State-of-the-art optical clocks [1] achieve fractional precisions of 10 −18 and below using ensembles of atoms in optical lattices [2, 3] or individual ions in radiofrequency traps [4, 5]. They are used as frequency standards and in searches for possible variations of fundamental constants [6], dark matter detection [7], and physics beyond the Standard Model [8, 9]. Promising candidates for novel clocks are highly charged ions (HCIs) [10] and nuclear transitions [11], which are largely insensitive to external perturbations and reach wavelengths beyond the optical range [12], now becoming accessible to frequency combs [13]. However, insufficiently accurate atomic structure calculations still

The determination of the effective electron neutrino mass via kinematic analysis of beta and electron capture spectra is considered to be model-independent since it relies on energy and momentum conservation. At the same time the precise description of the expected spectrum goes beyond the simple phase space term. In particular for electron capture processes, many-body electron-electron interactions lead to additional structures besides the main resonances in calorimetrically measured spectra. A precise description of the 163 Ho spectrum is fundamental for understanding the impact of low intensity structures at the endpoint region where a finite neutrino mass affects the shape most strongly. We present a low-background and high-energy resolution measurement of the 163 Ho spectrum obtained in the framework of the ECHo experiment. We study the line shape of the main resonances and multiplets with intensities spanning three orders of magnitude. We discuss the need to introduce an asymmetric line shape contribution due to Auger-Meitner decay of states above the auto-ionisation threshold.

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.