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 p
arts 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.
