Gamma width ofO*14(5.17 MeV) and the stellarN13(p,γ)14O reaction rate

We have determined the γ-ray branching ratio ${\mathrm{\Gamma }}_{\gamma }$/${\mathrm{\Gamma }}_{\mathrm{tot}}$ for the first excited state in ${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$ (${\mathit{E}}_{\mathit{x}}$=5.17 MeV) to be (3.1±1.7)×${10}^{\mathrm{-}4}$, corresponding to a γ width of 12±7 eV. This value was determined by measuring the ratio of the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(p,n${)}^{14}$ ${\mathrm{O}}_0$ to ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(p,n${)}^{14}$ ${\mathrm{O}}_1$ cross sections via neutron time of flight, and the ratio of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(p,n${)}^{14}$ ${\mathrm{O}}_0$ to ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(p,n${)}^{14}$ ${\mathrm{O}}_1$(γ${)}^{14}$ ${\mathrm{O}}_0$ cross sections at the same center-of-mass energy by bombarding a hydrogen target with a ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ beam and kinematically distinguishing the ${}_{}{}^{14}{}_{}{}^{}\mathrm{O}_0^{}{}_{}{}^{}$ recoils from the two reaction channels. The present value for ${\mathrm{\Gamma }}_{\gamma }$ is consistent with other measurements at the 2-σ level; a weighted mean of all measurements is used to calculate the stellar ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$(p,γ${)}^{14}$O reaction rate, and thereby determine the temperatures and densities at which the stellar carbon-nitrogen-oxygen (CNO) cycle is converted to the hot CNO cycle.