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Nuclear Shape Phase Transitions Using IBM Applied to Erbium and Ruthenium Nuclei

Abstract

The Hamiltonian of the sd version of the interacting boson model (sd IBM) is written in the consistent-Q-form and used to establish the nuclear shape phase transitional structures. The potential energy surfaces (PES’s) corresponding to the consistent-Q Hamiltonian are obtained by using the intrinsic coherent state formalism which introduces the shape variables \(\beta \) and \(\gamma \). The quadrupole–quadrupole interaction is constructed in terms of a new external factor as a linear function of the total number of bosons. The effect of this factor on the position of critical points is studied. We showed that the critical points take different positions for different choice of this external factor, the larger the factor value the smaller the critical point value. For applications to our model, the Erbium (Er) and Ruthenium (Ru) isotopic chains are taken as an examples in illustrating the U(5)–Su(3) and U(5)–O(6) shape phase transitions respectively. Some selected energy levels and reduced E2 transition probabilities B(E2) for each nucleus are calculated to adjust the model parameters by using a simulated computer search fitting program to fit the experimental data with the IBM calculations by minimizing the root mean square deviation between the experimental energies and reduced electric quadrupole transition probabilities and the calculated ones.

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Ramadan, M., Khalaf, A.M., Kotb, M. et al. Nuclear Shape Phase Transitions Using IBM Applied to Erbium and Ruthenium Nuclei. Phys. Part. Nuclei Lett. 18, 527–539 (2021). https://doi.org/10.1134/S1547477121050095

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Keywords:

  • interacting boson model
  • nuclear shape phase transitions