Evidence for ground-state electron capture of ${}^{40}$K

Abstract

Potassium-40 is a widespread isotope whose radioactivity impacts estimated geological ages spanning billions of years, nuclear structure theory, and subatomic rare-event searches - including those for dark matter and neutrinoless double-beta decay. The decays of this long-lived isotope must be precisely known for its use as a geochronometer, and to account for its presence in low-background experiments. There are several known decay modes for ${}^{40}$K, but a predicted electron-capture decay directly to the ground state of argon-40 has never been observed, while theoretical predictions span an order of magnitude. The KDK Collaboration reports on the first observation of this rare decay, obtained using a novel combination of a low-threshold X-ray detector surrounded by a tonne-scale, high-efficiency ${\hat{I}}^3$-ray tagger at Oak Ridge National Laboratory. A blinded analysis reveals a distinctly nonzero ratio of intensities of ground-state electron-captures ($I_{{\text{EC}}^0}$) over excited-state ones ($I_{{\text{EC}}^{\ast }}$) of $I_{{\text{EC}}^0}/I_{{\text{EC}}^{\ast }}=0.0095\stackrel{\text{stat}}{\pm }0.0022\stackrel{\text{sys}}{\pm }0.0010$ (68% CL), with the null hypothesis rejected at 4$\ddot{I}ƒ$ [Stukel et al., DOI:10.1103/PhysRevLett.131.052503]. This unambiguous signal yields a branching ratio of $I_{{\text{EC}}^0}=0.098\%\stackrel{\text{stat}}{\pm }0.023\%\stackrel{\text{sys}}{\pm }0.010$, roughly half of the commonly used prediction. This first observation of a third-forbidden unique electron capture improves understanding of low-energy backgrounds in dark-matter searches and has implications for nuclear-structure calculations. A shell-model based theoretical estimate for the $0\hat{I}½{\hat{I}}^2{\hat{I}}^2$ decay half-life of calcium-48 is increased by a factor of $7_{-2}^{+3}$. Our nonzero measurement shifts geochronological ages by up to a percent; implications are illustrated for Earth and solar system chronologies.

This is a companion submission to Stukel et al (KDK collaboration) "Rare ${}^{40}$K decay with implications for fundamental physics and geochronology" [arXiv:2211.10319; DOI: 10.1103/PhysRevLett.131.052503]. As such, both texts share some figures and portions of text. This version updates the text following its review and production process