Shake-up and shake-off spectra in the electron capture decay of atomic $^7$Be
The most stringent laboratory-based experimental limits on the existence of sub-MeV sterile neutrinos are currently set by decay spectroscopy of radioactive $^7$Be embedded into superconducting sensors. The systematic uncertainties are dominated by the modeling of the electron shake-up and shake-off spectra that are not based on state-of-the-art atomic theory and do not include electron correlations or relativistic effects. We have used the multiconfiguration Dirac-Fock formalism to obtain correlated wavefunctions ab initio and compute all single and double shake processes in the electron capture decay of atomic $^7$Be. The simulations can explain some but not all of the observed spectral features, likely because the wave functions are modified by the Ta sensor material that the $^7$Be is embedded into. The new models also show that the L/K electron capture ratio of $^7$Be in Ta has previously been slightly underestimated revising the previous value of 0.070(7) to a new value of 0.0756(20).