Natural-parity states in superdeformed bands and pseudo SU(3) symmetry at extreme conditions

The structure of recently discovered identical superdeformed bands in ${}_{}{}^{151}{}_{}{}^{}\mathrm{Tb}$ and ${}_{}{}^{152}{}_{}{}^{}\mathrm{Dy}$, and in ${}_{}{}^{150}{}_{}{}^{}\mathrm{Gd}$ and ${}_{}{}^{151}{}_{}{}^{}\mathrm{Tb}$ are discussed in terms of the strong-coupling approach. Based on the experimental evidence that the superdeformed core of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Dy}$ is extremely insensitive to the polarization effects induced by the odd particle, the bands are shown to exhibit the presence of the pseudo SU(3) symmetry at extreme conditions of large elongations and high spins.