Reassessing the gallium anomaly using self-consistent electron wave functions

The gallium anomaly, a persistent discrepancy exceeding $4\sigma$ in the $^{71}$Ga neutrino capture rates from $^{51}$Cr and $^{37}$Ar radioactive sources by the GALLEX, SAGE, and recently BEST experiments, has challenged particle physics and nuclear theory for over three decades. We present a new calculation of the neutrino capture cross section, abandoning the conventional leading-order approximation for electronic wave functions by numerically solving the Dirac-Coulomb equation for both bound and continuum electron states. Finally, we reevaluate the gallium anomaly, updating its global significance and presenting the most up-to-date status of its interpretation in terms of sterile neutrinos.