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Abstract
In this thesis, the cross correlation analysis was used to identify the collective motion in the low lying energy levels of even- even nuclei . this finding was built on linking the collective behavior as a function of parameters of some simple model, e.g. IBM > If a group of nuclei belong to the same symmery group, then levels of the same rank e.g. the nth level of given spin-parity in these nuclei are strongly correlated, since their excitation energies could be evaluated by the same formula but with different values of the model parameters. In the case of IBM, where the level energies linearly depend on the parameters, one even expects a linear relationship between several levels of nuclei belonging to the same symmetry group. in order to achieve this goal, we have proposed some parameters that may help us to understand the collective are the R 4/2 ratio the ratio between lowest 4 to 2 level states in each nucleus. The p-factor is defined as p= N N n + n represents the average number of interactions of each valench nucleon with those of the other type. Finally, we use the quadrupole deformation parameter B2.