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a b s t r a c tWe formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surfaceintegrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.

Carbon-carbon burning plays an important role in many stellar environments. Recently, Tumino et al. [Nature 557, 687 (2018)] reported a sharp rise of the astrophysical S factor for carbon-carbon fusion determined using the indirect Trojan Horse method. We demonstrate that the rise at low energies seen in the aforementioned work is an artefact of using an invalid plane-wave approximation that neglects the Coulomb interactions. Our analysis shows that such a rise disappears if the Coulomb (or Coulomb-nuclear) interactions in the initial and final states are included.

Utilizing the two-center convergent close-coupling method, we find a several order of magnitude enhancement in the formation of antihydrogen via antiproton scattering with positronium in an excited state over the ground state. The effect is greatest at the lowest energies considered, which encompass those achievable in experiment. This suggests a practical approach to creating neutral antimatter for testing its interaction with gravity and for spectroscopic measurements.

The Trojan Horse method is a powerful indirect technique that provides information to determine astrophysical factors for binary rearrangement processes x + A → b + B at astrophysically relevant energies by measuring the cross section for the Trojan Horse reaction a + A → y + b + B in quasi-free kinematics. We present the theory of the Trojan Horse method for resonant binary subreactions based on the half-off-energy-shell R matrix approach which takes into account the off-energy-shell effects and initial and final state interactions.

The two-centre convergent close-coupling method is used to calculate antihydrogen (H) formation via positronium (Ps) scattering on antiprotons (p) at near threshold energies. For excited Ps of energy ε, the 1/ε behavior of theH formation cross sections is valid strictly only at the respective threshold, as is the 1/ √ ε behaviour for Ps in the ground state. Simple equations are given for thē H(n ≤ 4) formation cross sections from Ps(n ≤ 3) from zero to around 0.1 eV above threshold. Some of the implications of usingp-Ps collisions to form antihydrogen in beams, and held in traps, are discussed.