Level matrix,N16β decay, and theC12(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 ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ β decay. The parametrized spectrum is fitted to data simultaneously with the E1 capture cross section of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(α,γ${)}^{16}$O reaction and the p-wave phase shift of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(α,α${)}^{12}$C. Our analysis shows that new measurements of the α spectrum from ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ β decay could be used to significantly reduce the uncertainty of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(α,γ${)}^{16}$O 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.