Resonant reactions of astrophysical interest studied by means of the Trojan Horse Method. Two case studies

Resonant reactions in astrophysics play and important role as un- expected resonances may enhance the astrophysical factor with respect to the direct reaction contribution, altering the predicted nucleosynthesis scenarios by changing, for instance, the expected nucleosynthesis path. They also are of great interest in nuclear structure studies, since the determination of energies, spin-parities and partial widths sheds light on the occurrence of cluster structures, for instance. However, nuclear reactions in most astrophysical environments usually take place at energies below about 1 MeV, leading to an exponential de- crease of the cross sections due to the effect of the penetration of the Coulomb barrier. Also, at energies so low to be comparable with those associated to elec- tronic degrees of freedom, the effect of atomic and/or molecular clouds cannot be neglected, resulting in a shielding of nuclear charges and in an enhancement of the cross sections with respect to the case of bare nuclei (the so called elec- tron screening effect). Owing to vanishingly small cross sections and ambigui- ties in the extrapolation due to the electron screening, supplying accurate cross sections for astrophysical modeling is extremely challenging. Indirect methods have been introduced to explore the energy range of astrophysical interest with no need of extrapolation, even guided by theoretical arguments. In particular, the Trojan Horse Method makes use of quasi-free reactions with three particles in the exit channel, a+A ^ c + C + s, to deduce the cross section of the reaction of astrophysical interest, a + x ^ c + C, under the hypothesis that A shows a strong x + s cluster structure. Even if measurements are carried out above astro- physical energies to be free from Coulomb suppression and electron screening, the range of astrophysical interest can be covered thanks to the x - s intercluster motion and binding energy. In these proceedings we will show the application of the THM, in the case of resonant reactions, using the generalised R-matrix approach introduced by A.M. Mukhamedzhanov. We will discuss the possibil- ity to extract resonance parameters from the Trojan Horse data and perform a full spectroscopic study of low-energy and even sub-threshold resonances. In particular, we will focus on the ¹⁹F(p, a)¹⁶O and the ¹³C(a, n)¹⁶O reactions, of particular importance in the case of asymptotic giant branch stars and in the synthesis of heavy elements by means of the s-process.