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The Trojan Horse Method (THM) represents an indirect path to determine the bare nucleus astrophysical S-factor for reactions among charged particles at astrophysical energies. This is achieved by measuring the quasi-free cross section of a suitable three-body process. The method is also suited to study neutron-induced reactions, especially in the case of radioactive ion beams. A comprehensive review of the theoretical as well as experimental features behind the THM is presented here. An overview is given of some recent applications to demonstrate the method's practical use for reactions that have a great impact on selected astrophysical scenarios.

In the environment of a hot plasma, as achieved in stellar explosions, capture and photodisintegration reactions proceeding on excited states in the nucleus can considerably contribute to the astrophysical reaction rate. Such reaction rates including the excited-state contribution are obtained from theoretical calculations as the direct experimental determination of these astrophysical rates is currently unfeasible. In the present study, ($\gamma$,p) and ($\gamma$,$\alpha$) reactions in the mass and energy range relevant to the astrophysical $p$ process are considered and the feasibility of measuring them with the ELISSA detector system at the future Variable Energy $\gamma$-ray (VEGA) facility at ELI-NP is investigated. The simulation results reveal that, for the ($\gamma$,p) reaction on twelve targets of $^{29}$Si, $^{56}$Fe, $^{74}$Se, $^{84}$Sr, $^{91}$Zr, $^{96,98}$Ru, $^{102}$Pd, $^{106}$Cd, and $^{115, 117, 119}$Sn, and the ($\gamma$,$\alpha$) reaction on five targets of $^{50}$V, $^{87}$Sr, $^{123,125}$Te, and $^{149}$Sm, the yields of the reaction channels with the transitions to the excited states in the residual nucleus are relevant and even dominant. It is further found that for each considered reaction, the total yields of the charged-particle $X$ may be dominantly contributed from one, two or three ($\gamma$,$X_{i}$) channels within a specific, narrow energy range of the incident $\gamma$-beam. Furthermore, the energy spectra of the ($\gamma$,$X_{i}$) channels with $0\leq i\leq 10$ are simulated for each considered reaction, with the incident $\gamma$-beam energies in the respective energy range as derived before. It becomes evident that measurements of the photon-induced reactions with charged-particle emissions considered in this work are feasible with the VEGA+ELISSA system and will provide knowledge useful for nuclear astrophysics., Comment: 11 figures, 17 pages

The abundance of 26Al carries a special role in astrophysics, since it probes active nucleosynthesis in the Milky Way and constrains the Galactic core-collapse supernovae rate. It is estimated through the detection of the 1809 keV γ-line and from the superabundance of 26Mg in comparison with the most abundant Mg isotope (A = 24) in meteorites. For this reason, high precision is necessary also in the investigation of the stable 27Al and 24Mg isotopes. Moreover, these nuclei enter the so-called MgAl cycle, playing an important role in the production of Al and Mg. Recently, high-resolution stellar surveys have shown that the Mg–Al anticorrelation in red-giant stars in globular clusters may hide the existence of multiple stellar populations, and that the relative abundances of Mg isotopes may not be correlated with Al. The common thread running through these astrophysical scenarios is the 27Al(p,α)24Mg reaction, which is the main 27Al destruction channel and directly correlates its abundance with the 24Mg one. Since available reaction rates show large uncertainties owing to the vanishingly small cross section at astrophysical energies, we have applied the Trojan Horse Method to deduce the reaction rate with no need of extrapolation. The indirect measurement made it possible to assess the contribution of the 84 keV resonance and to lower upper limits on the strength of nearby resonances. In intermediate-mass AGB stars experiencing hot bottom burning, a sizeable increase in surface aluminum abundance is observed at the lowest masses, while 24Mg is essentially unaffected by the change in the reaction rate.

