Shake-up and shake-off spectra in the electron capture decay of atomic $^7$Be

TL;DR

This work presents the first ab initio, correlated MCDF-based calculation of the full electron shake spectrum in the EC decay of atomic $^7$Be, including single and double shake-up and shake-off channels up to the 4s basis. It demonstrates that L-capture induces substantially stronger shake effects than K-capture, and shows how SU can be modeled with broadened Gaussians while SO spectra can be represented by analytic forms to reduce fit complexity. A key outcome is the revised L/K capture ratio in Ta, determined as $0.0756(20)$, which impacts BeEST background modeling and sterile neutrino searches. The study also highlights the limitations of isolated-atom calculations and the need to incorporate matrix effects from the detector environment for precise spectral modeling in high-precision EC experiments.

Abstract

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).

Figures (11)

• Figure 1: Schematic of the atomic processes after electron capture. The solid lines represent the capture events that result in the two main peaks of the BeEST spectra (K-GS, L-GS) and their excited state counterparts (K-ES, L-ES). The dashed lines represent shake-up channels and the dotted lines represent the onset of K and L electron shake-off after either K or L capture.
• Figure 2: Radial wavefunction of a bound $2s$ electron in the $^7$Be ground state $1s^2 2s^2$ and continuum wavefunctions (computed in the $^7$Li$^+$ potential) of an electron with kinetic energies of 20 eV, 100 eV or 1000 eV after a ground state L capture, $1s^2 + e^-$. The gray dashed line at $3.3$ Å is the lattice constant of the Ta host in the BeEST experiment.
• Figure 3: Total shake probabilities according to Eq. (\ref{['shake']}) as a function of the size of the basis space. All the single and double excitations up to the $4s$ orbital are included. The colored bands represent the $1\sigma$ intervals.
• Figure 4: Shake-up probability for $1s\rightarrow ns$ and $2s\rightarrow ns$ electron excitations after K or L shell capture in $^7$Be. The inset shows the sum of all of the SU channels with 2 eV FWHM Gaussian broadening to account for the detector resolution. Energies are shown relative to the $n=3$ SU channel of each dataset.
• Figure 5: Comparison of the Levinger shake-off profiles used in the BeEST phase-II analysis (red dashed line) and the ab initio calculations (blue solid line). All profiles are convolved with a 2 eV FWHM Gaussian to account for the detector resolution. The energy thresholds for the Levinger spectra are the fit values, and the computed values for the ab initio calculations.