Production of ⁴⁰Ar by an overlooked mode of ⁴⁰K decay with implications for K-Ar geochronology

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.