Etude des propriétés du noyau atomique et de quelques molécules à l’aide de l’équation de klein-gordon

Abstract

n this thesis, the model of Klein-Gordon equation describing the different nuclear interactions, properties and energies of the constituents of the atomic nucleus is studied. This model is solved by relying on the method of Heun’s bi-confluent equations and using the fractional type potential to determine the energy and the corresponding wave function. We apply this model on the constituents of the nucleus such as bottomonium, charmonium and some molecules like HCl, LiH, O2, and H2O. Indeed, by using the method of separating variables, we end up with two equations, one of which is a function of the parameter γ which represents the rotational motion of the particle and the equation of the motion of the particle which is a function of the parameter r. In order to determine the energy and the wave function of the system, the equation containing ther part is solved using Heun’s bi-confluent equation method and we obtain a transcendental energy equation. The energy of the spectrum obtained is a function of the parameters a, b and c which are very important parameters for our potential. The energies is are calculated for each molecule mentioned above, the mass spectrum applied and calculated for the two constituents of the atomic nucleus which are bottomonium and charmonium. The energies of the fundamental level, according to the numbers l and n are calculated. The different theoretical results of our model are compared with the results of the models of Ikot, Ikhdair, Ibekwe and Omugbe. It emerges from these results that the values obtained for our model are better in the case of bottomonium and charmonium because the values of the Sextic energies, of the four-term inverse potential and the values of the standard deviations theoretically obtained are smaller than those of the models of Ikot, IKhdair, Ibekwe and Omugbe. This shows that, the model is better than the one used in the model of Ikot. But on the other hand, for triatomic molecules, the results obtained show that the model is not well suited for the latter. The experimental method for the determination of energies with experienced devices made in Italy at the National Laboratory of Legnaro was carried out for lithium and lead cores. The experiment was performed using a 7Li3+ pulsed beam delivered by an XTU-Tanden accelerator. The reaction between Lithium and Lead was performed at beam energies of 25, 31, 33, 35 and 39 MeV covering the range from the bottom to the top of the Coulomb barrier. To perform the experiment, inside the Ball sector, a cylinder was installed and placed coaxially around the beam to reduce the opening of the active area of the telescope ball, count rate and downtime. In this way, the measurements were taken at the corners of the laboratory. Note also that for each level, the peak of the probability density distribution increases as the angular momentum quantum number increases. In addition, a comparison of the work carried out in the Laboratory on bottomonium and charmonium Ikot, IKhdair, Ibekwe are presented. These different results show that the model is better compared to the different models used by Ikot, IKhdair then Ibekwe. Finally, the various results obtained are mostly in good agreement with the experimental results.