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.

The ${}^6{\mathrm{L}\mathrm{i}(}^6\mathrm{Li},\alpha \alpha {)}^4\mathrm{He}$ three-body reaction has been studied in a kinematically complete experiment at $E_{6_{\mathrm{Li}}}=6\mathrm{}\mathrm{MeV},$ from which indirect information on the ${}^2{\mathrm{H}(}^6\mathrm{Li},\alpha {)}^4\mathrm{He}$ two-body reaction at $13<~E_{\mathrm{c}.\mathrm{m}.\mathrm{}}<~750\mathrm{}\mathrm{keV}$ has been extracted by applying the Trojan horse method. The method used a recent improved formulation. The derived astrophysical $S\left(E\right)\mathrm{}$ factor for the two-body process is compared with that obtained from direct experiments.

The ${}^{11}\mathrm{B}\left(p,{\alpha }_0\right){}^8\mathrm{Be}$ reaction was studied from $1\text{MeV}$ down to astrophysical energies by means of the Trojan-horse method applied to the ${}^2\mathrm{H}\left({}^{11}\mathrm{B},{\alpha }_o{}^8\mathrm{Be}\right)n$ three-body reaction performed at an incident energy of $27\text{MeV}$. Coincidence spectra measured in a kinematically complete experiment show the presence of the quasifree ${}^{11}\mathrm{B}‐p$ process. The astrophysical factor $S\left(E\right)$ for the ${}^{11}\mathrm{B}\left(p,{\alpha }_0\right){}^8\mathrm{Be}$ reaction was extracted from the three-body cross section at low neutron momentum. The result was compared with the behavior of the astrophysical factor from the directly measured two-body reaction.