We report the first (in)elastic scattering measurement of ^{25}Al+p with the capability to select and measure in a broad energy range the proton resonances in ^{26}Si contributing to the ^{22}Mg(α,p) reaction at type I x-ray burst energies. We measured spin-parities of four resonances above the α threshold of ^{26}Si that are found to strongly impact the ^{22}Mg(α,p) rate. The new rate advances a state-of-the-art model to remarkably reproduce light curves of the GS 1826-24 clocked burster with mean deviation

The $$^{27}\hbox {Al}(\hbox {p},\alpha )^{24}\hbox {Mg}$$ 27 Al ( p , α ) 24 Mg reaction, which drives the destruction of $$^{27}$$ 27 Al and the production of $$^{24}\hbox {Mg}$$ 24 Mg in stellar hydrogen burning, has been investigated via the Trojan Horse Method (THM), by measuring the $$^2\hbox {H}(^{27}\hbox {Al},\alpha ^{24}\hbox {Mg})\hbox {n}$$ 2 H ( 27 Al , α 24 Mg ) n three-body reaction. The experiment covered a broad energy range ($$E_\mathrm{c.m.}\le \,1.5\,\hbox {MeV}$$ E c . m . ≤ 1.5 MeV ), aiming to investigate those of interest for astrophysics. The results confirm the THM as a valuable technique for the experimental study of fusion reactions at very low energies and suggest the presence of a rich pattern of resonances in the energy region close to the Gamow window of stellar hydrogen burning (70–120 keV), with potential impact on astrophysics. To estimate such an impact a second run of the experiment is needed, since the background due the three-body reaction hampered to collect enough data to resolve the resonant structures and extract the reaction rate.

Background: The Li 6 ( p , γ ) Be 7 cross section influences a variety of astrophysical scenarios, including big-bang and stellar nucleosynthesis. In recent years, conflicting results of direct measurements have been published, reporting contradictory low-energy trends. Purpose: To shed light on the contradiction between the existing data sets, the reaction was studied using the asymptotic normalization coefficient (ANC) technique which was up-to-now never used for this reaction. Methods: To derive the ANC, the Li 6 ( He 3 , d ) Be 7 transfer reaction, studied at the Department of Physics and Astronomy of the University of Catania and at the John. D. Fox Superconducting Accelerator Laboratory at Florida State University, was re-analyzed, focusing on the proton transfer mechanism [the α transfer process is discussed by Kiss et al. [Phys. Lett. B 807, 135606 (2020)]. The energy of the He 3 beam impinging on a Li 6 target was E lab = 3 MeV and E lab = 5 MeV. The yield of the emitted deuterons was measured with high precision by using silicon Δ E - E telescopes. Results: From the DWBA analysis of the angular distributions of the emitted deuterons populating the ground ( E * = 0.0 MeV; 3 2 − ) and the first excited ( E * = 0.429 MeV ; 1 2 − ) states of Be 7 , the ANCs for the Li 6 + p → Be 7 system were deduced. Furthermore, the recently measured Li 6 ( p , γ ) Be 7 reaction cross sections [Piatti , Phys. Rev. C 102, 052802 (2020)] were also analyzed within this theoretical framework. Excellent agreement was found between ANC values derived indirectly and those determined from the direct data, which strengthens the conclusion of the present work. The astrophysical S factor—at energies characterizing the Sun—for the Li 6 ( p , γ ) Be 7 reaction was calculated using the weighted mean of the experimentally derived ANC values. Conclusions: The result of the present comprehensive study supports the extrapolation of Piatti [Phys. Rev. C 102, 052802 (2020)], Dong [J. Phys. G Nucl. Partic. 44, 045201 (2017)], and Gnech and Marcucci [Nucl. Phys. A 987, 1 (2019)], and thus disfavors the conclusions drawn by He [Phys. Lett. B 725, 287 (2013)] and Xu [Nucl. Phys. A 918, 61 (2013)].

