  In the framework of the model, where the scattering amplitude is determined
by the first and second moments of the GPDs, the qualitative description of all
existing experimental data at $\sqrt{s} \geq 52.8 $ GeV, including the Coulomb
range and large momentum transfers, is obtained with only 4 free parameters.
The spin-flip amplitude of the nucleon-nucleon elastic scattering is determined
taking into account the spin-dependence part of the second moment of the
generalized parton distributions (GPDs) with a new set of $t $-dependence.
  The corresponding value of the % analyzing power $A_N$ for the $pp$ at high
energy (RHIC) elastic scattering is obtained.
