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Modeling of electron emission processes accompanying Radon-$α$-decays within electrostatic spectrometers

Electrostatic spectrometers utilized in high-resolution beta-spectroscopy studies such as in the Karlsruhe Tritium Neutrino (KATRIN) experiment have to operate with a background level of less than 10^(-2) counts per second. This limit can be exceeded by even a small number of Rn-219 or Rn-220 atoms being emanated into the volume and undergoing alpha-decay there. In this paper we present a detailed model of the underlying background-generating processes via electron emission by internal conversion, shake-off and relaxation processes in the atomic shells of the Po-215 and Po-216 daughters. The model yields electron energy spectra up to 400 keV and electron multiplicities of up to 20 which are compared to experimental data.