Trojan Horse Particle Invariance: An Extensive Study

In the last decades, the Trojan Horse method (THM) has played a crucial role for the measurement of several particle (both neutron and charged one) induced cross sections for reactions of astrophysical interest. To better understand its cornerstones and its applications to physical cases, many tests were performed to verify all its properties and the possible future perspectives. The Trojan Horse nucleus invariance proves the relatively simple approach allowed by the pole approximation and sheds light in the involved reaction mechanisms. Here we shortly review the complete work for the binary 2H(d,p)3H, 6Li(d,α)4He, 6Li(p,α)3He, 7Li(p,α)4He reactions, by using the quasi free reactions after break-ups of different nuclides. Results are compared assuming the 6Li and 3He break-up in the case of the d(d,p)t, 6Li(d,α)4He reactions and considering the 2H and 3He break-up for 6Li(p,α)3He, 7Li(p,α)4He reactions. These results, regardless of the Trojan Horse particle or the break-up scheme, confirms the applicability of the standard description of the THM and suggests the independence of binary indirect cross section on the chosen Trojan Horse nuclei for a whole spectra of different cases. This gives a strong basis for the understanding of the quasi-free mechanism which is the foundation on which the THM lies

Measurement of sub threshold resonance contributions to fusion reactions: the case of the 13C(α, n)16O astrophysical neutron source

The 13C(α, n)16O reaction is the neutron source for the main component of the s-process. It is is active inside the helium-burning shell of asymptotic giant branch stars, at temperatures ≲ 108 K. In this temperature region, corresponding to an energy interval of 140 − 230 keV, the 13C(α, n)16O cross section is dominated by the −3 keV sub-threshold resonance due to the 6.356 MeV level in 17O. Direct measurements could not establish its contribution owing to the Coulomb barrier between interacting nuclei, strongly reducing the cross section at astrophysical energies. Similarly, indirect measurements and extrapolations yielded inconsistent results, calling for further investigations. The Trojan Horse Method was applied to the 13C(6Li, n16O)d quasi-free reaction to access the low as well as the negative energy region of the 13C(α, n)16O reaction. By using the generalized R-matrix approach, the asymptotic normalization coefficient (C̃17O(1/2+)α13C)2 of the 6.356 MeV level was deduced. For the first time, the Trojan Horse Method and the asymptotic normalization coefficient were used in synergy. Our indirect approach lead to (C̃17O(1/2+)α13C)2 = 7.7−1.5+1.6 fm−1, slightly larger than the values in the literature, determining a 13C(α, n)16O reaction rate slightly larger than the one in the literature at temperatures lower than 108 K, with enhanced accuracy

Overview on the Trojan Horse Method in nuclear astrophysics

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 givenDepartamento de Física Aplicad

The Treiman-Yang Criterion: validating the Trojan Horse Method by experimentally probing the reaction mechanism

Proper selection of the quasi-free (QF) break-up channel in a three-body reaction is a key aspect for the applicability of the Trojan Horse Method (THM). The Treiman-Yang (TY) Criterion is a model-independent experimental test for the dominance of the QF mechanism, and hence constitutes one of the strongest validity tests of the THM. An experiment was performed at LNS to apply the test to the d(10B, 7Be α)n reaction. Here, the criterion is described and some preliminary data from the experiment are shown

Measurement of the 13C(α, n)16O reaction at astrophysical energies using the Trojan Horse Method. Focus on the -3 keV sub-threshold resonance

Most of the nuclei in the mass range 90 ≲ A ≲ 208 are produced through the so-called s-process, namely through a series of neutron capture reactions on seed nuclei followed by β-decays. The 13C(α, n)16O reaction is the neutron source for the main component of the s-process. It is active inside the helium-burning shell of asymptotic giant branch stars, at temperatures ≲ 108 K, corresponding to an energy interval of 140 − 230 keV. In this region, the astrophysical S(E)-factor is dominated by the −3 keV sub-threshold resonance due to the 6.356 MeV level in 17O. Direct measurements could not soundly establish its contribution owing to the cross section suppression at astrophysical energies determined by the Coulomb barrier between interacting nuclei. Indirect measurements and extrapolations yielded inconsistent results, calling for further investigations. The Trojan Horse Method turns out to be very suited for the study of the 13C(α, n)16O reaction as it allows us to access the low as well as the negative energy re- gion, in particular in the case of resonance reactions. We have applied the Trojan HorseMethod to the 13C(6Li, n16O)d quasi-free reaction. By using the modified R-matrix approach, the asymptotic normalization coefficient (C˜α13 C17O(1/2+))2${\left( {\tilde C_{{\alpha ^{13}}{\rm{C}}}^{17{\rm{O(1/}}{{\rm{2}}^{\rm{ + }}}{\rm{)}}}} \right)^2}$ of the 6.356 MeV level has been deduced as well as the n-partial width, allowing to attain an unprecedented accuracy for the 13C(α, n)16O astrophysical factor. A preliminary analysis of a partial data set has lead to (C˜α13C17O(1/2+))2 = 6.7−0.6+0.9 fm−1,${\left( {\tilde C_{{\alpha ^{13}}{\rm{C}}}^{17{\rm{O(1/}}{{\rm{2}}^{\rm{ + }}}{\rm{)}}}} \right)^2}\, = \,6.7_{ - 0.6}^{ + 0.9}\,{\rm{f}}{{\rm{m}}^{ - 1}},$ slightly larger than the values in the literature, determining a 13C(α, n)16O reaction rate in agreement with the most results in the literature at ∼ 108 K, with enhanced accuracy thanks to this innovative approach

Neutron-Driven Nucleosynthesis in Stellar Plasma

A large uncertainty for the slow neutron capture nucleosynthesis (s-process) models is caused by the amount of neutrons available to the process itself. This quantity is strongly affected by the 13C(α,n)16O, and 22Ne(α,n)25Mg reaction cross sections, whose measurements at energies corresponding to the s-process thermal conditions (∼102 keV) are mainly hampered by the Coulomb barrier. For this reason, indirect approaches could offer a complementary way of investigation and, among these, the Trojan Horse Method (THM) has been applied to determine these cross sections overcoming the Coulomb barrier. With this approach, a low-energy binary reaction cross section can be obtained selecting the quasi-free contribution from a suitable three-body reaction cross section, taking advantage of the cluster structure of proper nuclei

Resonant C-Burning at Astrophysical Energies

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Low-energy d+d fusion via the Trojan Horse Method

The 2H(d,p)3H and 2H(d,n)3He reactions have been recently investigated from Edd=1.5 MeV down to 2 keV, by means of the Trojan Horse Method (THM) applied to the Quasi Free 3He+d interaction at 18 MeV [1]. The knowledge of their fusion cross section at low energies is of interest for pure and applied physics. Both reactions belong to the network of processes to fuel the first inertial confinement fusion reactors in the range of kT= 1 to 30 keV. These energies overlap with the burning temperatures of deuterium in the Pre-main sequence of stellar evolution. They are key processes in the Standard Big Bang Nucleosynthesis (SBBN), in an energy region from 50 to 300 keV and experimental data at least up to 1 MeV are required for an accurate calculation of the reaction rate. Providing experimental data for both channels from a single experiment and over the entire energy range of interest is crucial for an accurate calculation of the reaction rates. This is what has been obtained from the present Trojan Horse (TH) investigation with new reaction rates which deviate by more than 20% from available direct data. This represents also the first pioneering experiment in quasi free regime where the charged spectator is detected