  In the case of elastic high-energy hadron-hadron scattering, the impact of
the large-distance contributions on the behaviour of the slopes of the
spin-non-flip and of the spin-flip amplitudes is analysed. It is shown that the
long tail of the hadronic potential in impact parameter space leads to a value
of the slope of the reduced spin-flip amplitude larger than that of the
spin-non-flip amplitude. This effect is taken into account in the calculation
of the analysing power in proton-nucleus reactions at high energies. It is
shown that the preliminary measurement of AN obtained by the E950 Collaboration
indeed favour a spin-flip-amplitude with a large slope. Predictions for AN at
pL = 250 GeV/c are given.
