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

TL;DR

This paper investigates how Coulomb interactions influence the detection of relic neutrinos through beta decay in (semi)metals, focusing on quantum effects and hybridization suppression.

Contribution

It provides a theoretical analysis of Coulomb effects on neutrino detection methods involving beta decaying impurities in solid-state environments.

Findings

Coulomb interactions can impair energy resolution in neutrino detection.

Hybridization suppression affects the strength of Coulomb interactions.

Perturbation theory reveals the extent of Coulomb effects in different scenarios.

Abstract

Measuring the electron neutrino mass is a long-standing objective and requires a high energy resolution of certain $\beta$-decay experiments, as well as a visible cosmic neutrino background (C$\nu$B) spectrum. Many quantum mechanical and chemical effects could potentially impair the required resolution/visibility, e.g., the Coulomb interactions between the electrons in the $\beta$-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.