  The atomic pair 163 Holmium and 163 Dysprosium seems due to the small Q value
of about 2.3 to 2.8 keV the best case to determine the neutrino mass by
electron capture. The bolometer spectrum measures the full deexcitation energy
of Dysprosium by X rays, by Auger electrons and by the recoil of Holmium. The
spectrum has an upper energy limit given by the Q value minus the neutrino
mass. Till now this spectrum has been calculated allowing in Dysprosium
excitations with 3s1/2, 3p1/2, 4s1/2, 4p1/2, 5s1/2, 5p1/2 one-holes only.
Robertson calculated recently also the spectrum with two electron hole
excitations in Dy. He took the probability for the excitation for the second
electron hole from work of Carlson and Nestor for Z=54 Xenon. He claims, that
the bolometer spectrum with two holes is "not well enough understood to permit
a sensitive determination of the neutrino mass in this way."
  The purpose of the present work is to determine the theoretical bolometer
spectrum with two hole excitations more reliably directly in holmium and
dysprosium. In addition it will be shown, that the two-hole excitations do not
complicate more the determination of the neutrino mass compared to the
situation with one-hole states only. At the Q value the highest one-hole
resonance is dominant. Under the assumption of a Lorentzian line shape one has
to fit after inclusion of the experimental spectral function of the detector
four quantities to the data: (1) The neutrino mass, (2) the energy distance of
the dominant resonance to the Q value, (3) the line witdth and (4) the strength
of the resonance. Compared to Robertson this work includes major improvements
and it shows, that a determination of the neutrino mass is difficult but not
impossible.
