New analytic unitarization schemes

We consider two well-known classes of unitarization of Born amplitudes of hadron elastic scattering. The standard class, which saturates at the black-disk limit includes the standard eikonal representation, while the other class, which goes beyond the black-disk limit to reach the full unitarity circle, includes the U matrix. It is shown that the basic properties of these schemes are independent of the functional form used for the unitarization, and that U matrix and eikonal schemes can be extended to have similar properties. A common form of unitarization is proposed interpolating between both classes. The correspondence with different nonlinear equations are also briefly examined.