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Theory of the Trojan-Horse Method

The Trojan-Horse method is an indirect approach to determine the energy dependence of S-factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two-body and three-body cross sections becomes very transparent. The appearing Trojan-Horse integrals are studied in detail.