Strong effect of isospin mixing inO16

The intensity ratio of the ground state ($2^{-}$) to the 0.30 MeV ($3^{-}$) state of ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ as measured in the ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He})$ reaction and the intensity ratio of their analog states at 12.97 and 13.26 MeV in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ as measured in the ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}(d,t)$ and ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha )$ reactions consistently differ by about 50%. A largely model independent analysis of this isospin mixing effect in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ suggests ≥ 17% mixing of the $2^{-}$ states at 12.97 ($T=1\mathrm{}$) and 12.53 MeV ($T=0\mathrm{}$) as its dominant source, in which case a lower limit of the isospin mixing matrix element of (155 ± 30) keV is obtained.