Nuclear reactions within stars typically occur at energies significantly below 1 MeV. Consequently, the Coulomb barrier exponentially suppresses the cross section, reducing it to values as small as a few nanobarns for charged particles. This challenge in obtaining accurate input data for astrophysics has led to the introduction of indirect methods. Specifically, techniques such as ANC and THM have been employed to derive cross sections for reactions involving photons and charged particles in the exit channel, respectively, eliminating the need for extrapolation. The discussion delves into recent results from the application of these methods. For instance, the 6Li(3He,d)7Be measurement is utilized to deduce the ANC’s of the 3He+4He→ 7Be and p+6Li→ 7Be channels, along with their corresponding radiative-capture cross sections. Additionally, the THM measurement of the 27Al(p, α)24Mg cross section via the 2H(27Al,α 24Mg)n reaction is highlighted. In both cases, the cross section at astrophysical energies has been established with unprecedented accuracy.

In my presentation, I will discuss the use of transfer reactions as an indirect method of determining information important for nuclear astrophysics. Specifically, I will focus on peripheral reactions and their analysis with the Asymptotic Normalization Coefficients (ANC) method. I will present results from related experiments that have been conducted at the Cyclotron Institute, Texas A&M University with focus on the 0ptical Model Parameters obtained and the need for reliable calculations. Additionally, I will describe the im- provements in the measured data that we obtained after upgrading the detection system used.

It is well known that measuring cross-sections of thermonuclear reactions at the low energies typical of astrophysical sites is very difficult. This is due to the presence of the Coulomb barrier between the interacting nuclei. For non-explosive scenarios at astrophysical sites, the relevant energies typically span from few tens to few hundreds of keV while the Coulomb barrier is in the order of MeV. The fusion processes then proceed via tunnel effect and their cross-sections are strongly depending on the probability of penetration through the barrier. In a first approximation, this probability is given by the Gamow factor. Owing to the exponential decrease in this factor with energy, the cross-section values of thermonuclear fusion processes in stellar systems often reach values as small as micro- and nanobarn and even lower ones. Neutron-induced reactions, in spite of the absence of Coulomb barrier, are also difficult to measure. Indeed, it is the possible presence of a centrifugal barrier that can hinder the measurement of the values of the cross-sections of these processes. In either cases the cross-sections of astrophysical nuclear processes result in experimental difficulties, due to the low signal-to-noise ratio, that have been a challenge for scientists since the setting of this scientific field: Nuclear Astrophysics. In the last two to three decades, experimental improvements, including the construction of underground laboratories, allowed for the first time the measurement of cross-sections of astrophysical nuclear processes in the relevant energy region for astrophysics. Also, indirect methods were developed. As a general and common feature, using these methods it is possible to relate the features --typically the cross-section-- of a process that is experimentally simpler to measure, although not directly linked to astrophysics, to those of another process that is of interest for this latter field. This didactic paper will briefly describe some of these indirect methods with a special emphasis on Trojan Horse and on its application also to reactions that involve the use of radioactive ion beams and to neutron-induced reactions.

In the house of Trojan Horse Method (THM), I will say a few words about “other” indirect methods we use in Nuclear Physics for Astrophysics. In particular those using Rare Ion Beams that can be used to evaluate radiative proton capture reactions. I add words about work done with the Professore we celebrate today. With a proposal, and some results with TECSA, for a simple method to produce and use isomeric beam of 26m Al.

We discuss recent developments in indirect methods used in nuclear astrophysics to determine the capture cross sections and subsequent rates of various stellar burning processes, when it is difficult to perform the corresponding direct measurements. We discuss in brief, the basic concepts of Asymptotic Normalization Coefficients, the Trojan Horse Method, the Coulomb Dissociation Method, (d,p), and charge-exchange reactions.

In this book a collection of the lecture notes given during the Eighth European Summer School on Experimental Nuclear Astrophysics is given. The school, whose first edition was first held in 2003, took place from 13 to 20 of September 2015 in Santa Tecla, a small village about 15 km north of Catania, characterized by its position on the volcanic shores of the Ionian Sea, surrounded by the spectacular "Timpa" area, a green protected park specific for its mediterranean vegetation. 80 young students and researchers from more than 20 countries attended the lectures and were also encouraged to present their work and results.

