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 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 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 (ECground / β+) 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 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, this yields a partial decay constant for 40K direct to ground state 40Ar of 9.6 ± 3.8 × 10−13 a−1 (2σ). We calculate a partial decay constant of 40K to 40Ar of 0.590 ± 0.014 × 10−10 a−1, total decay constant of 5.473 ± 0.107 × 10−10 a−1 (2σ), and 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.
Two-phonon structures for beta-decay theory
