Self-consistent calculations for atomic electron capture

We present a comprehensive investigation of electron capture (EC) ratios spanning a broad range of atomic numbers. The study employs a self-consistent computational method that incorporates electron screening, electron correlations, overlap and exchange corrections, as well as shake-up and shake-off atomic effects. The electronic wave functions are computed with the Dirac-Hartree-Fock-Slater (DHFS) method, chosen following a systematic comparison of binding energies, atomic relaxation energies and Coulomb amplitudes against other existing methods and experimental data. A novel feature in the calculations is the use of an energy balance employing atomic masses, which avoids approximating the electron total binding energy and allows a more precise determination of the neutrino energy. This leads to a better agreement of our predictions for capture ratios in comparison with the experimental ones, especially for low-energy transitions. We expand the assessment of EC observables uncertainties by incorporating atomic relaxation energy uncertainties, in contrast to previous studies focusing only on Q-value and nuclear level energies. Detailed results are presented for nuclei of practical interest in both nuclear medicine and exotic physics searches involving liquid Xenon detectors ($^{67}\mathrm{Ga}$, $^{111}\mathrm{In}$, $^{123}\mathrm{I}$, $^{125}\mathrm{I}$ and $^{125}\mathrm{Xe}$). Our study can be relevant for astrophysical, nuclear, and medical applications.