The quantum shape phase transition between the spherical and deformed γ-unstable ( U ( 5 ) − O ( 6 ) ) 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 ( C 58 122 − 136 e ) 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.
