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This note is motivated by preparations of a new $ep$ elastic scatteringexperiment in the low transfer momentum region to be carried out in the 720 MeVelectron beam of the Mainz Microtron MAMI. This experiment will use aninnovative method allowing for detection of recoil protons in coincidence withthe scattered electrons. The goal is to measure the $ep$ differential crosssections in the $Q^2$ range from 0.001 GeV$^2$ to 0.04 GeV$^2$ and to determinethe proton charge radius with sub-percent precision.

Proton radius reconstruction from simulated electron-proton elastic scattering cross sections at low transfer momenta