Analysis of the recoil ion spectra for the β-decays of 16He, 19Ne and 35Ar

The recoil energy spectrum is calculated for allowed β-decay with all form factors up to the weak magnetism and axial tensor terms included. Finite nuclear size and electromagnetic corrections including bremsstrahlung are also given. The results are equivalent to evaluation of the electron neutrino angular correlation but are directly related to the observed quantities and thus more easily interpreted in terms of the higher order form factors. The formulae were applied to the experimental 6Li+ spectrum of Johnson et al. for the decay 6He → 6Li+ + e- + anti γ and the best fit yields a tensor form factor consistent with zero, in agreement with the approximate analysis of Calaprice. The implications for a possible second-class current are discussed. The theoretical recoil spectra for the 19Ne and 35Ar mirror decays are also calculated and it is shown that measurements of these spectra, with accuracy equivalent to the 6He data, would yield conclusive evidence for a possible second-class tensor form factor. (Auth.)