The Thick Target Inverse Kinematic (TTIK) approach was used to measure excitation functions for the elastic 17O ({\alpha}, {\alpha}) scattering at the initial 17O beam energy of 54.4 MeV. We observed strong peaks corresponding to highly excited {\alpha}-cluster states in the 21Ne excitation energy region of 8-16 MeV, which have never been investigated before. Additional tests were done at a 17O beam energy of 56.4 MeV to estimate a possible contribution of resonance inelastic scattering., Comment: 6 pages,3 figures, conference paper

The neutron capture reaction $$^{10}$$ B(n, $$\alpha $$ ) $$^{7}$$ Li has been investigated via the Trojan Horse Method from 0 to 1 MeV. The $$\alpha _{0}$$ and $$\alpha _{1}$$ channels, corresponding to $$^{7}$$ Li in its g.s. and 1st excited level respectively, have been analyzed and cross sections have been measured for the two reaction channels. Angular distributions for the $$^{11}$$ B energy levels in the explored range have been extracted and compared with literature, while the J $$^{\pi }$$ of the level at $$E_{11B}=11.450$$ MeV (4 keV before the $$\alpha $$ emission threshold) has been clearly determined for the first time.

The $^{26}\mathrm{Si}(p,\ensuremath{\gamma})^{27}\mathrm{P}$ reaction might be relevant in understanding the $^{26}\mathrm{Si}$ depletion and $^{26}\mathrm{Al}$ production in stars. The asymptotic normalization coefficients (ANC) for the $^{26}\mathrm{Si}(p,\ensuremath{\gamma})^{27}\mathrm{P}$ reaction were extracted earlier from the reanalysis of $^{26}\mathrm{Mg}(d,p)^{27}\mathrm{Mg}$ and $^{26}\mathrm{Mg}(t,d)^{27}\mathrm{Mg}$ reactions, in which the deduced ANC's show significant discrepancies. In this work, a dedicated ($d,p$) measurement is presented: the ANC for the $^{27}\mathrm{Mg}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{26}\mathrm{Mg}+n$ virtual decay is deduced from the $^{26}\mathrm{Mg}(d,p)^{27}\mathrm{Mg}$ reaction populating the ground and the first excited state of $^{27}\mathrm{Mg}$ using the distorted wave Born approximation (DWBA). The charge symmetry properties for mirror nuclei have been used to calculate the ANC for the direct capture $^{26}\mathrm{Si}+p\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{27}\mathrm{P}$ populating the ground state of $^{27}\mathrm{P}$. By means of the same formalism, the ${\mathrm{\ensuremath{\Gamma}}}_{p}$ width for the first excited state has also been deduced. The reaction rate is also updated using recent values for the ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}/{\mathrm{\ensuremath{\Gamma}}}_{p}$ ratio measured by [Sun et al., Phys. Rev. C 99, 064312 (2019); Sun et al., Phys. Lett. B 802, 135213 (2020)].

The cosmological lithium problem (CLP) stems from the outstanding discrepancy between theoretical predictions and astronomical observations of primordial lithium abundances. For the radiogenic production of 7Li, 7Be plays a pivotal role in the Big Bang nucleosynthesis (BBN). Nevertheless, the data for neutron-induced 7Be destruction processes were still sparse, and especially lacked information on the contributions of transitions to the 7Li excited states. In this work, we have determined the 7BeLi, 7BeLi*, and 7BeHe reaction cross sections by means of the Trojan Horse method. The present and the previous data were analyzed together by a multichannel R-matrix fit, providing an improved uncertainty evaluation of the channel and the first-ever quantification of the contribution in the BBN-relevant energy range. We implemented the revised total reaction rate summing both the and contributions in a state-of-the-art BBN code PRIMAT. As a consequence, the present nuclear-physics data offers a reduction of the predicted 7Li abundance by about one-tenth, which would impose a stricter constraint on BBN and head us in the correct direction to the CLP solution.

