Production of <sup>40</sup>Ar by an overlooked mode of <sup>40</sup>K decay with implications for K-Ar geochronology

Abstract

Abstract. The decay of 40K to the stable isotopes 40Ca and 40Ar is used as a measure of time for both the K-Ca and K-Ar geochronometers, the latter of which is most generally utilized by the variant 40Ar∕39Ar system. The increasing precision of geochronology has forced practitioners to deal with the systematic uncertainties rooted in all radioisotope dating methods. A major component of these systematic uncertainties for the K-Ar and 40Ar∕39Ar techniques is imprecisely determined decay constants and an incomplete knowledge of the decay scheme of 40K. Recent geochronology studies question whether 40K can decay to 40Ar via an electron capture directly to ground state (ECground), citing the lack of experimental verification as reasoning for its omission. In this study, we (1) provide a theoretical argument in favor of the presence of this decay mode and (2) evaluate the magnitude of this decay mode by calculating the electron capture to positron ratio (ECground/β+) and comparing calculated ratios to previously published calculations, which yield ECground/β+ between 150–212. We provide support for this calculation through comparison of the experimentally verified ECground/β+ ratio of 22Na with our calculation using the theory of β decay. When combined with measured values of β+ and β− decay rates, the best estimate for the calculated ECground/β+ for 40K yields a partial decay constant for 40K direct to ground-state 40Ar of 11.6±1.5×10-13 a−1 (2σ). We calculate a partial decay constant of 40K to 40Ar of 0.592±0.014×10-10 a−1 and a total decay constant of 5.475±0.107×10-10 a−1 (2σ), and we conclude that although omission of this decay mode can be significant for K-Ar dating, it is minor for 40Ar∕39Ar geochronology and is therefore unlikely to have significantly biased published measurements.

Evidence for ground-state electron capture of K40

“…Aside from the branches mentioned previously, an electron-capture decay directly to the ground state of 40 Ar (EC 0 ) has also been predicted by some [9,13,15,18], ignored or disputed by others [10,11], but never observed. This branch forms a particularly challenging background in rare-event searches as there is no high-energy γ ray from deexcitation that could be used to tag the low-energy radiation from the electron capture.…”

“…This veto method relies on identification of the high-energy γ ray from the de-excitation of 40 Ar following an EC * decay. In addition, the long halflife (slightly over a billion years) of this isotope makes it a useful geochronometer via the K/Ar and 40 Ar / 39 Ar dating techniques [8][9][10][11]. Finally, the presence of all three modes of β decay, some of which are extremely rare third-forbidden unique transitions, make this isotope of particular interest to nuclear structure theory [7,12,13].…”

“…In addition, this added background has been proposed [2] as a way to constrain the dark-matter interpretation of the longstanding, but controversial, DAMA/LIBRA Collaboration claim for discovery of dark matter [19]. From the standpoint of geochronology, the existence of this decay to ground state could mean that samples are up to tens of millions of years older than commonly believed [9]. An empirical frequency of this branch would also inform calculations in nuclear structure theory, including those for neutrinoless double-beta-decay half-lives.…”

Revised astronomically calibrated 40Ar/39Ar ages for the Fish Canyon Tuff sanidine – Closing the interlaboratory gap

“…FCTs ages were calculated relative to the astronomical ages for A1Ts (Rivera et al, 2011) and Mes4Ts (Kuiper et al, 2008), the atmospheric argon composition of Lee et al (2006), and the decay constants recommended by Min et al (2000). Note that the choice of decay constants (e.g., Steiger and Jäger, 1977;Renne et al, , 2011Carter et al, 2020) has negligible impact on calculated Rvalues and ages. Unless otherwise stated, uncertainties associated with R-values and ages are reported at the 2σ level and exclude uncertainties in the ages of A1Ts and Mes4Ts and decay constants.…”

A novel experimental system for the KDK measurement of the $^{40}$K decay scheme relevant for rare event searches

“…As discussed in [13,14,15], an outstanding issue of these dating methods is verifying the relevance (or existence) of the EC decay. Implications for K-Ar and Ar-Ar dating are reviewed in [16].…”