The Evolution of 174Yb, 176Hf, 178W and 180Os Isotones

The characteristics of 174Yb, 176Hf, 178W, and 180Os isotones are determined, followed by the calculation of their energy states. The first energy states 𝐸21+ and the ratios of the second excited energy states to the first excited energy states𝑅4/2 = 𝐸41 +/𝐸21+ provide primary information regarding the characteristics of the nuclei at low levels. To know the properties of high-energy states of nuclei, the behavior of the ground states band (GSB) studied by determine the back-bending curves which may occur and determine the change in the moment of inertia 2𝜗/ℏ2 and the rotation energy of gamma emitted at different states 2𝜔2, the E-GOS curve which study the gamma energy emitted from each state 𝐸𝐵🁡nd the behavior of the successive energy states in comparison with those states close to them 𝑟 (𝐼+2🀩 are drawn and studied. The relationship between GSB and NPB (the negative parity band) which give the odd staggering ∆𝐼 = 1 curve of each nucleus have been studied and determine the probability of change of the property of 174Yb, 176Hf, 178W, 180Os isotones. We used all of the information from the previous study to calculate the energy states of GSB using the appropriate equations for the different limits of the interacting boson model IBM-1. The interacting vector boson model IVBM was also utilized to compute the GSB and NPB of the isotones 174Yb, 176Hf, 178W, 180Os. A modification of IVBM was introduced to improve the results of calculations.