Abstract
Determining the electron neutrino mass by electron capture in 163Ho relies on an accurate understanding of the differential electron capture nuclear decay rate as a function of the distribution of the total decay energy between the neutrino and electronic excitations. The resulting spectrum is dominated by resonances due to local atomic multiplet states with core holes. Coulomb scattering between electrons couples the discrete atomic states, via Auger–Meitner decay, to final states with free electrons. The atomic multiplets are above the auto-ionisation energy, such that the delta functions representing these discrete levels turn into a superposition of Lorentzian, Mahan- and Fano-like line-shapes. We present an ab initio method to calculate nuclear decay modifications due to such processes. It includes states with multiple correlated holes in local atomic orbitals interacting with unbound Auger–Meitner electrons. A strong energy-dependent, asymmetric broadening of the resonances in good agreement with recent experiments is found. We present a detailed analysis of the mechanisms determining the final spectral line-shape and discuss both the Fano interference between different resonances, as well as the energy dependence of the Auger–Meitner Coulomb matrix elements. The latter mechanism is shown to be the dominant channel responsible for the asymmetric line-shape of the resonances in the electron capture spectrum of 163Ho.
Highlights
Despite observing only neutrinos with spin antiparallell to the neutrino momentum, extensive studies of neutrino flavour oscillations imply that neutrinos are massive particles
In Ref. 13 the sharp features as well as some of the apparent line broadening observed in the experimental spectra is explained by treating the full Coulomb interaction between the electrons restricted to a basis of bound-orbitals
In Ref. [13] we showed that the electron capture spectrum can be described within Kubo’s formalism using Green’s functions dΓ dω
Summary
Despite observing only neutrinos with spin antiparallell to the neutrino momentum, extensive studies of neutrino flavour oscillations imply that neutrinos are massive particles. The excited daughter atom undergoes subsequent decay via multiple channels leading to an energy spectrum rich of interesting structures The endpoint of this spectrum is determined by the energy difference of Ho and Dy ground-states minus the rest mass of the created neutrino. In Ref. 13 the sharp features as well as some of the apparent line broadening observed in the experimental spectra is explained by treating the full Coulomb interaction between the electrons restricted to a basis of bound-orbitals. In a recent experimental work [14] with higher statistics it was shown that the atomic multiplet resonances present in the EC spectrum of Ho have an asymmetric line-shape This yields noticeably more intensity outside the region of the resonances as one would expect from locally bound states broadened by a Lorentzian spectral-function. Mathematical and numerical details can be found in the appendices
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