Structure Evolution in the even-even Ba nuclei with IBM

 The nuclear structure  and electromagnetic transitions of even–even neutronrich 120–148Ba isotopes was studied in the framework of the collective models Interacting Boson Model (IBM-1 and IBM-2) and Dynamic Deformation Model (DDM). The reduced transition probabilities B(E2), B(M1), monopole matrix element )0(E , mixing ratio )1/2( ME  and )2/0( EEX  of these isotopes was calculated. A set of parameters was used in the calculation to approach the values with the measured data. It was pointed out that Interacting Boson Model (IBM-1 and IBM-2) are equitably reliable for the description of spectra and other nuclear properties. It was found that there is a rapid transition between spherical and rotational shapes. In this work, we depend on new methods to evaluate the effective  charges for proton and neutron boson )(e and  )(e, and new method to calculate the gyromagnetic ratio for proton boson )(g  and   )(g  Mixed symmetry states are also studied. It is found that some of the mixed symmetry states with moderate high spins change very fast with respect to the Majorana interaction. Under certain conditions, they become the yrast state or yrare state. These states are difficult to decay and become very stable. This study suggests that a possible new mode of isomers may exist due to the special nature in their proton and neutron degrees of freedom for these isotopes. The mixed-symmetry 3 ,2 4,213 and ,1states or at least a fragment of it have been identified in Ba isotopes. This enables us to trace the evolution of the one-phonon and two-phonon states in the even-even barium  isotopic chain from the γ-soft nuclei near N = 82 to the deformed nuclei towards   mid-shell. The Dynamic Deformation Model (DDM) of Kumar and Baranger is employed for studying variations of the nuclear structure of light 120-140 Ba isotopes.The potential energy surface parameters have been calculated and the low-lyingn levels spectrum is predicted along with the static and transition E2 moments.Comparison with experiment data and with other theories supports the validity of our treatment. The recent developments of the dynamic deformation model (DDM) make it readily applicable to a wide range of nuclei in periodic table. We study of the even-mass barium isotopes from N= 64 to the closed neutron shell at N= 84. Within this region there is experimental evidence for nuclei with the characteristics of  soft level sequences. We show that the DDM model is well able to account for these features as typified by energy levels, electric quadrupole vibrational, rotational or moments and gamma transition probabilities across this region when the only parameter which changes is the neutron number. For comparison the experimental data were also fitted to IBM-2 and the results from these fits are in general in good agreement with those from the DDM.