Small angle scattering andX-ray transform in classical mechanics

We consider the Newton equation

((*))

for |j|≤2 and some α>1. We give estimates and asymptotics for scattering solutions and scattering data for the equation (*) for the case of small angle scattering. We show that scattering data at high energies uniquely determine theX-ray transformsPF andPv. Applying results on inversion of theX-ray transformP we obtain that ford≥2 scattering data at high energies uniquely determineF andv. For the case of potentials with compact support we give a connection between boundary value data and scattering data and ford≥2 we obtain, using known results, a uniqueness theorem in the inverse scattering problem at fixed energy.