pp scattering in t and b spaces

We propose analytical forms, in both momentum transfer and impact parameter spaces, for the amplitudes of elastic pp scattering, giving coherent and accurate description of the observables at all energies $\sqrt{s}\geq 20$ GeV. The real and imaginary parts are separately identified through their roles at small and large t values. The study of the differential cross sections in b-space leads to the understanding of the effective interaction ranges contributing to elastic and inelastic processes.