Trojan Horse Method Research Articles

Indirect Measurement of the 3He(n,p)3H Reaction Cross Section at Big Bang Energies

Neutron-induced nuclear reactions play an important role in the Big Bang Nucleosynthesis. Their excitation functions are, from an experimental point of view, usually difficult to measure. Nevertheless, in the last decades, big efforts 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 3He(n,p)3H reaction after a detailed study of the 2H(3He,pt)H three-body process. Data extracted from the present measurement are compared with other published sets. The reaction rate is also calculated, and the impact on the Big Bang nucleosynthesis is examined in detail.

Asymptotic Normalization Coefficient Investigation of the 17O(d, p) Transfer for Astrophysical Application to the 17O(n, α)14C Reaction at Low Energies

Indirect methods have proven to be a complementary approach for extending our knowledge of nuclear structure and low-energy cross sections. Among these, the neutron-induced reaction cross sections appear to be of particular interest since their role both for unstable and stable beams. In view of this, we report here the combined study of the 17O(n, α)14C reaction accomplished by the Trojan Horse Method (THM) and the asymptotic normalization coefficient (ANC) method. The low-lying 8038, 8125, 8213, and 8282 keV resonances in 18O are studied, and their Γ n are derived. A comparison with recent direct data and recent THM experimental data is presented. The independent ANC investigation corroborates our previous THM results, confirms the consistence of the two indirect investigations, and shows new frontiers for neutron-induced reactions with radioactive ion beams. Moreover, we examined the impact of adopting the newly recommended 17O(n, α)14C reaction rate on asymptotic giant branch stars' nucleosynthesis. Our findings reveal significant variations (≳10%) in the production of the neutron-rich heavy isotopes sensitive to neutron density, underlining the neutron-poisoning effect of 17O on the s-process.

Determination of electron screening potential of 6Li(p, [formula omitted])3He reaction using Multi Layer Perceptron based neural network

Understanding nuclear reactions between light-charged nuclei in the sub-Coulomb energy region is crucial for several astrophysical processes. Accurate determination of the reaction cross-section within the astrophysically important Gamow range is challenging due to electron screening. Various methods, including polynomial fits, R-Matrix, and the indirect Trojan Horse Method (THM), have estimated electron screening energies that exceed the adiabatic limit. This study aims to derive the bare astrophysical S-factor for the reaction 6Li(p,α)3He and to extract electron screening energies using Multi-Layer Perceptron-based Artificial Neural Network (ANN) analysis. Experimental S-factors for 6Li(p,α)3He, obtained from the literature, are reanalyzed with the ANN algorithm to determine the energy-dependent S-factor. The bare astrophysical S-factor is calculated from data above 60 keV, where electron screening is negligible. The electron screening potential is then derived by comparing the shielded S-factor with the bare S-factor. The ANN-based analysis yields an electron screening potential of 220 eV, suggesting that ANN could be a viable tool for estimating electron screening potentials in light nuclei reactions.

Direct and Indirect Measurements of the 19F(p,α)16O Reaction at Astrophysical Energies Using the LHASA Detector and the Trojan Horse Method

Fluorine is one of the most interesting elements in nuclear astrophysics. Its abundance can provide important hints to constrain the stellar models since fluorine production and destruction are strictly connected to the physical conditions inside the stars. The 19F(p,α)16O reaction is one of the fluorine burning processes and the correction evaluation of its reaction rate is of pivotal importance to evaluate the fluorine abundance. Moreover, the 19F(p,α)16O reaction rate can have an impact for the production of calcium in the first-generation of Population III stars. Here, we present the AsFiN collaboration efforts to the study of the 19F(p,α)16O reaction by means of direct and indirect measurements. On the direct measurements side, an experimental campaign aimed to the measurement of the 19F(p,α0,π)16O reaction is ongoing, taking advantage of the new versatile arrays of silicon strip detectors, LHASA and ELISSA. Moreover, the Trojan Horse Method (THM) was used to determine the 19F(p,α0)16O reaction S(E)-factor in the energy range of astrophysical interest (Ecm≈ 0–1 MeV), showing, for the first time, the presence of resonant structures within the astrophysical energy range. THM has been also applied for the study of the 19F(p,απ)16O reaction; data analysis is ongoing.

