  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.
