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 transitional structure. A simplified Hamiltonian is used which is intermediate between the three dynamical symmetries of U(6), namely the spherical U(5), the prolate and oblate deformed SU(3) and the gamma-unstable O(6) limits. The potential energy surfaces (PESs) to the IBM Hamiltonian have been obtained using the intrinsic state formalism which introduces the shape variables beta and gamma. The Gadolinium (Gd) and Ruthenium (Ru) isotopic chains have been taken as examples in illustrating the U(5)-SU(3) and U(5)O( 6) shape phase transitions, respectively. We used the standard chi(2) test to get the IBM Hamiltonian parameters. The fit is performed by minimizing the chi(2) function for some selected experimental low-lying energy levels, the two neutron separation energies and B(E2) transition rates.