Calculation of the Energies and the Reduced Electric Quadrupole Transition Probability of Even-Even Isotopes

The property of even-even isotopes have been deduced, were the relation of the moment of inertia as a function of the square of the energy of the emitted photon when the nucleus translate from the state to the state ( back-bending curve) Also the relation of the gamma energy over spin as a function of the spin (E-GOS) have been drawn, these curves indicated that these isotopes have a transition property (SU(3)-O(6), with the X(5) proprety for isotopes. To insure this property the calculation of the energy of different states in the yrast band has been done using the standard relation for the three types of nuclei depending on their property (rotation, and vibration). Knowing the property of these isotopes, the calculation of electric quadrupole transition probability B(E2) has been done using Bohr and Mottelson model and the interacting boson model IBM-1 and compared with the experimental values.