Continuum spectroscopy with a ${}^{10}\mathrm{C}$ beam: Cluster structure and three-body decay

Resonance-decay spectroscopy is used to study particle-unbound excited states produced in interactions of $E/A=10.7\hspace{0.5em}\mathrm{MeV}$ ${}^{10}\mathrm{C}$ on Be and C targets. After inelastic scattering, structures associated with excited states in ${}^{10}\mathrm{C}$ were observed at 5.22, 5.29, 6.55, 6.56, 6.57, and 8.4 MeV which decay into the $2p+2\alpha$ final state. This final state is created via a number of different decay paths, which include prompt and sequential two-proton decay to the ground state of ${}^8\mathrm{Be}$, $\alpha$ decay to ${}^6\mathrm{Be}{}_{\mathrm{g}.\mathrm{s}.}$, and proton decay to the 2.345-MeV state of ${}^9\mathrm{B}$. For the sequential two-proton decay states (5.22 and 6.55 MeV), angular correlations between the first two decay axes indicate that the spin of these states are nonzero. For the prompt two-proton decay of the 5.29-MeV state, the three-body correlations between the two protons and the core are intermediate between those measured for ground-state ${}^6\mathrm{Be}$ and ${}^{45}\mathrm{Fe}$ decays. The 6.55- and 6.57-MeV structures are most probably associated with the same level, which has a 14% two-proton decay branch with a strong “diproton” character and a 86% sequential two-proton decay branch. Correlations between the fragments following the three-body decay of the 2.345-MeV state of ${}^9\mathrm{B}$ can be approximately described by sequential $\alpha$ decay to the ${}^5\mathrm{Li}$ intermediate state. The 8.06- and 9.61-MeV ${}^{10}\mathrm{B}$ states that decay into the $d+{}^6\mathrm{Li}{}_{2.186}$ channel are confirmed. Evidence for cluster structure in ${}^{13}\mathrm{N}$ is obtained from a number of excited states that decay into the $p+3\alpha$ exit channel.

Figure 1

Level diagrams for the mirror nuclei ${}^{10}\mathrm{Be}$ and ${}^{10}\mathrm{C}$. The dashed lines indicate the thresholds for particle decay.

Figure 2

Experimental excitation-energy distributions of the indicated subevents in the $2p+2\alpha$ exit channel. The results in (c) and (d) were obtained with a veto on the ${}^8\mathrm{Be}{}_{\mathrm{g}.\mathrm{s}.}$ peak in (a).

Figure 3

Comparison of experimental excitation-energy distributions obtained with the Be target (data points) and the C target (lines). The distributions are gated on (a) a ${}^9\mathrm{B}{}_{\mathrm{g}.\mathrm{s}.}$ intermediate, (b) a compound gate to select prompt two-proton emission, and (d) a ${}^6\mathrm{Be}{}_{\mathrm{g}.\mathrm{s}.}$ intermediate. The Be data have been normalized to the same product of beam atoms and target nuclei per unit area. The distribution shown in (c) was determined from $3p+2\alpha$ events detected with the C target where one of the protons was ignored and the event was then analyzed with the same gating condition as used for distribution (b).

Figure 4

Three-particle ($\alpha \alpha p$) vs four-particle excitation energies showing a new state in ${}^{10}\mathrm{C}$ at $E^{*}=8.4$ MeV that decays through the 2.345-MeV state of ${}^9\mathrm{B}$.

Figure 5

Experimental distribution of $\cos ({\theta }_{\mathit{pp}})$ for the 5.22-MeV state obtained with both the C and Be targets where ${\theta }_{\mathit{pp}}$ is the relative angle between the first two decay axes. This distribution is displayed in each panel and compared with predicted distributions for different assumed spins $J$ of this state. The curves are labeled by the total angular momentum removed by the first emitted proton.

Figure 6

As for Fig. 5, but for the 6.56-MeV state. In addition, the dashed curve in (b) shows a distribution obtained with mixed $j=1/2$ and 3/2 values with maximal interference.

Figure 7

Independent T and Y Jacobi systems for the core$\hspace{0.5em}+\hspace{0.5em}N+N$ three-body system in coordinate and momentum spaces.

