O14Decay Energy and the Fermi Interaction Constant

Abstract

The threshold energy of the ${\mathrm{C}}^{12}({\mathrm{He}}^3, n){\mathrm{O}}^{14}$ reaction has been measured precisely with the use of a Van de Graaff accelerator and an electrostatic analyzer, the value being 1436.2±0.9 kev. From this value, the ${\mathrm{O}}^{14}$ beta-decay end-point energy (for decay leading to the 2.312-Mev state in ${\mathrm{N}}^{14}$) is computed to be 1.8000 ±0.0065 Mev, based on the 1956 table of masses, and 1.8097 ±0.0015 Mev, based on the 1960 table of masses. A revised value of the Fermi interaction constant in beta decay is calculated and applied in the conserved vector current theory of Feynman and Gell-Mann. When (1) the radiative corrections and other corrections are applied to the decay of ${\mathrm{O}}^{14}$, (2) the corrected $\mathrm{ft}$ value is used to compute the vector coupling constant in beta decay, (3) the value of this vector coupling constant is assumed to be the same as that for the muon decay and is used to calculate the lifetime of the muon, and (4) this lifetime is corrected for radiation effects, the predicted mean life of the muon becomes 2.289±0.013 μsec (based on the 1960 table of masses and the radiative corrections of Kinoshita and Sirlin) or 2.245±0.013 μsec (based on the 1960 table of masses and the corrections, radiative and otherwise, of Durand and collaborators). The former value is 3.6% greater than a weighted average of several recent measurements of the muon mean life, 2.210±0.003 μsec, while the latter value is only 1.6% greater, and is within the combined experimental and theoretical uncertainties. However, the definitions of coupling constants used by Durand and collaborators differ somewhat from those used by others.