The nucleus ${}^{11}\mathrm{C}$ plays an important role in the boron-proton fusion reactor environment as a catalyzer of the ${}^{10}\mathrm{B}(p,\alpha ){}^7\mathrm{Be}$ reaction which, by producing a long-lived isotope of ${}^7\mathrm{Be}$, poisons the aneutronic fusion process ${}^{11}\mathrm{B}(p,2\alpha ){}^4\mathrm{He}$. The low-energy cross section of ${}^{10}\mathrm{B}(p,\alpha ){}^7\mathrm{Be}$ depends on the near-threshold states $7/2_1^{+}, 5/2_2^{+}, 5/2_3^{+}$ in ${}^{11}\mathrm{C}$ whose properties are primarily known from the indirect measurements. In this work, we present the theoretical analysis of these resonances and their collectivization via the coupling to the proton emission threshold. By using the shell model embedded in the continuum, we show that a significant collectivization takes place that enhances the spectroscopic factor of proton capture confirming the phenomenological value of Wiescher et al. [Phys. Rev. C 95, 044617 (2017)].

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• Nuclear astrophysics
• Nuclear physics of explosive environments
• 6 ≤ A ≤ 19
• Nuclear structure & decays