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Holmium 163 offers perhaps the best chance to determine the neutrino mass byelectron capture. This contribution treats the electron capture in 163 Holmiumcompletely relativistic for the overlap and exchange corrections and thedescription of the bolometer Spectrum. The theoretical expressions are derivedassuming single Slater determinants for the initial Ho and the final Dy Atoms.Electron capture is proportional to the probability to find the capturedelectron in the parent atom at the nucleus. Non-relativistically this is onlypossible for ns(1/2) electron states. Relativistically also p(1/2) electronshave a probability due to the lower part of the relativistic electron spinor,which does not disappear at the origin. Moreover relativistic effects increaseby contraction the electron probability at the nucleus. Capture from otherstates are suppressed. However they can be allowed with smaller intensity dueto finite nuclear size. The purpose of this work is to give a consistentrelativistic formulation and treatment of the overlap and exchange correctionsfor electron capture in 163 Ho to excited atomic states in 163 Dy and to showthe influence of the different configurations in the final Dy states. Theoverlap and exchange corrections are essential for the calorimetric spectrum ofthe deexcitation of the hole states in Dysprosium. The slope of the upper endof the spectrum, which contains the information on the electron neutrino mass,is different. In addition the effect of the finite energy resolution on thespectrum and on the determination of the neutrino mass is studied.

Electron Capture in 163Ho and Overlap plus Exchange Corrections and the Neutrino Mass