Background: Spectroscopy of the exotic, neutron unbound beryllium isotope ${}^{13}\mathrm{Be}$ is still a puzzle despite significant experimental efforts.

Purpose: We aim to observe $T=5/2$ states in ${}^{13}\mathrm{B}$, establish spin-parities and spectroscopic factors, and use isospin symmetry to inform spectroscopy of ${}^{13}\mathrm{Be}$.

Methods: Excitation functions for resonance elastic scattering of ${}^{12}\mathrm{Be}$ on protons were measured in the center-of-mass energy range from 1 to 5 MeV.

Results: Two $T=5/2$ states in ${}^{13}\mathrm{B}$ at excitation energies 18.25 and 19.95 MeV were observed. Unambiguous $1/2^{+}$ and $5/2^{+}$ spin-parity assignments were made, and spectroscopic factors were established using the $R$-matrix analysis of the measured ${}^{12}\mathrm{Be}+p$ excitation functions.

Conclusions: We provide the first direct and unambiguous spin-parity assignments and spectroscopic factor measurements for the resonances in the $A=13, T=5/2$ isobaric multiplet. This puts us on a solid footing to identify the 2.3 MeV state in ${}^{13}\mathrm{Be}$ as $5/2^{+}$ and infer the existence of an $s$-wave ($1/2^{+}$) resonance at around 0.6 MeV with relatively small spectroscopic factor.

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• Elastic scattering reactions
• Energy levels
• Nuclear spin & parity
• Unstable nuclei induced nuclear reactions
• 6 ≤ A ≤ 19