Studying subthreshold resonance using the Trojan horse method

The Trojan horse method was employed to indirectly measure the bare-nucleus reaction cross-section and astrophysical S-factor of the 9Be(p,α)6Li reaction in the low-energy region, utilizing the three-body reaction 2H(9Be,α6Li)n. Comparing the two-body reaction data extracted from the Trojan horse method with that obtained through direct measurements, compatibility is observed in the energy region above approximately 100 keV. Additionally, the THM data successfully reproduces the expected low-energy resonance peak around 270 keV. The THM extraction of the astrophysical factor yields S(0) = 21.0 ± 0.8 MeV b, which surpasses the extrapolation obtained from direct measurements. The 9Be(p,α)6Li reaction channel exhibits a subthreshold resonance with a width of 25 keV, positioned approximately -23 keV below the threshold. However, the strong electron shielding effect near the zero energy position in direct measurements often masks the influence of the subthreshold resonance on the low-energy region. In contrast, the THM method allows us to neglect the electron shielding effect. The THM experimental data were subjected to fitting using the Breit-Wigner function and subsequently compared with directly measured data. Following a comprehensive comparative analysis, it was discerned that the S(0) value obtained through THM exceeded the extrapolated value derived from direct measurements. This disparity was primarily attributed to the influence of the subthreshold resonance.

Sub-Coulomb nuclear studies using Indirect Methods: Recent results with the Trojan Horse Method

Our knowledge on how stars evolve depends on understanding two key factors: energy production and chemical evolution. Both factors are determined by thermonuclear reactions. Unfortunately, directly measuring them in a laboratory can be challenging: often, the reaction cross section are too small or require radioactive targets that are impractical to work with. To overcome these challenges, indirect techniques have been developed. One such technique, the Trojan Horse Method, makes use of transfer reactions to determine cross sections of reactions relevant in stellar burning processes. Here we will explore the Trojan Horse Method in the relevant details, explaining how it is used in nuclear astrophysics and we will delve into examples of THM measurements.

Nuclear astrophysics studies with the Trojan Horse Method

Our understanding of how stars evolve relies on two critical factors: energy production and chemical evolution. These factors are influenced by thermonuclear reactions. However, directly measuring these reactions in a laboratory setting can be challenging due to small reaction cross sections or the need for radioactive targets that are impractical to handle. To overcome these challenges, scientists have developed indirect techniques. One such method is the Trojan Horse Method (THM), which utilizes transfer reactions to determine cross sections of reactions relevant to stellar burning processes. In this paper, we will delve into the features of the Trojan Horse Method, its application in nuclear astrophysics, and provide examples of THM measurements.

The 19F(p, α1,2) reaction studied via Trojan Horse Method in astrophysical range of interest

The complex reaction network connected to the 19F stellar abundance is very sensitive to the physical condition in stars. To overcome difficulties present in the direct measurements, mainly the very low cross section in the astrophysical energy range due to the Coulomb repulsion, an indirect measurement of the 19F(p, α) reaction, with the Trojan Horse Method (THM), was performed at INFN-LNS. While the method had been successfully used to study α0 channel, in the present analysis focus was given to the α1,2 channels, where better knowledge of the reaction rates at low energies is required, obtainable by employing the THM method.

Exploring the Trojan Horse Method for Nuclear Fusion Data

The Trojan Horse Method (THM) is an indirect technique which extracts a two-body cross-section of interest from a related three-body reaction. The need for the application of the THM for obtaining fusion data is outlined, with a focus on the 93Nb(n, γ)94Nb cross-section. The basic features of THM are explained, with a particular focus on the quasi-free (QF) kinematics and the resulting energy relations, which provide a way to link the spectator momentum to the interaction energy of interest. The QF kinematics are then applied to the 93Nb(d, pγ)94Nb reaction, with some experimental considerations being outlined. A follow-up measurement to validate the THM result using the High-Flux Accelerator Driven Neutron Facility (HF-ADNeF) is proposed.

