ fragment from $\mathrm{p}+{}^8{\mathrm{Be}}_{\mathrm{g}.\mathrm{s}.}$ correlations. (c) ${}^6\mathrm{Be}$ fragments from $p+p+\alpha$ events. (d) ${}^9\mathrm{B}$ fragments from $p+\alpha +\alpha$ events which do not decay through ${}^8{\mathrm{Be}}_{\mathrm{g}.\mathrm{s}.}$.

Figure 5

Distributions of the two proton energies in the ${}^{10}\mathrm{C}$ center-of-mass frame for the two excited states at $E^{*}=5.30$ and 6.57 MeV for events from group two: (a) Experimental distribution. Simulated distributions are shown for (b) sequential and (c) random decay. The dashed lines indicate approximate thresholds associated with the ${}^9{\mathrm{B}}_{\mathrm{g}.\mathrm{s}.}$ gate.

Figure 6

Distributions of relative angle between the two protons for events from group two. Panels (a) and (b) give the distributions gated on the 5.30 MeV and 6.57 MeV peaks, respectively. The histograms are experimental data. The data points in (b) are an estimate of the background contribution. The solid and dashed curves are predictions from the random and sequential simulations, respectively.