High-precision calculation of the branching ratio of the 40K decay constant.

40K is of great importance in Earth science, particularly for K/Ar, 40Ar/39Ar and K/Ca geochronology. The decay scheme of the 40K includes two different modes of decay, beta and electron capture followed by gamma-ray emission, which yield two different products, 40Ca* and 40Ar*. The relative probability that 40K decay following one of the two schemes is known as the branching ratio. An original method of calculation to obtain the value of the 40K branching ratio (λβ- /λtot) based on the K/Ar technique, is proposed. λβ- /λtot is obtained by combining the 40Ar*/40K value of Fish Canyon sanidine (FCs) secondary standard derived from four primary 40Ar/39Ar standards, with the current best estimates of the age of FCs and the value of the 40K total decay constant. The latest estimation of the 40K total decay constant and the age of FCs by Mundil et al. (2006), through comparison with U/Pb ages, yields a λβ- /λtot value of 89.59 ± 0.03% (1σ; relative error = ± 0.035%). Indirect measurement of the age of FCs by orbital tuning (Kuiper et al., 2008) combined with the value of 40K total decay constant measured by liquid scintillation counting by Kossert and Gunther (2004) yields a statistically indistinguishable value for the branching ratio of 89.61 ± 0.03%, with an average between the two values of 89.60 ± 0.04%. The method proposed here allows can easily be applied to further constrain the value of the 40K branching ratio as future refinements of the 40K decay constant and FCs age are produced, although it is expected that the adopted value will be close to λβ- /λtot = 89.60 ± 0.04%. Kossert and Gunther, 2004. Appl. Radiat. Isot. 60, 459-464. Kuiper et al., 2008. Science 320, 500-504. Mundil et al. 2006, Eos Trans. AGU, 87(52)