Determination of the neutrino mass in 163 Ho

KATRIN plans to determine the electron anti-neutrino mass in the Tritium decay. Electron capture in 163 Ho can measure the electron neutrino mass supported by the small decay energy \({\rm{Q}}=2.8{\text{keV}}_{67}^{163}{\text{Holmium}}+{\text{electron}}{\to }_{66}^{163}{\text{Dysprosium}}+{\nu }.\) The decay energy of 2.8 keV is used to emit a neutrino and to excite the Dy atom. The neutrino mass is then given by the difference between the Q value and the upper end of the Dy deexcitation spectrum. The Dirac-Hartree-Fock approach is used for the bound and the continuum states in Holmium and in Dysprosium. The present background must be reduced by at least two orders to extract the neutrino mass from the spectrum. The present work discuses the one- and the two-hole excitations in Dy. The two-hole states are excited by shake-up of an electron into a free bound state and the shake-off into the continuum. The shake-off contribution can practically be neglected. It seems not to influence the neutrino mass determination.