Pigmy and giant dipole states in stable and unstable oxygen isotopes

We have studied dipole states of oxygen isotopes in large scale shell model calculations. The calculated photoreaction cross sections in ¹⁶O, ¹⁷O and ¹⁸O give reasonable agreement with experimental observations both in the low energy region below ?ω=15 MeV and in the high energy giant resonance region (15 MeV < ?ω ≤ 30 MeV). We found that the transition strength below dipole giant resonance (?ω ≤ 15 MeV) exhausts about 10% of the classical Thomas-Reiche-Kuhn sum rule and more than 40% of the cluster sum rule in heavier oxygen isotopes than ¹⁷O. The predicted Pigmy strengths in ²⁰O and ²²O are also confirmed by recent Coulomb excitation experiment at GSI.