Shedding light on 17O(n,α)14C reaction at astrophysical energies with Trojan Horse Method and Asymptotic Normalization Coefficient

Shedding light on ¹⁷O(n,α)¹⁴C reaction at astrophysical energies with Trojan Horse Method and Asymptotic Normalization Coefficient

Measurement of the 27Al(p, α)24Mg fusion reaction at astrophysical energies via the Trojan Horse Method

In astrophysics, the abundance of 26Al is essential for understanding nucleosynthesis in the Milky Way and Galactic core-collapse supernovae rates. Detection methods involve γ-ray lines and comparing 26Mg overabundance with the common Mg isotope in meteorites. Therefore, stable isotopes 27Al and 24Mg play a crucial role and the MgAl cycle affecting aluminum and magnesium production has to be carefully studied. Recent surveys reveal complexities in stellar populations whose understanding may also benefit from better constraining the closure of the MgAl cycle. The 27Al(p, α)24Mg fusion reaction, a key 27Al destruction channel, is central to these scenarios. Due to uncertainties, the Trojan Horse Method is applied, allowing high-precision spectroscopy on the compound nucleus 28Si. It reveals crucial fusion cross section information in the astrophysically relevant energy range. The indirect measurement by means of the 2H(27Al,α24Mg)n process made it possible to assess the contribution of the 84.3 keV resonance and to set upper limits on nearby resonances. This study evaluates the THM recommended rate’s impact on intermediate-mass asymptotic giant branch stars, showing a notable increase in surface aluminum abundance at lower masses due to fusion cross section modification, while 24Mg remains largely unaffected.

Investigating the Primordial Universe through nuclear physics

Big Bang Nucleosynthesis (BBN) requires several nuclear physics inputs and nuclear reaction rates. An up-to-date compilation of direct cross sections of is given, being these ones among the most uncertain bare-nucleus cross sections. A particular attention is devoted to recently indirectly measured cross-section which give important hints for the nuclear astrophysics community.In reality, a significant experimental effort has been made over the past 10 years to explore reactions important to the BBN and determine their astrophysical S(E)-factor using the Trojan Horse Method (THM). Then, numerical calculations are made in the relevant temperature ranges for BBN (0.01<T9 <10) to determine the reaction rates and the relative error for the four reactions of interest. The effects of these values on the calculated primordial abundances and isotopical composition for H, He, and Li were then assessed by using them as input physics for computations of primordial nucleosynthesis. Additionally, recent findings regarding the 7Be(n,alpha)4He reaction rate were taken into consideration. These were put up against estimates of primordial abundance derived from observation at various astrophysical places. Additionally, perspectives on reactions will be examined.

Shedding light on 17O(n,α)14C reaction at astrophysical energies with Trojan Horse Method and Asymptotic Normalization Coefficient

Indirect methods have been established in the past as a complementary way of increasing our knowledge about nuclear structure and low-energy cross section measurements. Among these, the neutron induced reaction cross sections appear to be of particular interest because of their role both for unstable and stable beams. In view of this, we report here the combined study of the 17O(n,α)14C reaction accomplished by the Trojan Horse Method (THM) and the Asymptotic Normalization Coefficient (ANC) method. The low lying resonances 8038, 8125, 8213, and 8282 keV in 18O are studied and Γn are derived. A comparison with direct data and recent THM experimental data is presented. The independent ANC investigation corroborates our previous THM results, confirms the consistence of the two indirect investigation and shows new frontiers also in view of neutron induced reactions with RIB’s.

