Abstract
Nucleosynthesis in primordial stellar environments may lead to a substantial production of $^{10}\mathrm{B}$ isotopes, which either are converted by the $^{10}\mathrm{B}(p,\ensuremath{\alpha})^{7}\mathrm{Be}$ reaction to $^{7}\mathrm{Be}$ or processed further by $^{10}\mathrm{B}+\ensuremath{\alpha}$ reactions towards the carbon, nitrogen, and oxygen range. This paper focuses on low energy studies of the $^{10}\mathrm{B}(\ensuremath{\alpha},p)^{13}\mathrm{C}$ and $^{10}\mathrm{B}(\ensuremath{\alpha},d)^{12}\mathrm{C}$ reactions to determine the low energy cross section and the reaction rates in stellar environments using $R$-matrix analysis techniques. The experimental results cover a broad energy range, from 0.21 MeV up to 1.4 MeV in the center of mass frame, extending down to the Gamow energy range. A substantial increase in the reaction rate compared to previous predictions is found, due to the identification of near threshold $\ensuremath{\alpha}$-cluster resonance structures.
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