Reassessing the gallium anomaly using exact electron wave functions

Abstract: The gallium anomaly, a persistent discrepancy exceeding $4\sigma$ in the $^{71}$Ga neutrino capture rates from $^{51}$Cr and $^{37}$Ar calibration 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 for 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 re-evaluate the gallium anomaly, updating its global significance and presenting the most up-to-date status of its interpretation in terms of sterile neutrinos.