  Using previously described functional techniques for some non--perturbative,
gauge invariant, renormalized QCD processes, a simplified version of the
amplitudes --- in which forms akin to Pomerons naturally appear --- provides
fits to ISR and LHC--TOTEM $pp$ elastic scattering data. Those amplitudes rely
on a specific function $\varphi (\vec b)$ which describes the fluctuations of
the transverse position of quarks inside hadrons.
