Percent-level production of <sup>40</sup>Ar by an overlooked mode of <sup>40</sup>K decay

Abstract

<p><strong>Abstract.</strong> The decay of <sup>40</sup>K to the stable isotopes <sup>40</sup>Ca and <sup>40</sup>Ar 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 <sup>40</sup>Ar/<sup>39</sup>Ar 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 <sup>40</sup>Ar/<sup>39</sup>Ar techniques is imprecisely determined decay constants and an incomplete knowledge of the decay scheme of <sup>40</sup>K. Recent studies question whether <sup>40</sup>K can decay to <sup>40</sup>Ar via an electron capture directly to ground state (EC<sub>ground</sub>), citing the lack of experimental verification as reasoning for its omission. In this study, we (1) provide a theoretical argument in favour of the presence of this decay mode, and (2) evaluate the magnitude of this decay mode by calculating the electron capture to positron ratio (EC<sub>ground</sub> / <i>β</i><sup>+</sup>) and after combining it with other estimates, provide a best estimate of 175 ± 65 (2σ). We provide support for this calculation through comparison of the experimentally verified EC<sub>ground</sub> / <i>β</i><sup>+</sup> ratio of <sup>22</sup>Na with our calculation using the theory of <i>β</i> decay.When combined with measured values of <i>β</i><sup>+</sup> and <i>β</i><sup>-</sup> decay rates, this yields a partial decay constant for <sup>40</sup>K direct to ground state <sup>40</sup>Ar of 9.6 ± 3.8 × 10<sup>−13</sup> a<sup>−1</sup> (2σ). We calculate a partial decay constant of <sup>40</sup>K to <sup>40</sup>Ar of 0.590 ± 0.014 × 10<sup>−10</sup> a<sup>−1</sup>, total decay constant of 5.473 ± 0.107 × 10<sup>−10</sup> a<sup>−1</sup> (2σ), and conclude that although omission of this decay mode can be significant for K-Ar dating, it is minor for <sup>40</sup>Ar/<sup>39</sup>Ar geochronology and is therefore unlikely to have significantly biased published measurements.</p>