Determination of the neutrino mass by electron capture in 163 Holmium and the role of the three-hole states in 163 Dysprosium

Abstract

163 Holmium to 163 Dysprosium is probably due to the small Q value of about 2.5 keV the best case to determine the neutrino mass by electron capture. The energy of the Q value is distributed between the excitation of Dysprosium (and the neglected small recoil of Holmium) and the relativistic energy of the emitted neutrino including the restmass. The reduction of the upper end of the deexcitation spectrum of Dysprosium below the Q value allows to determine the neutrino mass. The excitation of Dysprosium can be calculated in the sudden approximation of the overlap of the electron wave functions of Holmium minus the captured electron and one-, two-, three- and multiple hole-excitations in Dysprosium. Robertson and the author have calculated the influence of the two-hole states on the Dysprosium deexitation spectrum. Here for the first time the influence of the three-hole states on the deexcitation bolometer spectrum of 163 Dysprosium is presented. The electron wave functions and the overlaps are calculated selfconsitently in a fully relativistic and antisymmetrized Dirac-Hartree-Fock approach in Holmium and in Dysprosium. The electron orbitals in Dysprosium are determined including the one-hole states in the selfconsistent iteration. The influence of the three-hole states on the deexcitation (by X-rays and Auger electrons) spectrum is hardly visible. The three-hole states seem not to be important for the determination of the neutrino mass.

arXiv comment4 figures. arXiv admin note: text overlap with arXiv:1501.04338

References in corpus (6)

• Neutrino mass limit from tritium beta decay
• Current Direct Neutrino Mass Experiments
• Characterization of low temperature metallic magnetic calorimeters having gold absorbers with implanted ${}^{163}$Ho ions
• Examination of the calorimetric spectrum to determine the neutrino mass in low-energy electron capture decay
• Electron Capture in 163Ho and Overlap plus Exchange Corrections and the Neutrino Mass
• Improved Description of One- and Two-Hole States after Electron Capture in 163 Holmium and the Determination of the Neutrino Mass

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• Algorithms for Identification of Nearly-Coincident Events in Calorimetric Sensors
• Ab initio calculation of the electron capture spectrum of 163Ho: Auger-Meitner decay into continuum states
• Direct Neutrino Mass Experiments
• Neutrino Mass, Electron Capture and the Shake-off Contributions
• $\text{Ab initio}$ calculation of the calorimetric electron capture spectrum of ${}^{163}$Holmium: Intra-atomic decay into bound-states
• First Calorimetric Measurement of Electron Capture in ${}^{193}$Pt with a Transition Edge Sensor