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Basic features of a new surface-integral formulation of scattering theory are outlined. This formulation is valid for both short-range and Coulombic longe-range interactions. New general definitions for the potential scattering amplitude are given. 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 amplitudes of breakup, direct and rearrangement scattering in a Coulombdoi:10.1088/1742-6596/194/1/012017 fatcat:zwvd52vsuza7tcihtvgyjvnrji