On the momentum transfer dependence of the phase in elastic scattering

The question is discussed: to what extent the often assumed independence of the phase of the elastic scattering amplitude from the momentum transfer \textit{in the region of only small values} of $t$ limits $t$-dependence of the phase generally. Analyticity allows to give a proof that if the phase of a strong interaction scattering amplitude is independent on the transferred momentum $t$ at small values of $t$ then it does so in all physical region. Moreover, if such an independence holds in any physical energy $\sqrt{s}$ region including the values infinitesimally close to the first inelastic threshold from below the whole scattering amplitude vanishes. Relationship of the $t$-dependence of the phase with the size of the interaction range is also discussed.