Reassessing the gallium anomaly using self-consistent electron wave functions

The gallium anomaly, a persistent discrepancy exceeding <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>4</a:mn> <a:mi>σ</a:mi> </a:mrow> </a:math> in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mmultiscripts> <c:mrow> <c:mi>Ga</c:mi> </c:mrow> <c:mprescripts/> <c:none/> <c:mrow> <c:mn>71</c:mn> </c:mrow> </c:mmultiscripts> </c:mrow> </c:math> neutrino capture rates from <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mmultiscripts> <e:mrow> <e:mi>Cr</e:mi> </e:mrow> <e:mprescripts/> <e:none/> <e:mrow> <e:mn>51</e:mn> </e:mrow> </e:mmultiscripts> </e:mrow> </e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mmultiscripts> <g:mrow> <g:mi>Ar</g:mi> </g:mrow> <g:mprescripts/> <g:none/> <g:mrow> <g:mn>37</g:mn> </g:mrow> </g:mmultiscripts> </g:mrow> </g:math> 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.