Quasi-eikonal and quasi-U-matrix unitarization schemes beyond the Black Disk Limit

Quasi-eikonal and quasi-U-matrix unitarization of the standard Regge-pole amplitude for $\alpha (0)>1$ have been considered. We show that some violation of unitarity even at high energy exists in both models. We have found in quasi-eikonal model a bump-oscillation structure of $\mathrm{I}\mathrm{m}H(s,b)$ at large values of impact parameter $b$ but where $\mathrm{I}\mathrm{m}H(s,b)$ is closed to the maximal value. We argue that it is possible to choose the parameter regulating deviation of generalized models from pure eikonal or U-matrix modes in order to restore unitarity.