Etude des états déformés des noyaux de platine à l’aide de la mécanique quantique supersymétrique

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 Super symmetric quantum mechanics method and using the Hulthen plus Sreened Kratzer potential to determine the energy of the spectrum and the wave function. We apply this model to the isotopes of 192,194,196 Pt. 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 γ . In order to determine the energy and wave function of the system, the equation containing the β part is solved using the Super symmetric quantum method. Normalized energy ratios, probabilities of electric B(E2) transitions and quadrupole moments are calculated for each isotope of platinum . The calculations of the energies in the ground state band, the β and γ band are obtained using the selection rules imposed by the Clebsch-Gordan coefficients, i.e., the allowed transitions are those which satisfy the equation ∆α = ±2. For all the plati- num isotopes it appears that the results obtained by our model are found to be in good agreement with experimental data and improved in comparison with predictions from Morse and killingbeck plus Morse potential. This shows that our model is better suited for platinum. 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 num- ber increases. Finally, the various results obtained are mostly in good agreement with the experimental data.