Improved Description of One- and Two-Hole States after Electron Capture in 163 Holmium and the Determination of the Neutrino Mass

Abstract: 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.