  The measurements of high energy \bar p p and pp elastic at ISR, SPS and
Tevatron colliders have provided usefull informations on the behavior of the
scattering amplitude. A large step in energy domain is accomplished with the
LHC collider presently running, giving a unique opportunity to improve our
knowledge on the asymptotic regime of the elastic scattering amplitude and to
verify the validity of our theoretical approach, to describe the total cross
section \sigma_{tot}(s), the total elastic cross section \sigma_{el}(s), the
ratio of the real to imaginary parts of the forward amplitude \rho(s) and the
differential cross section d\sigma (s,t)/dt.
