High-energy scattering by a superposition of two power potentials

For a superposition of two power potentials the scattering amplitude and the total cross section are evaluated making use of the high-energy formula derived byBlankenbecler andGoldberger. The scattering amplitude is expressed by a finite sum of impact-parameter pole contributions in analogy to Regge poles in the angular momentum plane. It is shown that each pole contribution can be expressed in terms of known functions. Furthermore the large momentum transfer asymptotics of an impact parameter pole is investigated in detail.