Rational Form of Amplitude and Its Asymptotic Factorization

We provide arguments for the use of rational form unitarization, its relation with diffraction peak shrinkage and asymptotics inelastic cross-section. The particular problems Regge model exponential unitarization a factorized eikonal are discussed as well. A central role belongs to asymptotic amplitude factorization resulting from Mandelstam analyticity symmetry over scattering variables.