Study of the $^{19}$F(p,$\alpha$)$^{16}$O reaction through the Trojan Horse Method and its astrophysical enviroment

Fluorine nucleosynthesis takes place in the hydrogen-helium intershell region of Asymptotic Giant Branch (AGB) stars and in the same region also the $s$ elements are produced. Because fluorine is produced in the He-intershell and then dredged up to the surface together with $s$ process elements, its abundance is used as probe for AGB models and nucleosynthesis and is one of the most important input parameters for an analysis of $s$ process in AGB star conditions. The problem is that current models fail to explain the highest F enhancements found in the low-mass AGB stars. A possible way to explain this abundance found in AGB star envelopes might be provided by a revision of the uncertainties in the nuclear reaction rates involved in the synthesis of this nuclide in these stars. In particular, The $^{19}$F(p,$\alpha$)$^{16}$O reaction is the main destruction channel of fluorine at the bottom of the convective envelope in AGB stars, where it can experience temperatures large enough to determine its destruction, owing to extra-mixing processes. Because of the Coulomb barrier, measurements available in the literature do not have access to the energy region of astrophysical interest, corresponding to the Gamow peak (E$_{c.m.}$ = 38 keV). Direct measurements of the cross section stop at about 500 keV for the $\alpha_0$ channel (with $^{16}$O being left in its ground state following $^{20}$Ne decay), thus the astrophysical factor was then extrapolated to low energies assuming a non resonant energy trend. In the case of extra-mixing phenomena, which are characterized by a maximum temperature of about 10$^7$ K, the energy region below 500 keV is of key importance, thus requiring further and accurate investigations to evaluate the contribution of possible resonances, which could significantly enhance the reaction rate at such low temperatures. So, a new experimental study through the Trojan Horse Method (THM) is important because the method is particulary suited for the study of low-enegy resonances in the case of charged particle induced reactions. It is an experimental indirect technique which selects the quasi-free contribution of an appropriate three-body reaction performed at energies well above the Coulomb barrier, to extract a charged-particle two-body cross section at astrophysical energies free from coulomb suppression. Two experimental runs were performed using the THM, extracting the quasi-free contribution to the $^2$H($^{19}$F,$\alpha$$^{16}$O)n three-body reaction. In this work I focused on the second run especially because of the improved angular and energy resolution allowed to draw accurate quantitative conclusions from the data for the $\alpha_0$ channel. The measurement was performed at the Laboratori Nazionali di Legnaro in July 2012 where the Tandem accelerator provided a 55 MeV $^{19}$F beam which impinged onto CD$_2$ targets. The experimental setup consisted of a telescope devoted to oxygen detection, made up of an ionization chamber and a silicon position sensitive detector (PSD) on one side with respect to the beam direction and one additional PSD on the opposite side for coincident detection of the $\alpha$ particles. In the beginning of the experimental work, I described the reason leading to the choice of the three-body reaction, of the beam energy, of the setup and of the detection angles. After the off-line analysis in which I widely described the detector calibration, the three-body reaction channel selection, the study of reaction mechanism and the selection of the quasi-free contribution are discussed. Finally the cross-section reaction are extracted and compared with the available direct measurement. The analysis of the $\alpha_0$ channel shows the presence of resonant structure never observed before that could lead to a significant increase in the reaction rate at astrophysical temperatures, with important consequences for stellar nucleosynthesis.