$\text{Ab initio}$ calculation of the calorimetric electron capture spectrum of ${}^{163}$Holmium: Intra-atomic decay into bound-states

Abstract

The determination of the electron neutrino mass by electron capture in ${}^{163}$Ho relies on a precise understanding of the deexcitation of a core hole after an electron capture event. We here present an \textit{ab intio} calculation of the electron capture spectrum in ${}^{163}$Ho, including all intra-atomic decay channels into bound-states. We use theoretical methods developed for the calculation of core level spectroscopy on correlated electron compounds. Our comparison critically tests the reality of these theories. We find that relativistic interactions beyond the Dirac equation, i.e. quantum-electro dynamics, only lead to minor shifts of the spectral peaks. The electronic relaxation after an electron capture event due to the changed nuclear potential leads to a mixing of different edges, but due to conservation of angular momentum of each scattered electron, no additional structures emerge. Many-body Coulomb interactions lead to the formation of multiplets and to additional peaks with multiple core-holes due to Auger decay. Multiplets crucially change the appearance of the resonances on a Rydberg energy scale. The additional structures due to Auger decay are, although clearly visible, relatively weak compared to the one core hole states and accidentally far away from the end-point region of the spectrum. As the end-point of the spectrum is effected most by the neutrino mass these additional states do not influence the statistics for determining the neutrino mass directly. The multiplet broadening and Auger shake-up of the main core-level edges do change the apparent line-width and accompanying lifetime of these edges, thereby invalidating experimentally obtained lifetimes at the resonance for regions far away from the resonance.

References in corpus (11)

• Multiplet ligand-field theory using Wannier orbitals
• Current Direct Neutrino Mass Experiments
• HOLMES - The Electron Capture Decay of 163Ho to Measure the Electron Neutrino Mass with sub-eV sensitivity
• Direct Measurement of the Mass Difference of Ho163 and Dy163 Solves the Q-Value Puzzle for the Neutrino Mass Determination
• Bands, resonances, edge singularities and excitons in core level spectroscopy investigated within the dynamical mean field theory
• Examination of the calorimetric spectrum to determine the neutrino mass in low-energy electron capture decay
• Theory of Core-Level Photoemission and the X-ray Edge Singularity Across the Mott Transition
• Determination of the neutrino mass by electron capture in 163 Holmium and the role of the three-hole states in 163 Dysprosium
• Improved Description of One- and Two-Hole States after Electron Capture in 163 Holmium and the Determination of the Neutrino Mass
• Neutrino Mass, Electron Capture and the Shake-off Contributions
• The calorimetric spectrum of the electron-capture decay of ${}^{163}$Ho. The spectral endpoint region

Cited by in corpus (12)

• Direct Measurements of Neutrino Mass
• ${}^{159}$Dy electron-capture: a strong new candidate for neutrino mass determination
• Ab initio calculation of the electron capture spectrum of 163Ho: Auger-Meitner decay into continuum states
• High-precision electron-capture $Q$ value measurement of ${}^{111}$In for electron-neutrino mass determination
• Metallic magnetic calorimeter arrays for the first phase of the ECHo experiment
• Signal processing and spectral modeling for the BeEST experiment
• Overlap of electron shells in $\beta$ and double-$\beta$ decays
• Neutrino mass measurements using cryogenic detectors
• New targets for relic antineutrino capture
• Phenomenological Modeling of the ${}^{163}$Ho Calorimetric Electron Capture Spectrum from the HOLMES Experiment
• Status and Perspectives of Neutrino Physics
• Data reduction for a calorimetrically measured ${}^{163}\mathrm{Ho}$ spectrum of the ECHo-1k experiment