First Observation of the $\beta 3\alpha p$ Decay of ${}^{13}\mathrm{O}$ via $\beta$-Delayed Charged-Particle Spectroscopy

The $\beta$-delayed proton decay of ${}^{13}\mathrm{O}$ has previously been studied, but the direct observation of $\beta$-delayed $3\alpha p$ decay has not been reported. Rare $3\alpha p$ events from the decay of excited states in ${}^{13}{\mathrm{N}}^{\star }$ provide a sensitive probe of cluster configurations in ${}^{13}\mathrm{N}$. To measure the low-energy products following $\beta$-delayed $3\alpha p$ decay, the Texas Active Target (TexAT) time projection chamber was employed using the one-at-a-time $\beta$-delayed charged-particle spectroscopy technique at the Cyclotron Institute, Texas A&M University. A total of $1.9\times {10}^5$ ${}^{13}\mathrm{O}$ implantations were made inside the TexAT time projection chamber. A total of 149 $3\alpha p$ events were observed, yielding a $\beta$-delayed $3\alpha p$ branching ratio of 0.078(6)%. Four previously unknown $\alpha$-decaying excited states were observed in ${}^{13}\mathrm{N}$ at 11.3, 12.4, 13.1, and 13.7 MeV decaying via the $3\alpha +p$ channel.

Figure 1

Example $3\alpha +\mathit{p}$ event where the color (online) corresponds to the energy deposition within each voxel after projection into 2D. The proton tracks extends from the vertex to the lower-left of the figure as evidenced by the lower energy deposition. Invariant mass reconstruction designated this event as decaying through the ${}^9\mathrm{B}(\mathrm{g}.\mathrm{s}.)+\alpha$ channel.

Figure 2

Relative energy spectrum for pairs of $\alpha$ particles with the smallest relative energy of the three $\alpha$ tracks. The ${}^9\mathrm{Be}(\mathrm{g}.\mathrm{s}.)$ at 92 keV is well reproduced.

Figure 3

For events that do not decay via the Hoyle state, the relative energy spectrum is shown here which is generated by selecting the two $\alpha$ particles that produce the ${}^9\mathrm{Be}(\mathrm{g}.\mathrm{s}.)$ and then reconstructing the ${}^9\mathrm{B}$ relative energy with the proton. Overlaid in dashed red are simulated data for the ground state contribution and in solid red are the ${\frac{1}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ states from single channel $R$-matrix calculations convoluted with a Gaussian with $\sigma =0.23\mathrm{MeV}$. The ${\frac{1}{2}}^{+}$ parameters are those obtained by Wheldon et al. [17], which show excellent agreement.

Figure 4

Invariant mass spectrum from $3\alpha$ particles assuming a ${}^{12}\mathrm{C}$ origin. A peak at 7.65 MeV is seen, well reproducing the Hoyle state energy, and a broad peak is seen at higher excitation energies which correspond to events that decay via ${}^9\mathrm{B}+\alpha$. No peaks from higher excited states in ${}^{12}\mathrm{C}$ can be seen.

Figure 5

Excitation spectrum in ${}^{13}\mathrm{N}$ for $3\alpha +p$ separated by channels. Black dashed arrows show previously known states populated by $\beta$ decay, and new states observed are shown by solid magenta arrows.

Figure 6

Level scheme of measured $3\alpha +p$ states in ${}^{13}\mathrm{N}$ in the central column with the proposed spin-parity assignments. The location of the thresholds for proton and $\alpha$ decay are shown in red with the equivalent excitation energy shown. The corresponding states in the daughter nuclei (${}^{12}\mathrm{C}$ and ${}^9\mathrm{B}$) are also shown.