Evolution of shapes in even–even nuclei using the standard interacting boson model

The sd-version of the interacting boson model(IBM) is used to establish the shape phase transitionalstructure. A simplified Hamiltonian is used which is intermediatebetween the three dynamical symmetries ofU(6), namely the spherical U(5), the prolate and oblatedeformed SU(3) and the c-unstable O(6) limits. The potentialenergy surfaces (PESs) to the IBM Hamiltonianhave been obtained using the intrinsic state formalismwhich introduces the shape variables b and c. The Gadolinium(Gd) and Ruthenium (Ru) isotopic chains have beentaken as examples in illustrating the U(5)–SU(3) and U(5)–O(6) shape phase transitions, respectively. We used thestandard v2 test to get the IBM Hamiltonian parameters.The fit is performed by minimizing the v2 function forsome selected experimental low-lying energy levels, thetwo neutron separation energies and B(E2) transition rates.