Figure 8

Full correlations in both the T and Y Jacobi systems for the 5.29-MeV state. In the T system, the star symbols indicate the coordinates at which the velocity vectors of the ${}^8\mathrm{Be}$ intermediate and one of the protons are identical.

Figure 9

Projected correlations in both the T and Y Jacobi systems for the 5.29-MeV state. The solid, dotted, and dashed curves show the predictions of the phase-space, sequential, and diproton simulations, respectively, which include the effect of the detector bias and resolution via the Monte Carlo simulations. In (c) all three predictions are identical and thus the curves are not separated.

Figure 10

Same as Fig. 8, but for the 6.57-MeV state.

Figure 11

Same as Fig. 9, but for the 6.57-MeV state.

Figure 12

Predicted full correlations in the Jacobi T system for the three decay simulations. These predictions take into account the effect of the detector bias and resolution via the Monte Carlo simulations.

Figure 13

Comparison of experimental angular distributions in the T systems and energy distributions in the Y systems for ${}^6\mathrm{Be}{}_{\mathrm{g}.\mathrm{s}.}$ [8], ${}^{10}\mathrm{C}$, and ${}^{45}\mathrm{Fe}{}_{\mathrm{g}.\mathrm{s}.}$ [30] decay. For ${}^{10}\mathrm{C}$, results are shown for the 5.29-MeV (solid lines) and the 6.57-MeV (dotted lines) states.

Figure 14

Comparison of experimental energy distributions in the T systems and angular distributions in the Y system for ${}^6\mathrm{Be}{}_{\mathrm{g}.\mathrm{s}.}$ [8], ${}^{10}\mathrm{C}$, and ${}^{45}\mathrm{Fe}{}_{\mathrm{g}.\mathrm{s}.}$ [30] decay. For ${}^{10}\mathrm{C}$, results are shown for the 5.29-MeV (solid lines) and the 6.57-MeV (dotted lines) states.

Figure 15

Excitation-energy distribution of ${}^9\mathrm{B}$ fragments obtain from the $p+2\alpha$ events where the two $\alpha$ particles are not associated with ${}^8\mathrm{Be}{}_{\mathrm{g}.\mathrm{s}.}$ decay.

Figure 16

Full correlation plots in both the T and Y Jacobi systems for the decay of the 2.345-MeV state of ${}^9\mathrm{B}$. In the T system, the star symbols indicate the coordinates at which the velocity vectors of the proton and one of the $\alpha$ particles are identical.

Figure 17

Projected correlation plots in both the T and Y Jacobi systems for the 2.345-MeV state of ${}^9\mathrm{B}$. The dashed and dotted curves show the predictions of sequential $\alpha +{}^5\mathrm{Li}{}_{\mathrm{g}.\mathrm{s}.}$ and $p+{}^8\mathrm{Be}{}_{2^{+}}$ decay simulations including the effects of the detector resolution and efficiency.

Figure 18

(a) Distribution of $E_1$, the energy released in the first step of the sequential decay of the ${}^9\mathrm{B}{}_{2.345}$ state, for the two decay simulations. (b) Sequential-decay angular correlations discussed in the text.

Figure 19

Simulated correlations in the Jacobi T system for $\alpha +{}^5\mathrm{Li}{}_{\mathrm{g}.\mathrm{s}.}$ decay and $p+{}^8\mathrm{Be}{}_{2^{+}}$ decay. The star symbols indicate the coordinates at which the velocity vectors of the proton and one of the $\alpha$ particle are identical.

Figure 20

Excitation-energy distributions for the indicated subevents obtained for the $d+2\alpha$ exit channel with both the Be and C targets.

Figure 21

Excitation-energy distributions for ${}^{10}\mathrm{B}$ nuclei determined for the indicated decay paths with both the C and Be targets. The arrows indicate the locations of previously known narrow states. In (c), the solid curve is a fit to the distribution used to extract the peak widths; the dashed curve shows the fitted background.

Figure 22

Excitation-energy distributions for the indicated subevents obtained from the $p+3\alpha$ exit channel with both the C and Be targets.

Figure 23

Excitation-energy distributions for ${}^{13}\mathrm{N}$ nuclei determined for the indicated decay paths for both the C and Be targets. The arrows in (a)–(c) give the energies of previously unknown levels. In (d) the arrows show the location of known levels with energies consistent with the observed peaks.