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.

arXiv comment10 pages and 5 figures

References in corpus (5)

• Status of three-neutrino oscillation parameters, circa 2013
• Current Direct Neutrino Mass Experiments
• HOLMES - The Electron Capture Decay of 163Ho to Measure the Electron Neutrino Mass with sub-eV sensitivity
• Characterization of low temperature metallic magnetic calorimeters having gold absorbers with implanted ${}^{163}$Ho ions
• Electron Capture in 163Ho and Overlap plus Exchange Corrections and the Neutrino Mass

Cited by in corpus (15)

• Sterile Neutrino Dark Matter
• A White Paper on keV Sterile Neutrino Dark Matter
• Direct Measurements of Neutrino Mass
• Development of holmium-163 electron-capture spectroscopy with transition-edge sensors
• The use of low temperature detectors for direct measurements of the mass of the electron neutrino
• ${}^{159}$Dy electron-capture: a strong new candidate for neutrino mass determination
• Determination of the neutrino mass by electron capture in 163 Holmium and the role of the three-hole states in 163 Dysprosium
• 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
• 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
• Light sterile neutrino sensitivity of 163Ho experiments
• Constraints on the Active and Sterile Neutrino Masses from Beta-Ray Spectra: Past, Present and Future
• First Calorimetric Measurement of Electron Capture in ${}^{193}$Pt with a Transition Edge Sensor
• Phenomenological Modeling of the ${}^{163}$Ho Calorimetric Electron Capture Spectrum from the HOLMES Experiment