The effect of Coulomb interactions on relic neutrino detection via beta decaying impurities in (semi)metals

Measuring the electron neutrino mass is a long-standing objective and requires a high energy resolution of certain \beta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>β</mml:mi> </mml:math> -decay experiments, as well as a visible cosmic neutrino background ( C\nu B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>ν</mml:mi> <mml:mi>B</mml:mi> </mml:mrow> </mml:math> ) spectrum. Many quantum mechanical and chemical effects could potentially impair the required resolution/visibility, e.g., the Coulomb interactions between the electrons in the \beta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>β</mml:mi> </mml:math> -decaying impurity and in the solid-state environment. We analyze the effect when hybridization is suppressed completely using a dielectric spacer, and also when hybridization is present up to the lowest nontrivial order in perturbation theory.