Axisymmetric Coulomb Interaction and Research of Its Stability by System Galactica

Joseph J. Smulsky

Institute of the Earth’s Cryosphere, Siberian Branch of Russian Academy of Sciences, Tyumen, Russia.

DOI: 10.4236/oalib.1100773                

Abstract

Indeterministic consideration of micro-world based on quantum mechanics has resulted in its probabilistic understanding. At the same time the study of the micro-world based on Coulomb interactions in some cases gives deterministic view of it. However, at this way it is necessary to solve complex problems of many particles interaction. The program Galactica have to be developed for the numerical solution with high accuracy gravitational problems of many-bodies. The paper considers a modification of the program algorithm for solution of Coulomb interaction. For integrating differential equations of motion, the initial conditions have to be given, which are determined by the geometry of the interacting particles. Since in contemporary physics the atoms geometry is not specified, as an example, their axisymmetric models are studied. They consist of positively charged nucleus and are symmetrically arranged on the plane of the electrons. The necessary tasks were solved to determine positions and velocities of particles at the initial time. Based on their results, the program in environment MathCad for creation of a file of inital conditions is developed. Using the modified program Galactica, the motion of particles in an axisymmetric structure with eight peripheral electrons is researched. It has appeared that they are unstable. For comparison, a similar problem was studied with the gravitational interaction. It also proved to be unstable. So more detailed studies of the problem of stability of axisymmetric structures were made. They showed that the stability of the structure increases with the decrease of the interaction parameters. Such stable structure with eight peripheral bodies is considered for gravitational interaction. The paper also considers an example of a helium atom at axisymmetric interaction with two peripheral electrons. This structure is also unstable. At the same time two-particle interaction on the example of the hydrogen atom, considered using the Galactica, is stable and the results of numerical solutions coincide with the exact analytical solution. The studies showed that the program Galactica can be used to research the Coulomb interactions. The paper shows that axially symmetric structure of the atom can be used to create his other geometries. The developed methods and programs may be used in these studies. In the future, they will increase the degree of determinateness of micro-world. This paper, as well as the book, will be useful to physicists, students, senior pupils and everything who are interested in the scientific worldview. The programs are the free access (http://www.ikz.ru/~smulski/GalactcW/) and can be used for student projects.

Keywords

Coulomb Interactions, The Exact and Numerical Solutions, The Structure of the Atom

Conflicts of Interest

The authors declare no conflicts of interest.

References

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