Cluster structure of $3\alpha +p$ states in ${}_{13}N$

Background: Cluster states in ${}_{13}N$ are extremely difficult to measure due to the unavailability of ${}_{9}B+\alpha$ elastic-scattering data.

Purpose: Using $\beta$-delayed charged-particle spectroscopy of ${}_{13}O$, clustered states in ${}_{13}N$ can be populated and measured in the $3\alpha +p$ decay channel.

Methods: One-at-a-time implantation and decay of ${}_{13}O$ was performed with the Texas Active Target Time Projection Chamber. $149\beta 3\alpha p$ decay events were observed and the excitation function in ${}_{13}N$ reconstructed.

Results: Four previously unknown $\alpha$-decaying excited states were observed in ${}_{13}N$ at an excitation energy of 11.3, 12.4, 13.1, and 13.7 MeV decaying via the $3\alpha +p$ channel.

Conclusions: These states are seen to have a ${[}^{9}B(g.s)⨂\alpha /p+{}_{12}C\left(0_2^{+}\right)], {[}^{9}B\left({\frac{1}{2}}^{+}\right)⨂\alpha ], {[}^{9}B\left({\frac{5}{2}}^{+}\right)⨂\alpha ]$, and ${[}^{9}B\left({\frac{5}{2}}^{+}\right)⨂\alpha ]$ structure, respectively. A previously seen state at 11.8 MeV was also determined to have a $[p+{}_{12}C(g.s.)/p+{}_{12}C\left(0_2^{+}\right)]$ structure. The overall magnitude of the clustering is not able to be extracted, however, due to the lack of a total width measurement. Clustered states in ${}_{13}N$ (with unknown magnitude) seem to persist from the addition of a proton to the highly $\alpha$-clustered ${}_{12}C$. Evidence of the ${\frac{1}{2}}^{+}$ state in ${}_{9}B$ was also seen to be populated by decays from ${}_{13}N_{★}$.