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

Potassium-40 is a widespread, naturally occurring 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 potassium-40, but a predicted electron-capture decay directly to the ground state of argon-40 has never been observed. The existence of this decay mode impacts several fields, while theoretical predictions span an order of magnitude. Here we report on the first, successful observation of this rare decay mode, obtained by the KDK (potassium decay) Collaboration 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 ($I_{{\mathrm{EC}}^0}$) over excited-state ones ($I_{{\text{EC}}^{*}}$) of $I_{{\mathrm{EC}}^0}/I_{{\text{EC}}^{*}}=0.0095\stackrel{\text{stat}}{\pm }0.0022\stackrel{\text{sys}}{\pm }0.0010$ (68% CL), with the null hypothesis rejected at $4\sigma$ [Stukel et al., Phys. Rev. Lett. 131, 052503 (2023)]. In terms of branching ratio, this unambiguous signal yields $I_{{\mathrm{EC}}^0}=0.098\%\stackrel{\text{stat}}{\pm }0.023\%\stackrel{\text{sys}}{\pm }0.010\%$, roughly half of the commonly used prediction. This first observation of a third-forbidden unique electron capture improves our understanding of low-energy backgrounds in dark-matter searches and has implications for nuclear-structure calculations. For example, a shell-model based theoretical estimate for the neutrinoless double-beta 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.

Figure 1

${}^{40}\mathrm{K}$ decay scheme, with branching ratios and half-life calculated from our determination of $I_{{\mathrm{EC}}^0}/I_{{\text{EC}}^{*}}$ (this work and [14]) and from literature values for $T^{-}$ (partial half-life of the ${\beta }^{-}$ decay) and $T^{*}$ (partial half-life of ${\mathrm{EC}}^{*}$) [15] (also shown: transition energy [16], $Q_{{\text{EC}}^0}$ and $Q^{-}$ [17]).

Figure 2

Schematic displaying the cross-section of MTAS, along with the SDD. The SDD housing is centered in MTAS.

Figure 3

${}^{40}\mathrm{K}$ coincidence spectrum between the SDD and MTAS. SDD and MTAS data obtained with the enriched ${}^{40}\mathrm{K}$ source using a nominal $2\mu \mathrm{s}$ coincident window is binned into a $250\times 250$ grid over the displayed energy ranges.

Figure 4

SDD coincidence and anticoincidence spectra. Results of simultaneous fit to coincident (top) and anticoincident (bottom) SDD spectra at a 2 $\mu \mathrm{s}$ coincidence window. Signal counts are shown in green. Various fluorescence peaks and an exponential background model are included. The total minimization has an associated goodness of fit of $p=0.4$.

Figure 5

Distributions of $\rho$ and its statistical error from systematic checks. The value of $\rho$ and its associated statistical error ${\sigma }_{\rho }^{\text{stat}}$ obtained from 10 000 systematic-varying fits are displayed. The width of the $\rho$ distribution is equivalent to the systematic error. Contour lines of the fit function correspond to the color bar on the right.

Figure 6

Measured ground-state electron-capture branching ratio compared to predictions from Engelkemeir (1962) [18], $logft$ (1999) [34, 35], Mougeot (2019) [12], Carter (2020) [9], Kossert (2022) [15], and this work (Sec. 3b). All error bars correspond to a 68% C.L., with no uncertainty reported for Engelkemeir.

Figure 7

Effect of KDK on the thermal history of the Acapulco meteorite. ${}^{40}\mathrm{Ar}/{}^{39}\mathrm{Ar}$ ages of the Acapulco meteorite [44] calculated for various sets of decay constants [10, 15, 43] (Fig. 4(c) in [14]) are plotted along with the corresponding estimated closure temperature of $300\pm 25{}^{\circ }\mathrm{C}$ (temperatures shifted for visibility). Age-temperature data obtained using Pb/Pb (updated from [45]) and Sm/Nd [48] also shown. For reference, the Pb/Pb age of the oldest dated solid in the solar system, a calcium-aluminum inclusion from the CV chondrite Efremovka, is $4567.35\pm 4.65$ Ma [49]. All uncertainties correspond to a 68% confidence level, and include decay constant uncertainties.