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Register a new user$textit{Ab initio}$ calculation of the calorimetric electron capture spectrum of $^{163}$Holmium: Intra-atomic decay into bound-states
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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.
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The electron-neutrino mass (or masses and mixing angles) may be directly measurable in weak electron-capture decays. The favoured experimental technique is calorimetric. The optimal nuclide is $^{163}$Ho, and several experiments (ECHo, HOLMES and NuMECS) are currently studying its decay. The most relevant range of the calorimetric-energy spectrum extends for the last few hundred eV below its endpoint. It has not yet been well measured. We explore the theory, mainly in the cited range, of electron capture in $^{163}$Ho decay. A so far neglected process turns out to be most relevant: electron-capture accompanied by the shake-off of a second electron. Our two main conclusions are very encouraging: the counting rate close to the endpoint may be more than an order of magnitude larger than previously expected; the pile-up problem may be significantly reduced.
It is in principle possible to measure directly the electron neutrino mass (or masses and mixing angles) in weak electron-capture decays. The optimal nuclide in this respect is $^{163}$Ho. The favoured experimental technique, currently pursued in various experiments (ECHo, HOLMES and NuMECS) is calorimetric. The calorimetric energy spectrum is a sum over the unstable vacant orbitals, or holes, left by the electrons weakly captured by the nucleus. We discuss the current progress in this field and analize the preliminary data. Our conclusion is that, as pointed out by Robertson, the contribution of two-hole states is not negligible. But --in strong contradistinction with the tacit conclusion of previous comparisons of theory and observations-- we find a quite satisfactory agreement. A crucial point is that, in the creation of secondary holes, electron shakeoff and not only electron shakeup must be taken into account.
The isotope $^{163}$Ho undergoes an electron capture process with a recommended value for the energy available to the decay, $Q_{rm EC}$, of about 2.5 keV. According to the present knowledge, this is the lowest $Q_{rm EC}$ value for electron capture processes. Because of that, $^{163}$Ho is the best candidate to perform experiments to investigate the value of the electron neutrino mass based on the analysis of the calorimetrically measured spectrum. We present for the first time the calorimetric measurement of the atomic de-excitation of the $^{163}$Dy daughter atom upon the capture of an electron from the 5s shell in $^{163}$Ho, OI-line. The measured peak energy is 48 eV. This measurement was performed using low temperature metallic magnetic calorimeters with the $^{163}$Ho ion implanted in the absorber. We demonstrate that the calorimetric spectrum of $^{163}$Ho can be measured with high precision and that the parameters describing the spectrum can be learned from the analysis of the data. Finally, we discuss the implications of this result for the Electron Capture $^{163}$Ho experiment, ECHo, aiming to reach sub-eV sensitivity on the electron neutrino mass by a high precision and high statistics calorimetric measurement of the $^{163}$Ho spectrum.
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