  An unified systematic of elastic (anti)proton-proton scattering data is
proposed based on a simple expression for the process amplitude - f(q)=A[(\pi
dq)/sh(\pi dq)][i J_1(Rq)/(Rq)+\rho J_0(Rq)]. The parameters R and d are
obtained at a fitting of (anti)proton-proton experimental data on differential
cross sections from Plab=1 GeV/c up to ISR energies. The fitting gives
extra-ordinary good results, \chi^2/NoF ~ 1 of below at |t|< 1.75 (GeV/c)^2. An
extrapolation of the parameter's energy dependencies to the LHC energies allows
excellent description of the Totem data up to the second diffraction maximum.
Predictions for other LHC energies are presented also. The amplitude provides
one with parameterizations of total and elastic cross sections. Its impact
parameter representation corresponds to the 2-dimensional Fermi-function -
1/[1+exp((b-R)/d)], which is very useful for Glauber calculations of
nucleus-nucleus cross sections at super high energies. It is shown for the
first time that experimental high |t| elastic scattering has a weak energy
dependency. This allows to describe high |t| tail of the Totem data.
