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The characteristics of the low-lying mixed-symmetry states for 140Ba and 142Ce in the even-even N=84 isotones are investigated within the framework of the IBM-2 model. Electromagnetic transitions, B(E2) and B(M1) were calculated. Results showed that the lowest mixed-symmetry state is for 140Ba and 142Ce nuclei. A good agreement is found between experiment and predictions made using the U (5) limit of IBM-2.

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The characteristics of low-lying mixed-symmetry states in 158-168Hf isotopes have been investigated in the framework of the interacting boson model. The obtained results of the low energy spectra, B(E2) and mixing ratio δ(E2/M1) for all isotopes are compared with empirical values . The effect of the Majrona terms on the energy levels have been investigated. The 2ms+ and 1+ states are the lowest mixed-symmetry for vibrational 158-164Hf nuclei and for rotational 166,168Hf nuclei, respectively.

The low-lying positive and negative parity states of even–even [Formula: see text]Nd isotopes are studied using the interacting boson model (IBM). The negative parity states are involved within the IBM model by adding a single angular momentum ([Formula: see text]) boson with intrinsic negative parity [Formula: see text]-boson to [Formula: see text] and [Formula: see text]-bosons model space. For these nuclei, the potential energy surfaces [Formula: see text], transition probability [Formula: see text], [Formula: see text] and [Formula: see text] are calculated. Phase transition from the [Formula: see text] limit to the [Formula: see text] limit is observed in the chain and the critical point has been determined for [Formula: see text]Nd isotope. It is found that the calculated positive and negative parity energy spectra of Nd-isotopes agree well with the experimental data.