Bounds are obtained on near-forward scattering amplitudes that violate the Pomeranchuk theorem. It is proved that these amplitudes have zeros in $C^{\prime }<\left|t\right|\mathrm{}{\ln }^{2}s<\mathrm{}{C}^{\prime \prime }$. Experimental consequences are estimated, including phases of near-forward amplitudes, growth of the forward peak and shrinkage of its width, and possible oscillations. A narrow peak in the Coulomb region cannot be excluded and may invalidate experimental estimates of total cross sections.

• Received 20 August 1970

DOI:https://doi.org/10.1103/PhysRevD.3.2286