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

Holmium 163 offers perhaps the best chance to determine the neutrino mass by electron capture. This contribution treats the electron capture in 163 Holmium completely relativistic for the overlap and exchange corrections and the description of the bolometer Spectrum. The theoretical expressions are derived assuming single Slater determinants for the initial Ho and the final Dy Atoms. Electron capture is proportional to the probability to find the captured electron in the parent atom at the nucleus. Non-relativistically this is only possible for ns(1/2) electron states. Relativistically also p(1/2) electrons have a probability due to the lower part of the relativistic electron spinor, which does not disappear at the origin. Moreover relativistic effects increase by contraction the electron probability at the nucleus. Capture from other states are suppressed. However they can be allowed with smaller intensity due to finite nuclear size. The purpose of this work is to give a consistent relativistic formulation and treatment of the overlap and exchange corrections for electron capture in 163 Ho to excited atomic states in 163 Dy and to show the influence of the different configurations in the final Dy states. The overlap and exchange corrections are essential for the calorimetric spectrum of the deexcitation of the hole states in Dysprosium. The slope of the upper end of the spectrum, which contains the information on the electron neutrino mass, is different. In addition the effect of the finite energy resolution on the spectrum and on the determination of the neutrino mass is studied.