Soft Proton Scattering Efficiency Measurements on X-Ray Mirror Shells

In-orbit experience has shown that soft protons are funneled more efficiently through focusing Wolter-type optics of X-ray observatories than simulations predicted. These protons can degrade the performance of solid-state X-ray detectors and contribute to the instrumental background. Since laboratory measurements of the scattering process are rare, an experiment for grazing angles has been set up at the accelerator facility of the University of T\"ubingen. Systematic measurements at incidence angles ranging from 0.3{\deg} to 1.2{\deg} with proton energies around 250 keV, 500 keV, and 1 MeV have been carried out. Parts of spare mirror shells of the eROSITA (extended ROentgen Survey with an Imaging Telescope Array) instrument have been used as scattering targets. This publication comprises a detailed description of the setup, the calibration and normalization methods, and the scattering efficiency and energy loss results. A comparison of the results with a theoretical scattering description and with simulations is included as well.