The Trojan Horse Method (THM) lays its foundations on the cluster structure of light nuclei which are usually used as “Trojan horses”. Many of them were successfully employed in the last decades to shed light to numerous astrophysical problems. Cluster structure and dynamics also suggest a series of tests which may be performed in order to strengthen the basis of the method. Among them pole invariance was investigated for three different situations. In fact, the cross sections for the $$^6$$ Li(d, $$\alpha )^4$$ He, $$^2$$ H(d,p) $$^3$$ H and $$^7$$ Li(p, $$\alpha )^4$$ He binary reactions were measured for several break-up schemes and analyzed within the framework of the Plane Wave Impulse Approximation (PWIA). The indirect results extracted by using different Trojan Horse nuclei (e.g. $$^2$$ H, $$^3$$ He, $$^6$$ Li) were compared with each other as well as with direct measurements of the corresponding astrophysical reactions. The very good agreement obtained confirms the applicability of the pole approximation and of the pole invariance method, namely the independence of binary indirect cross section on the chosen Trojan Horse nucleus, at least for the cases investigated. Moreover, we can verify that the effect of using a charged or a neutral particle as a spectator implies negligible corrections consistent with the experimental errors. In addition, the dynamics of clusters inside the Trojan Horse nucleus and their fingerprints on the measured momentum distribution play a key role for THM applications. In this article we will therefore discuss also these assertions studied in different systems( $$^2$$ H, $$^3$$ He, $$^6$$ Li, $$^9$$ Be, $$^{14}$$ N) and in particular for the deuteron case the relative impact of s and d waves in the momentum distribution will also be examined.

Nuclear reactions play a key role in the framework of the Big Bang Nucleosynthesis. A network of 12 principal reactions has been identified as the main path that drove the elemental nucleosynthesis in the first 20 min of the history of the Universe. Among them an important role is played by neutron-induced reactions, which, from an experimental point of view, are usually a difficult task to be measured directly. Nevertheless big efforts in the last decades have led to a better understanding of their role in the primordial nucleosynthesis network. In this work we apply the Trojan Horse Method to extract the cross section at astrophysical energies for the $$^3\text {He}$$ (n,p) $$^3\text {H}$$ reaction after a detailed study of the $$^2\hbox {H}$$ ( $$^3\text {He}$$ ,pt)H three-body process. Data extracted from the present measurement are compared with other published sets.

We report the first (in)elastic scattering measurement of ^{25}Al+p with the capability to select and measure in a broad energy range the proton resonances in ^{26}Si contributing to the ^{22}Mg(α,p) reaction at type I x-ray burst energies. We measured spin-parities of four resonances above the α threshold of ^{26}Si that are found to strongly impact the ^{22}Mg(α,p) rate. The new rate advances a state-of-the-art model to remarkably reproduce light curves of the GS 1826-24 clocked burster with mean deviation9% and permits us to discover a strong correlation between the He abundance in the accreting envelope of the photospheric radius expansion burster and the dominance of ^{22}Mg(α,p) branch.

The $^{7}\mathrm{Li}(\ensuremath{\gamma},t)^{4}\mathrm{He}$ ground state cross section was measured for the first time using monoenergetic $\ensuremath{\gamma}$ rays with energies between 4.4 and 10 MeV at the High Intensity Gamma-ray Source. The reaction is important for the primordial Li problem and for testing our understanding of the mirror $\ensuremath{\alpha}$-capture reactions $^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Li}$ and $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$. Although over the last 30 years most measurements of the $^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Li}$ reaction have concentrated in an energy range below ${E}_{\ensuremath{\gamma}}=3.65$ MeV, measurements at higher energies could potentially restrict the extrapolation to astrophysically important energies. The experimental arrangement for measuring the $^{7}\mathrm{Li}(\ensuremath{\gamma},t)^{4}\mathrm{He}$ reaction included a large-area silicon detector array and several beam characterization instruments. The experimental astrophysical $S$ factor of $^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})$ calculated from the present data was fitted using the $R$-matrix formalism. The results are in disagreement with previous experimental measurements in the same energy range but the extrapolated $S$ factor agrees with the potential model calculation and lower energy experimental data.

