Bethe phase including proton excitations

We evaluate the contribution of inelastic intermediate states (such as $p\to N^*$ excitations) to the phase between the one-photon-exchange and the nuclear' high energy $pp$ scattering amplitudes as $t\to 0$, caused by multiphoton diagrams. It turns out to be rather small - much smaller than to have any influence on the experimental accuracy of the measurements of $\rho$, defined to be the ratio of the real to imaginary parts of the forward nuclear’ amplitude.