Volume 22: Pages 268-287, 2009
The dynamic bi-Laplacian equation in polar coordinates and the magic numbers of atomic nucleus
G. Bellotti 1
1Via S. Gaudenzio 14/C, 10015 IVREA (TO), Italy
The logic of the research is a new conception of a dynamic bi-Laplacian equation that contains more information than Schrödinger equation. In fact, by solving the dynamic bi-Laplacian equation in polar coordinates it is possible to gain three different sets of solutions, whereas by solving Schrödinger equation with the Laplacian only one set of solutions can be obtained. Moreover Schrödinger equation is contained in the dynamic bi-Laplacian equation. In order to confirm the high potential informative of the dynamic bi-Laplacian equation, the magic numbers (2, 8, 20, 50, 82, and 126) of the atomic nucleus have been calculated. The model simulates the atomic nucleus as a superimposition of electromagnetic spherical standing waves (equivalent in first approximation to an electrically charged spherical solid body of radius r0) and uses the bi-Laplacian operator in order to develop the mathematical problem. It is notable that the resolution of the angular part of the dynamic bi-Laplacian equation shows the presence of three different solutions related to the magnetic quantum numbers m=±2 and of two different equations related to the other values of m. This result modifies the number of associated equations to each shell 1d, 2d, 1f, 3d, 1g, and 2f in comparison with the nuclear shell model. So the proposed nuclear solid model allows to get the magic numbers of atomic nucleus just summing up the number of associated equations to each shell. Moreover in Appendix B some basic considerations and intuitions are shown in order to develop a complete relativity theory that, beside Einstein’s postulate of the light speed insurmountable limit, considers a further postulate valid for the very low speeds, stating that under a limit-speed u0 a particle cannot move. This would allow to consider such minimal speed u0 the equivalent of a void speed; so the particle moving by this speed can be considered physically still. Finally, it was possible to obtain the transformation equations (similar to the Lorentz transformations) for the complete relativity. The complete relativity theory allows to obtain some interesting results, i.e., a maximum mass for a particle that moves with the light speed (for the electron to the maximum mass corresponds to an energy of 220.0 MeV), a minimum finite value for the length contraction measured along the motion direction for a physical object that moves with the light speed, and the possibility to study the particles and the matter as a superimposition of electromagnetic spherical standing waves.
Keywords: Dynamic Bi-Laplacian Equation, Atomic Nucleus, Magic Numbers, Polar Coordinates, Complete Relativity, 220 MeV
Received: March 28, 2008; Accepted: April 29, 2009; Published Online: July 14, 2009