  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.
