Self-consistent calculations for atomic electron capture

This paper presents a comprehensive study of electron capture (EC) ratios across a wide range of nuclei using a self-consistent computational method. We have incorporated important effects such as overlap and exchange corrections, shake-up and shake-off effects in the EC formalism. The electronic wave functions were computed in the Dirac-Hartree-Fock-Slater (DHFS) framework, accounting for electron screening and correlations in the atomic structure description. The DHFS framework was chosen based on the systematic comparison of binding energies and Coulomb amplitudes with previous theoretical models and experimental data. The main feature of this paper is the refined determination of the emitted neutrino energy, which requires extensive atomic structure calculations but leads to much better agreement between theoretical predictions and experimental values, especially for low-energy transitions. Detailed results are presented for nuclei of practical interest ($^{67}\mathrm{Ga}$, $^{111}\mathrm{In}$, $^{123}\mathrm{I}$, $^{125}\mathrm{I}$ and $^{125}\mathrm{Xe}$) in nuclear medicine and exotic physics searches involving liquid Xenon detectors. This study provides a robust and comprehensive understanding of EC ratios, with significant implications for astrophysical, nuclear, and medical applications.