Pigmy and giant dipole states in oxygen isotopes

We have studied dipole states of oxygen isotopes in large scale shell model calculations. The calculated photoreaction cross sections in ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ give reasonable agreement with experimental observations both in the low energy region below $ħ\omega =15\mathrm{}\mathrm{MeV}$ and in the high energy giant resonance region $(15\mathrm{}\mathrm{MeV}<\mathrm{}\mathrm{ħ}\mathrm{\omega }<~30\mathrm{}\mathrm{MeV}).\mathrm{}$ We found that the transition strength below giant dipole resonance $(ħ\omega <~15\mathrm{MeV})$ exhausts about 10% of the classical Thomas-Reiche-Kuhn sum rule value in heavier oxygen isotopes than ${}^{18}\mathrm{O}.$ The $T_{>}$ GDR (giant dipole resonance) appears in ${}^{18}\mathrm{O}$ and ${}^{20}\mathrm{O}$ having comparable transition strengths with the $T_{<}$ GDR, while $T_{>}$ strengths become much smaller than $T_{<}$ ones in ${}^{22}\mathrm{O}$ and ${}^{24}\mathrm{O}.$