The Trojan Horse Method is an indirect method to measure reaction cross sections at energies of interest for nuclear astrophysics, exploiting the nuclei clustering properties. Here it is presented with its general features and detailed for the case of the ^22H(d,p)^33H and ^22H(d,n)^33He measurements, where interesting results for astrophysics and energy fusion power plants have been obtained.

Among the indirect methods to determine nuclear cross-section present in literature, the so-called Asymptotic Normalization Coefficient (ANC) has proven to be useful in retrieving the direct part of a radiative capture cross-section in reactions of interest for astrophysics. In this work, the method will be presented, and some results obtained in collaboration between NPI CAS and INFN-LNS will be presented.

A new study of the quasi-free contribution to the $$^3\hbox {He}+\,^9\hbox {Be}\rightarrow 3\alpha $$ reaction (Q value = 19.004 MeV) at low $${E}_{^3{{\mathrm{He}}}}$$ energy is presented. The reaction was studied in a kinematically complete experiment at beam energy of 4 MeV. To clarify the presence of the quasi-free mechanism, the $$^4{\hbox {He}}$$–$$^5\hbox {He}$$ momentum distribution of the $$^9\hbox {Be}$$ ground state was extracted. Standard tests were also carried out to confirm the presence of the quasi-free contribution and are reported in this work. The full width at half maximum of the $$^4\hbox {He}$$–$$^5\hbox {He}$$ inter-cluster momentum distribution inside $$^9\hbox {Be}$$ was measured with improved accuracy, by adopting several different approaches that all led to consistent results. These preliminary investigations on the reaction mechanism are fundamental for future studies employing the Trojan Horse Method, with the $$^5\hbox {He}$$ unbound nucleus as a virtual projectile.

Neutron induced reactions are fundamental for the nucleosynthesis of elements in the universe. Indeed, to correctly study the reactions involved in the well-known s-process in stars, which produce about half of the elements beyond the iron peak, it is mandatory to know the neutron abundance available in those stars. The 17O(n, a)14C reaction is one of the so-called “neutron poisons” for the pro- cess and it could play an important role in the balance of the neutron abundance. The reaction is therefore investigated in the energy range of astrophysical inter- est between 0 and 350 keV in the center of mass by applying the Trojan Horse Method to the three body reaction 2H(17O, a14C)H.

We present preliminary data of elastic scattering and inclusive breakup cross sections for the 7Li+ 119Sn reaction, recently measured at the Laboratori Nazionali del Sud (LNS-INFN) (Catania, Italy) at energies around the Coulomb barrier (E lab = 21.2 and 26.5 MeV). The experimental data have been analyzed under the Optical Model and Continuum-Discretized Coupled-Channels methods.

In the network of reactions present in the Big Bang nucleosynthesis, the 3He(n, p)3H has an important role which impacts the final 7Li abundance. The Trojan Horse Method (THM) has been applied to the 3He(d, pt)H reaction in order to extract the astrophysical S(E)-factor of the 3He(n, p)3H in the Gamow energy range. The experiment will be described in the present work together with the first preliminary results.

Abundance of 19F exceeds by far the predicted one. This problem represents one of the unanswered questions of stellar modelling. A source of large uncertainties at relevant energies are the 19F(p, α)16O and 19F(α, p)22Ne reactions. Although the lowest energy point from direct experiments are at about ∼660 keV, the astrophysical relevant energy region is only known by R-Matrix calculations. In this work we apply the Trojan Horse Method (THM) to the appropriate quasi-free three-body reactions. The THM application allowed us to study the sub-Coulomb energy region and to get the corresponding S(E)-factor values, thus allowing for a detailed evaluation of its astrophysical impact.

