  An empirical model for the $pp$ elastic differential cross section is
proposed. Inspired by early work by Barger and Phillips, we parametrize the
scattering amplitude in building blocks, comprising of two exponentials with a
relative phase, supplementing the dominant term at small $-t$ with the proton
form factor. This model suitably applies to LHC7 and ISR data, enabling to make
simple predictions for higher LHC energies and to check whether asymptotia
might be achieved.
