  We present a bound on the imaginary part of the single helicity-flip
amplitude for spin 1/2-spin 1/2 scattering at small momentum transfer. The
variational method of Lagrange multipliers is employed to optimize the
single-flip amplitude using the values of the total cross section, the elastic
cross section and diffraction slope as equality constraints in addition to the
inequality constraints resulting from unitarity. Such bounds provide important
information related to the determination of polarization of a proton beam. In
the case of elastic proton collisions the analyzing power at small scattering
angles inside the Coulomb Nuclear Interference region offers a method of
measuring the polarization of a proton beam, the accuracy of the polarization
measurement depending on the single helicity-flip amplitude. The bound obtained
on the imaginary part of the single helicity-flip amplitude indicates that the
analyzing power for proton-proton collisions in the Coulomb nuclear
interference region should take positive nonzero values at high energies.
