Testing Lepton Wave Function Factorization in $^{71}\text{Ge}$ Electron Capture

Abstract

Electron-capture ratios provide precision tests of atomic wave functions and of possible non-factorization effects in nuclear electron capture. By exploiting exact leptonic wave functions, we present a general framework for predicting the electron capture rates of $^{71}\mathrm{Ge}$. Adopting a non-factorized treatment of the transition matrix element, we investigate the interplay between the nuclear transition density, which encodes the nuclear structure contribution, and the leptonic wave functions. Using phenomenologically constrained transition densities, we quantify the impact of non-factorization effects on the capture rates. Finally, we compare our theoretical predictions for the $L/K$, $M/K$ and $M/L$ electron capture ratios with the current experimental world averages, providing an up-to-date assessment of the theoretical and experimental status of $^{71}\mathrm{Ge}$ electron capture.