Etude de la déformation des noyaux Triaxiaux en utilisant le Hamiltonien de Bohr

Abstract

In this Thesis, we study Bohr Hamiltonian model describing the different nuclear interactions, motions and deformations that the atomic nucleus undergoes. This model is solved by relying on the Nikivorov-Uvarov method and using Kratzer screened potential to determine the energy of the spectrum and the wave function. We apply this model to the isotopes of 126,128,130,132,134Xe and 192,194,196Pt. Indeed, by using the technique of separating variables, we end up with two equations, one of which is a function of the parameter which represents the rotational motion and the equation of the vibrational motion which is a function of the parameter . In order to determine the energy and wave function of the system, the equation containing the _ part is solved using the Nikivorov-Uvarov method. Normalized energy ratios, probabilities of electric B(E2) transitions and quadrupole moments are calculated for each isotope of platinum and xenon. The calculations of the energies in the ground state band, the _ and band are obtained using the selection rules imposed by the Clebsch-Gordan coefficients, i.e., the allowed transitions are those which satisfy the equation Δ_ = ±2. For all the platinum isotopes and some isotopes of 126Xe and 130Xe, it appears that the results obtained by our model are closer to the experimental results than those of the models of Chabab (2015) and Morse (2010). On the other hand, these results are more distant from the experimental results for the isotopes of 128Xe, 132Xe and 134Xe. This shows that our model is better suited for platinum and some xenon isotopes. For the wave function, we also note that for each energy level, the peak of the probability density distribution increases as the angular momentum quantum number increases. Finally, the various results obtained are mostly in good agreement with the experimental data.