The nature of $K^{\pi }=0_2^{+}$, $0_3^{+}$ bands in ¹⁵⁸Gd

The cross over of β-, and γ-band at $N=94$ in ¹⁵⁸Gd signifies a major change in the nuclear structure of Gd isotopes. Using the microscopic dynamic pairing plus quadrupole (DPPQ) model, we reproduce this transition. The spectral features of the $K^{\pi }=0_3^{+}$, $2_1^{+}$ and $4_1^{+}$ bands besides the lower three: ground, β- and γ-bands have been analyzed. The B(E2) values from the $K^{\pi }=0_2^{+}$ and $K^{\pi }=0_3^{+}$ bands are analyzed to interpret the nature of these two bands. The $K^{\pi }=0_2^{+}$ band is confirmed as the axially symmetric β-vibration. The $K^{\pi }=0_3^{+}$ band is shown to be collective vibration, but instead of 2β vibration, it indicates very special features with large anharmonicity. The five excited $0^{+}$ states below 2.0 MeV identified in ¹⁵⁸Gd from $(p,t)$ reaction work are also predicted from the DPPQ model. The relative variation of β- and γ-band head energies and of $K^{\pi }={0_3}^{+}$ bands, and of $K^{\pi }=4^{+}$ band with neutron number N in ${}^{152\text{-}160}$Gd isotopes is reproduced. But the vibrational energy scale of the excited bands remains expanded. The algebraic interacting sd-boson model is also applied for evaluating the energy spectrum and the B(E2) ratios in these K-bands and for prediction of the multi-phonon $0^{+}$ states.