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The properties of 170 Er, 172Yb, 174Hf, and 176Wisotones have been studied and their energy states calculated. To identify the properties of each isotone, the values of the first excited states, E 2 1 + and the ratio of the second excited states to the first excited states, R 4 / 2 = E 4 1 + / E 2 1 + for all nuclei under consideration were adopted. To determine the properties of each nucleus, the relationship between the moment of inertia 2𝜗/ℏ 2 and the square of the angular frequency, ℏ 2 𝜔 2, the relationship between successive excited states to those preceding them r ( I + 2 ) I ) and the ΔI = 1 staggering between the GSB and the NPB states were studied for all states of 170Er, 172Yb, 174Hf, and 176W isotones. After identifying the properties of each isotone, the rotational limit in the interacting boson model IBM-1 and the IVBM model was used to calculate the energy states for each isotone and the results were compared with the experimental values. and good agreement was observed with some exception. The inaccuracy of some calculations in the IBM-1 results from the lying of some high states out the range of the rotational properties that were used.

The properties of even-even158Er, 160Yb and 162Hf isotones are studied and its energy states calculated. To identify the properties of each isotone, the values of the first excited states E 2 1 + and the ratio of the second to the first excited states R 4 / 2 = E 4 1 + / E 2 1 + were adopted. The phenomenon of back-bending, the E-GOS curve and the odd-even staggering were studied. Examining the algebraic structure of the Bohr model (BM) clarified the relationship with the interacting vector boson model (IVBM) and the interacting boson model (IBM) which it has related solvable limits and corresponding dynamical symmetries. BM, IVBM and IBM were used to calculate the energy states for each isotone and compared with the experimental data. The results showed that the BM and IVBM are more comfort than the calculation of IBM-1. The contour plots of the potential energy surface (PES) to the IBM Hamiltonian for Er–Hf with N = 90 have been obtained using the intrinsic coherent state and evolve from deformed shapes to γ- unstable with decreasing the boson number.

The phenomenological description of Barium nuclei which have proton number (56) and neutron numbers 74 and 75 have been calculated by Interacting Boson – Fermion Model. Yrast and excited bad, probability of electric transition B(E2) and potential energy surface have been estimated. The input parameters which are used in the present study the best approximation that has been carried out so far. These calculations show that a good agreement with those of experimental data for Barium nuclei.

In this paper, the nuclear structure of Barium nuclei has been studied by interacting boson model. The properties of eigenstates and reduce probability of electric transition and potential energy surface have been calculated. The nuclei understudy has proton number equal 56 and neutron numbers 75 and 76. The results of energy states and B(E2) values have been compared with the experimental data. These comparisons show that acceptable between the calculations and experimental data. The parameters which used in the calculation have been estimated and give best approximation. The shape of potential energy surface show that the even-even nucleus have O(6) dynamical symmetry.

In this study, the Palladium nuclei have been studied by interacting boson fermion model for even-odd nuclei. The isotopes under study have proton number 46 and neutron numbers 63-67. The calculations involved the eigenstates and reduce electric probability. The calculations show that the energy levels are reasonable with experimental data. The B(E2) values compared with those of experimental and are in good agreements. All calculations compared with experimental and give more data for reader.

The some properties, Energy levels, B(E2) values and potential energy surface, for even-even 122,124Cd isotopes have been studied using the interacting boson model. The predicted levels (energies, spins and parities) and B(E2) values results were reasonably consistent with the experimental data. The contour plot of the potential energy surfaces shows all interest nuclei were deformed and have O(6)-U(5) transition symmetry.

The Hamiltonian is determined in the Interacting Boson Model-1 (IBM-1) frame work for 80Se and 82Kr nuclei. Fit values of parameters are used to construct the Hamiltonian, energy levels, electromagnetic transitions (B(E2) and B(M1)) and multipole mixing ratios (E2/M1) for some even-even Se and Kr nuclei. These properties are calculated. The potential energy surfaces (PESs) to the IBM Hamiltonian have been obtained by using the intrinsic coherent state.

The interacting boson model has been applied to calculate the low-lying positive parity yrast bands in Gd, Dy and Er nuclei for N = 96 neutrons. The results closed to the SU(3) limit in this model. Reasonable agreement with available energies and B(E2) transition rates. The potential energy surfaces (PESs) to the IBM Hamiltonian have been obtained using the intrinsic coherent state.

Energy levels and B(E2) transitions for palladium isotopes with proton number Z=46 and neutron numbers (n) between 57 and 67 have been calculated through the interacting boson-fermion model. The set of parameters used in this calculation is the best approximation that has been carried out so far. Good agreement was found from comparison between the calculated energy levels and the transition probabilities B(E2) with those of experimental.

The energy levels, transition energy, B(E2) values, intrinsic quadrupole moment Q0 and potential energy surface for even-even 184W and 184Os nuclei were calculated using IBM-1. The predicted energy levels, transition energy, B(E2) values and intrinsic quadrupole moment Q0 results are reasonably consistent with the experimental data. A contour plot of the potential energy surfaces shows that two interesting nuclei are deformed and have rotational characters.