The Trojan Horse Method: A Nuclear Physics Tool for Astrophysics

Abstract

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. Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 71 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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

“…In this formalism, a is referred to as the Trojan Horse (TH) nucleus, the x cluster is called the participant, while s is called the spectator. Indeed, under the QF kinematic conditions, the momentum transfer to the cluster s is negligible acting as a spectator of the interaction between x and A [9]. Since the break-up of the TH nucleus occurs in the nuclear field between a and A, one of the advantages of the method is that the two-body reaction is not hindered by any barrier effects, both Coulombian and centrifugal, or effected by the electron screening [9].…”

Horizons: Nuclear Astrophysics in the 2020s and Beyond

“…or compact coincidence detection configurations at TUNL's LENA [111]. In addition, indirect experimental methods such as the Trojan Horse Method or those used to extract Asymptotic Normalization Coefficients have been developed, enabling the determination of reaction rates that are too low for direct measurements [112,113,114]. In addition, the prediction of reaction rates by ab initio many-body theory (or "from first principles") has made remarkable progress [115,116]), and the calculation of reactions beyond the lightest nuclei has now become feasible, e.g., for α-capture reactions [117] and nucleon scattering [118,119].…”

“…While direct measurements of neutron capture on very shortlived nuclides are presently not feasible, multiple indirect experimental techniques and advances in nuclear-reaction theory make it possible to obtain constraints for important reaction rates (Fig. 3): β-delayed neutron emission [244,245], the β-Oslo [246,247] and inverse-Oslo [248] methods, transfer reactions [249,250,251], the surrogate reaction method [252,253,254], and the Trojan Horse Method [114] offer pathways to study neutron-capture reactions on short-lived isotopes. In addition, measurements of evaporation spectra at stable-beam facilities [255] provide complementary information for nuclei just off stability, e.g., for those relevant to i-process nucleosynthesis.…”

“…SeGA, GRETINA (and GRETA in the future), and Gammasphere) [412,413,414,374,375,415], γ-particle coincidence techniques (e.g. GODDESS) [416,417], the Trojan Horse reaction Method [114], the Asymptotic Normalization Coefficient method [418], elastic scattering [419,420], constraints on statistical nuclear properties (e.g. with ( 3 He, n) neutron time-of-flight measurements at Ohio University and the University of Notre Dame) [421,422], as well as chargedparticle spectroscopy with high-resolution charged particle detector arrays [423,424] and the recently refurbished Split-Pole spectrographs at TUNL [425,426], Florida State University [427], and University of Notre Dame [428].…”

Trojan Horse Method for n-induced reaction investigations at astrophysical energies

“…Their interest ranges from the primordial nucleosynthesis up to the "stellar cauldrons" where neutron capture reactions could take place via the s-or the r-processes. In the last years, several efforts have been made to investigate neutron induced reactions via the indirect technique of the Trojan Horse Method (THM) [1,2] by using the deuteron as a source of virtual neutrons [3] thus overcoming practical difficulties typical of direct measurements. The main idea of the THM is to extract the cross section of the binary reaction of interest for astrophysics…”