Recursividad en las bases teóricas estructurales de los modelos de la gota liquida y modelo de capas

Abstract

This dissertation is an exhaustive treatment of some fundamentals concepts of Nuclear Physics: Alpha Particles Dispersion Theory, the Semi-empirical Atomic Mass Formula, and the nuclear Density and Radii. Alpha Particles Dispersion Theory was retaken, assuming it would account for the magnitude of the Coulombian nuclear radius and be a conceptual link to the nuclear structure. But nevertheless, the theoretical and numerical analysis done in this work showed that the coulombian cannot be determined through this theory, due that the maximum approach length does not converge, independently of the alpha particle energy. On the other hand, the coulombian nuclear radius can be calculated by recurrence from the associated coefficient to the electric potential energy. An alternative semi-empirical nuclear mass formula is derived. This formula includes 5 terms, which depend on the atomic and mass numbers, to describe the nuclear characteristics experimentally observed. This derivation is based on two constants: one to account for the energy associated to the nuclear volume, and the other to account for the relationship between the nuclear volume and the number of nucleons or mass number. These were accomplished by developing a method to simultaneously calculate four of five formula coefficients. Using these coefficients, the theoretical masses were calculated and compared to the experimental masses for 237 stable isotopes. The average of absolute differences between calculated and experimental masses for the 237 isotopes was 0.00228 u, equivalent to energy of 2.1237 MeV, and the standard deviation is on the order of 0.00259 u = 2.4125 MeV. Even though the absolute differences are similar than those obtained from the Arya coefficients and formula, the magnitude of the standard deviation indicates that, theoretically, the semi-empirical formula does not faithfully consider nuclear forces.