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

TL;DR

This paper reports the first observation of ground-state electron capture in potassium-40, a rare decay mode with implications for geochronology, nuclear theory, and low-background experiments, achieved through a novel detection method.

Contribution

It provides the first experimental evidence of ground-state electron capture in $^{40}$K, refining decay rates and impacting multiple scientific fields.

Findings

Detected nonzero ground-state electron capture ratio in $^{40}$K

Measured branching ratio of approximately 0.098% for ground-state decay

Implications for geochronology and nuclear structure calculations

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 $\gamma$-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 ($I_{\text{EC}^*}$) of $I_{\text{EC}^0} / I_{\text{EC}^*}=0.0095\stackrel{\text{stat}}{\pm}0.0022\stackrel{\text{sys}}{\pm}0.0010$ (68% CL), with the null hypothesis rejected at 4$\sigma$ [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 $0\nu\beta\beta$ decay half-life of calcium-48 is increased by a factor of $7^{+3}_{-2}$. Our nonzero measurement shifts geochronological ages by up to a percent; implications are illustrated for Earth and solar system chronologies.