Taking into account the different forms of the Coulomb-hadron interference phase and the possible spin-flip contribution the new analysis of the experimental data of the proton-antiproton elastic scattering at 3.8 < p L < 6.0 GeV/c and small momentum transfer is carried out. It is shown that the size of the spin-flip amplitude can be determined from the form of the differential cross sections at small t, and the deviation of ρ(s, t) obtained from the examined experimental data of the pp scattering from the analysis [1], based on the dispersion relations, is conserved in all examined assumptions. The analysis of the proton-proton elastic scattering at 9 < p L < 70 GeV/c also shows the impact of the examined effects on the form of the differential cross sections.