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Several current searches for physics beyond the standard model are based onmeasuring the electron capture (EC) decay of radionuclides implanted intocryogenic high-resolution sensors. The sensitivity of these experiments hasalready reached the level where systematic effects related to atomic-stateenergy changes from the host material are a limiting factor. One example is aneutrino mass study based on the nuclear EC decay of $^7$Be to $^7$Li insidecryogenic Ta-based sensors. To understand the material effects at the requiredlevel we have used density functional theory and modeled the electronicstructure of lithium atoms in different atomic environments of thepolycrystalline Ta absorber film. The calculations reveal that the Li 1sbinding energies can vary by more than 2 eV due to insertion at differentlattice sites, at grain boundaries, in disordered Ta, and in the vicinity ofvarious impurities. However, the total range of Li 1s shifts does not exceed 4eV, even for extreme amorphous disorder. Further, when investigating theeffects on the Li 2s levels, we find broadening of more than 5 eV due tohybridization with the Ta band structure. Materials effects are shown tocontribute significantly to peak broadening in Ta-based sensors that are usedto search for physics beyond the standard model in the EC decay of $^7$Be, butthey do not explain the full extent of observed broadening. Understanding thesein-medium effects will be required for current- and future-generationexperiments that observe low-energy radiation from the EC decay of implantedisotopes to evaluate potential limitations on the measurement sensitivity.

Material Effects on Electron Capture Decays in Cryogenic Sensors