Recent THM investigations on neutron induced reactions at astrophysical energies

Neutron induced reactions on stable and unstable nuclei play a significant role in the nucleosynthesis of the elements in the cosmos. In the last years, several efforts have been made to investigate the possibility of applying the Trojan Horse Method (THM) to neutron induced reactions mostly by using deuteron as “TH-nucleus”. Here, the main advantages of using THM will be given together with a more focused discussion on the recent 7Be(n,α)4He and the 14N(n,p)14C reactions.

Few-Body Reactions with the Trojan Horse Method

The Trojan Horse method (THM) is a well-established experimental technique to measure nuclear reactions of astrophysical interest avoiding the suppression of the Coulomb barrier affecting experimental direct measurements. In this paper it will describe some of the THM studies involving few-body system of interest for both nuclear physics and nuclear astrophysics, such as the sub-Coulomb proton-proton elastic scattering and the deuteron-deuteron fusion at energies of interest for primordial nucleosynthesis. Moreover, the role of the intercluster motion in nuclei used for THM measurement will be highlight for the discussed physics cases.

The 12C +16 O fusion reaction in carbon burning: Study at energies of astrophysical interest using the Trojan Horse Method

The carbon-burning process in massive stars mainly occurs via the 12C +12 C. However, at temperatures higher than 109K and considering the increased abundance of 16O produced during the later stages of the heliumburning,the 12C+16O fusion can also become relevant. Moreover, 12C+16O also plays a role in the scenario of explosive carbon burning. Thus, the astrophysical energy region of interest ranges from 3 to 7.2 MeV in the center-of-mass frame. However, the various measurements of the cross-section available in the literature stop around 4 MeV, making extrapolation necessary. To solve this uncertainty and corroborate direct measurement we applied the Trojan Horse Method to three-body processes 16O(14N, α24Mg)2H and 16O(14N, p27Al)2H to study the 12C(16O, α)24Mg and 12C(16O, p)27Al reactions in their entire energy region of astrophysical interest. In this contribution, after briefly describing the method used, the experiment and the preliminary phases of the data analysis will be presented and discussed.

Trojan Horse Method: A general introduction

Owing the presence of the Coulomb barrier at astrophysically relevant kinetic energies, it is very difficult, or sometimes impossible to measure astrophysical reaction cross sections in laboratories, especially for the presence of the electron screening effect. This is why different indirect techniques are being used along with direct measurements. The Trojan Horse Method (THM)is a unique indirect technique allowing one to measure astrophysical rearrangement reactions down to astrophysical relevant energies. The basic principle and a review of the main applications of the THM are presented.

Study of the 12C +16 O fusion reaction in carbon burning via the Trojan Horse Method

12C +12 C is the main reaction during core and shell carbon burning in massive stars, however, at temperatures higher than 109K when most of the carbon is depleted and its abundance is lower than 16O, the 12C +16 O fusion can also become relevant. Moreover, 12C +16 O reaction can ignite also in the scenario of explosive carbon burning. The astrophysical energy region of interest thus ranges from 3 to 7.2 MeV in the center-of-mass frame. There are various measurements of the cross-section available in the literature, however, they all stop around 4 MeV, making extrapolation necessary at lower energies. To try to solve this uncertainty and corroborate direct measurement the Trojan Horse Method was applied to three-body processes 16O(14N, α24Mg)2H and 16O(14N, p27Al)2H to study the 16O(12C, α)24Mg and 16O(12C, p)27Al reactions.

The long-standing connection of BBN and Indirect measurements: The 3He(n,p)3H reaction at Big Bang energies

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 which drives the elemental nucleosynthesis in the first twenty minutes 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 hard 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 3He(n,p)3H reaction after a detailed study of the 2H(3He,pt)H three–body process. The experiment was performed using the 3He beam, delivered at a total kinetic energy of 9 MeV by the Tandem at the Physics and Astronomy Department of the University of Notre Dame. Data extracted from the present measurement are compared with other published sets available in literature. Astrophysical applications will also be discussed in details.

A New Reaction Rate of the 27Al(p/α)24Mg Reaction Based on Indirect Measurements at Astrophysical Energies and Implications for 27Al Yields of Intermediate-mass Stars

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.