The detection of the neutrinos produced in the p − p chain and in the CNO cycle can be used to test the Standard Solar Model. The 3He( α , γ )7Be reaction is the first reaction of the 2nd and 3rd branch of the p − p chain, therefore, the uncertainty of its cross section sensitively influences the prediction of the 7Be and 8B neutrino fluxes. Despite its importance and the large number of experimental and theoretical works devoted to this reaction, the knowledge on the reaction cross section at energies characterizing the core of the Sun (15 keV - 30 keV) is limited and further experimental efforts are needed to reach the desired (≈ 3%) accuracy. The precise knowledge on the external capture contribution to the 3He( α , γ )7Be reaction cross section is crucial for the theoretical description of the reaction mechanism. In the present work the indirect measurement of this external capture contribution using the Asymptotic Normalization Coefficient (ANC) technique is reported. To extract the ANC, the angular distributions of deuterons emitted in the 6Li(3He,d)7Be α-transfer reaction were measured with high precision at E H 3 e = 3.0 MeV and E H 3 e = 5.0 MeV. The ANCs were then extracted from comparison of DWBA calculations to the measured data and the zero energy astrophysical S-factor for 3He( α , γ )7Be reaction was found to be 0.534 ± 0.025 keVb.

The use of the Trojan Horse Method (THM) appears as one of the most suitable tools for investigating nuclear processes of interest for astrophysics. THM has been demonstrated to be useful for exploring different nuclear reactions intervening both in stellar and primordial nucleosynthesis as well. Some recent results will be here discussed together with a brief discussion of the fundamental theoretical description. General details about the recently studied 7Be(n,α)4He reaction will be given.

The spectroscopy of F is of interest for nuclear astrophysics and nuclear structure. In these proceedings we will focus on the astrophysical implications and on the perspectives of the use of elastic scattering for the investigation of reactions of astrophysical importance. In astrophysics, fluorine and the reactions producing and destroying it play a key role in constraining models of stars in different evolutionary stages, such as the asymptotic giant branch (AGB) stars, responsible of the production of about half of the elements heavier than Fe. Indeed, s-nuclei are produced and brought to the surface thanks to mixing phenomena, together with fluorine that is produced in the same region from the same neutron source. Since the last stage in fluorine nucleosynthesis is the N(α, γ) F radiative capture, the study of the N + α elastic scattering may cast light on the fluorine synthesis. Also, F states are responsible of the appearance of resonances in the O(p,α) N reaction, leading to the production of N, later burnt to F in AGB stars through α-captures. Finally, the F spectroscopy may help constraining nuclear properties of the radioactive mirror nucleus Ne, whose states play a key role in novae modeling through the F(p,α) O reaction. In this work, the N - α elastic scattering is studied using the thick target inverse kinematics approach, allowing us to span a very large fluorine excitation energy range (∼ 6 - 10 MeV). A R-matrix analysis of the measured differential cross sections was also carried out, making it possible to determine the spin-parity and widths of a number of F states, including some previously not reported in the literature.

The Trojan Horse Method is applied to the investigation of the18F(p,α)15O reaction, by extracting the quasi free contribution to the2H(18F,α15O)nprocess. For the first time the method is applied to a reaction of astrophysical importance involving a radioactive nucleus. After investigating the reaction mechanism populating the a +15O + n exit channel, we could extract the18F(p,α)15O cross section and calculate the astrophysical factor over the 0 – 1 MeV energy interval. The possibility of exploring the cross section with no need of extrapolation allowed us to to point out the possible occurrence of a 7/2+state at 126 keV, which would strongly influence the trend of the astrophysical factor at the energies of astrophysical interest. However, the low energy resolution prevents us to draw definite conclusions. Possible astrophysical consequences are also discussed, motivating further work on this reaction.

We discuss experimentally and theoretically neutron production from the laser driven explosion of gas clusters prepared near the liquid-gas critical point. We let deuterated methane that was prepared very close to its critical temperature and pressure expand through a conical nozzle to create clusters, and then irradiated those clusters with a high intensity pulse from the Texas Petawatt Laser. After ionization, the clusters explode producing energetic ions, some of which fuse with resultant neutron emission. We show that the critical fluctuations present in the nozzle before the expansion influence the dynamics of neutron production. Neutron production near the critical point follows a power law, which is a signature of a second order phase transition and it is consistent with the Fisher model. This result might be relevant for energy production from fusion reactions.

