Isospin splitting of the giant resonance. I. Isodoublets

We study the isospin splitting of the giant resonance of $T=\frac{1}{2}$ nuclei with sum rules. The particular isospin geometry involved in this case permits a number of simplifications in the isospin sum rules and several largely model independent relations are obtained and discussed. It turns out that for several light isodoublets the "symmetry" energy $U$ tends to be smaller that $60(T+1){A}^{\ensuremath{-}1}$ MeV.NUCLEAR STRUCTURE $T=\frac{1}{2}$ nuclei; calculated isospin splitting of $E1$ resonance with sum rules, model independent results discussed.