Level matrix, 16N β decay, and the 12C(α,γ)16O reaction

The level matrix corresponding to the scrK-matrix parametrization of a resonant nuclear reaction is derived and applied to the spectrum of α particles emitted following 16N β decay. The parametrized spectrum is fitted to data simultaneously with the E1 capture cross section of the 12C(α,γ)16O reaction and the p-wave phase shift of 12C(α,α)12C. Our analysis shows that new measurements of the α spectrum from 16N β decay could be used to significantly reduce the uncertainty of the 12C(α,γ)16O astrophysical S factor at 0.3 MeV. Various constraints on the parameters are analyzed and suggestions are made for further reducing the uncertainty in this crucial reaction rate.