Study of Nuclear Structure Properties and Electromagnetic Transitions for even - even Kr , Xe , Nd , Ge Nuclei in the Framework of Interacting Boson Model

        Nuclear structure Properties and electromagnetic transitions of some even - even Kr, Xe, Nd and Ge isotopes have been studied in this work, by using the collective Interacting Boson Model-2 (IBM-2).  The Interacting Boson Model (IBM-2) has been very successful in describing the collective properties of nuclei. This work concerns a systematic applications of the model, involving configuration mixing of bosons. There have been extensive IBM studies of low-lying positive parity bands, which are based on the ground state and the quadrupole degree of freedom.The results for energy levels, B(E2), B(M1), mixing ratios , quadrupole and magnetic dipole moments and monopole transitions, were compared with some previous experimental and theoretical values. It was found that an acceptable degree of agreement between the predictions of the IBM-2 and the experiment can be achieved. The  Kr isotope (Z = 36) lies in the transitional region closer to the vibrational range of nuclei. Energy , levels B(E2), B(M1) and the mixing ratios δ(E2/M1) and X(E0/E2) for selected transitions in this isotope were calculated in the framework of the interacting boson model (IBM-2). All results were compared with experimental data. Some experimental X(E0/E2) ratios were calculated from available experimental data. Majorana parameters were found to have a great effect on the calculated energy levels of the  ,  ,  and  states which indicates they have mixed symmetry properties.The results of IBM-2 for Xe isotopes were compared with the theoretical predictions assuming a critical point symmetry E(5) which leads to conclude that ¹²⁸Xe is not an E(5) isotope as previously suggested. In this case of the ¹²⁸Xe  the observable   is intermediate between the value for E(5)   and gamma soft limit . The ratio suggests that ¹²⁸Xe  should lie between E(5) and O(6). Similar test  using ¹³⁰Xe as a most likely candidate amongst the Xe isotopes, conclusively demonstrate a how well E(5) is realized in the best case. The energy ratio confirmed that this isotope an E(5) critical point symmetry. The ¹³²Xe and  ¹³⁴Xe show vibrational-like character (SU(5) limit. 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   states or at least a fragment of it have been identified in Xe isotopes. This enables us to trace the evolution of the one-phonon  states in the even-even xenon isotopic chain from the vibrators near N = 82 to the γ-soft nuclei towards mid-shell.We have studied the nuclear properties of Neodymium  isotopes with(A =144-154) in IBM-2. A good agreement results with the experimental data.^144-150Nd lie in the transitional region (virational - rotational limit SU(5)→SU(3)). For the ^152-154Nd  isotopes the energy ratio are well described by the rotational limit SU(3).  The X(5)  symmetry would take place when moving continuously from the pure U(5) symmetry to the SU(3) symmetry and it implies a definite relations among the level energies and among the E2 transition strengths. It was recently shown that a signature of phase transition is observed in the chain of Nd isotopes, ¹⁵⁰Nd display the predicted features of the X(5) symmetry and mark therefore the critical point. However, more detailed studies and experiments are needed to get ideas about this signature. At the end, we have concluded that some of  Nd isotopes display X(5) symmetry features. The  and  are mixed symmetry states in Nd isotopes.The even-even isotopes of  germanium are of special interest because of the coexistence of two sets of bands, of very different character, in the lighter  nuclei. The IBM-2 with configuration mixing provides a good description, both of states built on the normal ground state and of those associated with a proton pair excitation across the Z =28 closed-shell gap. Ge  isotopes are studied, ranging from the middle of the neutron shell to very near the doubly closed shell at  ⁸²Ge. Same Hamiltonian is used for all the nuclei studied, with parameters which are constant or smoothly varying.