The ground state of the proton-rich nucleus 23Al has been studied by one-proton removal on a carbon target at about 50 MeV/nucleon using the EXOGAM + SPEG experimental setup at GANIL. Longitudinal momentum distributions of the 22Mg breakup fragments, inclusive and in coincidence with gamma rays de-exciting the residues, were measured. The ground-state structure of 23Al is found to be a configuration mixing of a d-orbital valence proton coupled to four core states - 0$^{+}_{gs}$, 2$^{+}_{1}$, 4$^{+}_{1}$, 4$^{+}_{2}$. We confirm the ground state spin and parity of 23Al as $J^{\pi} = 5/2^{+}$. The measured exclusive momentum distributions are compared with extended Glauber model calculations to extract spectroscopic factors and asymptotic normalization coefficients (ANCs). The spectroscopic factors are presented in comparison with those obtained from large-scale shell model calculations. We determined the asymptotic normalization coefficient of the nuclear system $^{23}$Al$_{gs}$ $\rightarrow$ $^{22}$Mg(0$^{+}$) + p to be $C^{2}_{d_{5/2}}$($^{23}Al_{gs}$) = (3.90 $\pm$ 0.44) $\times$ 10$^{3}$ fm$^{-1}$, and used it to infer the stellar reaction rate of the direct radiative proton capture $^{22}$Mg(p,$\gamma$)$^{23}$Al. Astrophysical implications related to $^{22}$Na nucleosynthesis in ONe novae and the use of one-nucleon breakup at intermediate energies as an indirect method in nuclear astrophysics are discussed.

Difficulties in cross-section measurements at very low energies, when charged particles are involved, led to the development of some indirect methods. The Trojan horse method (THM) allows us to bypass the Coulomb effects and has been successfully applied to several reactions of astrophysical interest. A brief review of the THM applications is reported together with some of the most recent results.

Our understanding of stellar evolution depends on knowing beta-decay rates and reaction cross sections for a wide range of nuclear capture reactions. Direct laboratory measurements of important stellar reaction rates are hindered by low cross sections and, in some cases, the need for radioactive targets. Indirect techniques have been developed to determine reaction rates for systems that are particularly difficult to measure in a direct experiment. One of the indirect techniques involves measurements of Asymptotic Normalization Coefficients (ANCs) which determine the direct-capture contribution to a capture reaction. Also ANCs can be used to understand the role of subthreshold states in stellar capture. This essay gives an introduction to ANCs and describes how they are used in nuclear astrophysics. Examples are given of measurements which have been carried out with both stable and radioactive beams.

We discuss the use of one-nucleon breakup reactions of loosely bound nuclei at intermediate energies as an indirect method in nuclear astrophysics. These are peripheral processes, therefore we can extract asymptotic normalization coefficients (ANC) from which reaction rates of astrophysical interest can be inferred. To show the usefulness of the method, three different cases are discussed. In the first, existing experimental data for the breakup of 8B at energies from 30 to 1000 MeV/u and of 9C at 285 MeV/u on light through heavy targets are analyzed. Glauber model calculations in the eikonal approximation and in the optical limit using different effective interactions give consistent, though slightly different results, showing the limits of the precision of the method. The results lead to the astrophysical factor S_17(0)=18.7+/-1.9 eVb for the key reaction for solar neutrino production 7Be(p,\gamma)8B. It is consistent with the values from other indirect methods and most direct measurements, but one. Breakup reactions can be measured with radioactive beams as weak as a few particles per second, and therefore can be used for cases where no direct measurements or other indirect methods for nuclear astrophysics can be applied. We discuss a proposed use of the breakup of the proton drip line nucleus 23Al to obtain spectroscopic information and the stellar reaction rate for 22Mg(p,\gamma)23Al.

Breakup of loosely bound nuclei at intermediate energies as indirect method in nuclear astrophysics: 8B, 9C and the S17, S18 astrophysical factors