The decay path of the Hoyle state in ${}^{12}\mathrm{C}$ ($E_x=7.654\mathrm{MeV}$) has been studied with the ${}^{14}\mathrm{N}(d,{\alpha }_2){}^{12}\mathrm{C}(7.654)$ reaction induced at 10.5 MeV. High resolution invariant mass spectroscopy techniques have allowed us to unambiguously disentangle direct and sequential decays of the state passing through the ground state of ${}^8\mathrm{Be}$. Thanks to the almost total absence of background and the attained resolution, a fully sequential decay contribution to the width of the state has been observed. The direct decay width is negligible, with an upper limit of 0.043% (95% C.L.). The precision of this result is about a factor 5 higher than previous studies. This has significant implications on nuclear structure, as it provides constraints to $3\alpha$ cluster model calculations, where higher precision limits are needed.

Studying interactions of radioactive ions with neutrons is particularly demanding and has been performed only in a few cases. Some of these interactions are crucial in several astrophysical contexts. In the present work, the case of the ⁷Be destruction induced by the (n, α) reaction is investigated at the energies typical of the primordial nucleosynthesis by means of the Trojan Horse Method applied to the ²H(⁷Be, αα)p quasi-free reaction. The ⁷Be(n, α)⁴He cross-section has been measured in a single experiment from ∼2 MeV down to cosmological energies. The corresponding deduced reaction rate has been adopted to evaluate the impact on big bang nucleosynthesis and on the lithium problem.