Abstract
This report presents a project of an experiment for precision studies of the elastic electron proton scattering in the low momentum transfer region. The project is based on an innovative experimental method which allows for detection of recoil protons in a hydrogen "active target". The goal of the experiment is to measure the $ep$ elastic scattering differential cross section in the $Q^2$ range from 0.001 GeV$^2$ to 0.04 GeV$^2$ with 0.1% relative and 0.2% absolute precision and to determine the proton charge radius with a sub-percent precision. The important advantages of the proposed experiment are low radiative corrections, inherent to the recoil proton method, and absolute measurements of the differential cross sections. The experiment will be performed in the 720 MeV electron beam of the Mainz electron accelerator MAMI. This accelerator can provide an electron beam with optimal for this experiment parameters. The Proposal was approved by the MAMI Program Advisory Committee, and a special Agreement aimed at realization of this experiment was signed between Petersburg Nuclear Physics Institute and Institute of Nuclear Physics of the Mainz University. Also, scientists from the following institutes will participate in this project: GSI Centre for Heavy Ion Research, Germany; Joint Institute for Nuclear Research, Russia; William and Mary College, USA; Mount Allison University, Canada; University of Regina, Canada; Saint Mary's University, Canada. The first measurements should be started in 2020.
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