We discuss how the new measurement of the $^{12}C+^{12}C$ fusion cross section carried out with the Trojan Horse Method (Tumino, A., Spitaleri, C., La Cognata, M., et al., 2018, Nature 57, 687) affects the compactness of a star, i.e. basically the binding energy of the inner mantle, at the onset of the core collapse. In particular, we find that this new cross section significantly changes the dependence of the compactness on the initial mass with respect to previous findings obtained in Chieffi & Limongi 2020 (ApJ 890, 43) by adopting the classical cross section provided by Caughlan, G.R., and Fowler, W.D. 1988 (At. Data Nucl. Data Tables 40, 283). A non monotonic but well defined behavior is confirmed also in this case and no scatter of the compactness around the main trend is found. Such an occurrence could impact the possible explodability of the stars.

The Trojan Horse Method represents an indirect approach to investigate reactions of astrophysical relevance at the energies of interest, free of Coulomb suppression and electron screening effects. In this review, we will examine how the Trojan Horse Method has evolved from the study of the quasi-free reaction mechanism. We will first present the basic features of the quasi-free reaction mechanism in the framework of the theory of direct reactions, from quasi-free scattering to quasi-free reactions processes, and its evolution towards the Trojan Horse Method with its modern theory. We will review the validity tests to assess the technique, the procedure to analyze the data and to extract the astrophysical factor. Finally, we will discuss some of the most important experimental results recently published related to nuclear astrophysics and applications.

Compton γ -ray sources have been in operation for over 30 years with new facilities being under construction or proposed. The gamma beam system under implementation at the Extreme Light Infrastructure - Nuclear Physics facility in Romania will deliver brilliant γ -ray beams with energies up to 19.5 MeV. Several instruments for measuring the parameters of the γ -ray beam are under development at ELI-NP. One of these instruments based on a High Purity Germanium detector is routinely used for beam energy measurements at other facilities. Here we investigate the use of a High Purity Germanium detector to continuously monitor the intensity of the ELI-NP gamma beam by measuring the inelastic scattering of photons. This method relies on both experimental and simulated data and it has been successfully tested during a recent experiment at the High Intensity γ -ray Source facility.

In AGB environment, Fluorine and Sodium production and destruction pathways are still not completely understood: their abundances are therefore still matter of debate. \(^{19}\mathrm {F}\) (only stable isotope of fluorine) abundance is strongly related to standard and extra-mixing processestype typical of the interior AGB-stars. Furthermore, the destruction channels for this element are far from being well understood. About \(^{23}\)Na, its presence in Globular Clusters along with the well-known anticorrelation with oxygen, underline that this element has been produced in previous generations of stars: in particular, intermediate-mass AGB stars are one of the possible candidates for its production. For this reason we studied the \(^{19}\mathrm {F}\)(\(\alpha \),p)\(^{22}\mathrm {Ne}\) and \(^{23}\mathrm{Na}(\mathrm{p},\alpha )^{20}\)Ne reactions in the energy range of relevance for astrophysics via the Trojan Horse Method (THM), using the three-body reactions \(^{6}\mathrm {Li}\)(\(^{19}\mathrm {F}\), p\(^{22}\mathrm {Ne}\))d and \(^{23}\mathrm {Na}\) (d, pn)\(^{20}\mathrm {Ne}\).

Owing the presence of the Coulomb barrier at astrophysically relevant kinetic energies, it is very difficult, or sometimes impossible to measure astrophysical reaction rates in laboratory. To overcome the problems related to the use of extrapolation procedure, the Trojan Horse Method (THM) has been applied extensively for the last 25 years to measure nuclear reaction cross sections of astrophysical interest. Although it has been mainly applied for charged particle-induced reactions, recently the THM has been found to have also a relevant role for neutron-induced ones. Here, the basic principle and a review of the main application of the Trojan Horse Method are presented, following a step-by-step description of the results concerning the study of the 17O(n,α)14C reaction.

