Contribution of Subthreshold States to the Residual Energy Distribution of $^{159}$Dy

TL;DR

This paper reveals that subthreshold atomic states significantly influence the residual energy distribution in electron capture of $^{159}$Dy, leading to enhanced rates and new experimental possibilities for neutrino mass research.

Contribution

It introduces the inclusion of subthreshold atomic states into spectral analysis, showing their impact on EC rates and experimental determination of $P(E)$.

Findings

Subthreshold states cause over an order of magnitude increase in EC rate.

Enhanced EC rates grow with larger $Q$ values, contrary to expectations.

Experimental determination of $P(E)$ can resolve endpoint ambiguities.

Abstract

We investigate the residual energy distribution in the electron capture (EC) process of $^{159}$Dy, emphasizing the role of subthreshold atomic states, which have typically been omitted in conventional spectral analyses. By incorporating these energetically forbidden hole states into the spectral function $P(E)$, we demonstrate a significant enhancement - over an order of magnitude - in the EC rate near the zero-momentum neutrino emission region. This enhancement increases further with larger $Q$ values, contrary to standard expectations. Our analysis shows that $P(E)$ can be experimentally determined, resolving ambiguities near the endpoint and enabling new approaches to 'ultra-low $Q$ value' EC reactions for neutrino mass studies.