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

TL;DR

This paper investigates how deviations from simple models of nuclear scattering amplitudes and the $t$-dependence of the $ ho$-parameter affect phase measurements in high-energy elastic $pp$ scattering, finding these effects to be minimal.

Contribution

It introduces a detailed analysis of phase deviations caused by complex nuclear amplitude behaviors and $t$-dependence of $ ho$, showing these effects are negligible for current measurements.

Findings

Deviations from conventional phase models are very small.

The $t$-dependence of $ ho$ has minimal impact on phase determination.

Experimental accuracy in $ ho(t=0)$ extraction remains unaffected.

Abstract

We evaluate the possible deviation (from the conventional Cahn's result) of the 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 at the possible role of the $t$-dependence of the $\rho(t) \equiv$ Real/Imaginary amplitude ratio. It turns out that both effects are rather small - much smaller than to have any influence on the experimental accuracy of $\rho(t=0)$ extracted from the elastic proton-proton scattering data.