The \(^{19}\)F(p,\(\alpha \))\(^{16}\)O reaction is an important channel of fluorine destruction in H-rich environments as the outer layers of Asymptotic Giant Branch (AGB) stars. Measurements of the \(^{19}\)F(p,\(\alpha _0\))\(^{16}\)O reaction via the Trojan Horse Method (THM) have shown the presence of resonant structures not observed before. As a consequence, the reaction rate at astrophysical temperatures (about \(10^{7}\)–\(10^{8}\) K) exceeds up to a factor 1.7 the one previously adopted. Here we present the result of an experiment in which THM was used to extract the Quasi-Free (QF) contribution of the \(^{2}\)H(\(^{19}\)F,\(\alpha \) \(^{16}\)O)n reaction to the \(^{19}\)F(p,\(\alpha _1\))\(^{16}\)O channel, corresponding to the population of the first excited state of the \(^{16}\)O. Three resonances in the E\(_{cm}\) energy region below about 500 keV have been observed. This result hints to an enhancement of the \(^{19}\)F(p,\(\alpha \))\(^{16}\)O destruction rate, with respect to what presently predicted.

In the framework of the experimental campaign of the ($ p,\alpha$) and ($ n,\alpha$) reactions cross sections measurement involving the 10, 11B isotopes, different ($ n,\alpha$) cross section measurements have been performed at ultra-low energy. In this work, the 10B(n,$ \alpha$)7Li reaction was investigated through the Trojan Horse Method, by means of the Quasi-Free (QF) 2H(10B,$ \alpha^{7}$Li)1H reaction at 30 MeV of beam energy. As in the standard THM approach, the measurement has been performed in inverse kinematics using a 10B beam. The excitation function of the 10B(n,$ \alpha$)7Li reaction has been measured at a center-of-mass energy between 0 and 700 keV. The data were compared with the existing experimental ones. Even if the energy resolution of the present experiment did not allow a separation between the channels ($ n,\alpha_0$) and ($ n,\alpha_1$) the low energy cross section and the angular distribution are presented, pointing out once more the ability of the method in studying neutron induced reactions using deuteron as source of virtual neutrons.

We present the progress in the measurements of the nuclear reaction rates for \(^{6,7}\)Li, \(^9\)Be and \(^{10}\)B (p,\(\alpha \)) burning channels derived using the Trojan Horse Method (THM). The effects on the predicted stellar surface abundances of such elements in pre-main sequence stars are evaluated using the Pisa up-to-date stellar evolutionary code. The present analysis is restricted to the pre-MS evolution of low-mass stars.

We performed indirect measurements of the neutron-induced reactions \(^{7}\)Be(n,p)\(^{7}\)Li and \(^{7}\)Be(n,\(\mathsf \alpha \))\(^{4}\)He simultaneously by the Trojan Horse method relevant to the cosmological \(^7\)Li problem. Preliminary excitation functions for \((n,p_0)\) and \((n,\alpha )\) are basically consistent with the previous studies, and new information about the \((n,p_1)\) contribution suggests possible enhancement of the total reaction rate.

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., This work has been partially supported by the Italian Ministry of the University under grant RBFR082838 and "LNS-Astrofisica Nucleare (fondi premiali)." J.M. and G.D'A. acknowledge MEYS, under the project SPIRAL2-CZ, EF16-013/0001679. C.A.B. acknowledges support from the U.S. NSF grant No 1415656 and the U.S. DOE grant No. DE-FG02-08ER41533. S.H. acknowledges "JSPS KAKENHI (grant No. 15K17631)."

The cosmologically relevant \(^7\)Be(n,\(\alpha \))\(^4\)He has been matter of recent studies aimed at contributing to the long-standing Li-problem. Here a brief description of the twin THM investigations will be shown and the main results discussed.