Quantum entanglement of SO(6)-U(5) transitional nuclei in the interacting boson model-2 (IBM-2)

The quantum shape phase transition between the spherical and deformed γ-unstable ($U\left(5\right)-O\left(6\right)$) even-even nuclei within the frameworks of Interacting Boson Model-1 and 2 (IBM-1,2) for low-lying states, using the “entanglement entropy” (S) has been studied. In both frameworks, the theoretical results showed that there exist minimum and maximum entanglement values between s bosons in the U(5) and O(6) limits, respectively. In order to confirmation of the theoretical results, we have calculated and analyzed the entanglement entropy of $s-d$ bosons and proton (π) - neutron (ν) bosons in Cerium (${}_{58}{}^{122-136}Ce$) isotopes. The results indicate that the entanglement entropy correctly describes the transition from U(5) to O(6), for ground state ($0_1^{+}$), but it cannot accurately determine the transitional nucleus.