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We evaluate the possible deviation (from the conventional Cahn's result) ofthe phase between the one-photon-exchange and the `nuclear' high energy $pp$scattering amplitudes in a small $t\to 0$ region caused by a more complicated(not just $exp(Bt)$) behaviour of the nuclear amplitude. Furthermore we look atthe possible role of the $t$-dependence of the $\rho(t) \equiv$ Real/Imaginaryamplitude ratio. It turns out that both effects are rather small - much smallerthan to have any influence on the experimental accuracy of $\rho(t=0)$extracted from the elastic proton-proton scattering data.

Bethe phase variation due to a non-exponential nuclear amplitude and the  possibility of using a $t$-dependent phase to determine the $\rho$-parameter  from elastic scattering data