Simultaneous analysis of rotational and vibrational spectra in even–even deformed nuclei: a study on \(^{168}\)Er

Theoretical studies of nuclear structure play a crucial role in understanding the collective properties of nuclei. In this study, we investigated the collective properties of even–even deformed nuclei with simultaneous nuclear rotational and vibrational spectra. From the nuclear Hamiltonian, the low-lying energy levels, and interband and intraband E2 transition probabilities were derived analytically. The Hamiltonian proposed in this study is based on the geometrical model proposed by Bohr and Mottelson representing a typical collective model, and the algebraic model proposed by Arima and Iachello. The energy levels and E2 transition ratios of \(^{168}\) $_{}^{168}$ Er were calculated and compared with the experimental data. This theoretical approach effectively described the structure of the deformed nucleus \(^{168}\) $_{}^{168}$ Er.