Fergana Polytechnic Institute, Fergana city, Fergana region, Republic of Uzbekistan
ABSTRACT
The paper considers the mathematical analysis of a nuclear reaction with bombarding elementary particles with high and low kinetic energies in the classical form and in the resonant state of a nuclear reaction. At the beginning, the general equation of the nuclear reaction is given, after which an energy analysis is carried out, followed by an analysis of the effectiveness of the reaction under study. The next stage of reaction analysis is the process of determining the effectiveness of the delivered nuclear reaction with the calculation of the nuclear effective cross section, the percentage of current entering the nuclear reaction, as well as the resulting product currents. Theoretical research, in particular, was limited to modeling a charged particle accelerator with high monochromaticity, which made it possible to analyze resonant nuclear reactions. In conclusion, the main conclusions are listed, reflecting the results of a mathematical study of a resonant nuclear reaction.
KEYWORDS
Resonant nuclear reactions, exa-energetic nuclear reactions, endo-energetic nuclear reactions, Coulomb barrier, nuclear effective cross section.
INTRODUCTION
As is known, nuclear reactions formed under the influence of bombardment of charged particles with various kinetic energies have been theoretically and experimentally studied in nuclear physics and elementary particle physics [1—6, 8—9]. But in these studies, the processes themselves are studied separately. In these works, the process of bombarding target nuclei with low-energy and high—energy charged particles on various types of accelerators – from linear accelerators and cyclotrons to synchrophasotrons – has been studied. In the research works carried out, the main attention is focused on the experimental aspect of the study, and the theoretical analysis has not been carried out sufficiently. Therefore, conducting research on nuclear reactions of bombardment of charged particles with different kinetic energies with the conclusion of their effectiveness is relevant.
It is important to note that until now there has not been a single comprehensive model for the analysis of nuclear reactions, which also made it possible to determine a new type of nuclear reactions – resonant nuclear reactions, except for the existing classical exo-energy and endo-energy type reactions, thermonuclear reactions and decay reactions. Hence the need to mathematically determine the resonant state of nuclear reactions on a type of accelerators with high monochromaticity.
MATERIALS AND METHODS
To study the above processes, various theoretical approaches to the analysis and solution of multidimensional physical and mathematical expressions have been selected. The objects of the study were nuclear reactions taking place after bombardment by charged particles of target nuclei with high and low kinetic energies in a classical form, in a resonant state.
RESEARCH
First, we can consider some types of nuclear reactions: reactions with one nucleus and a directed particle, or with two directed particles. Each of these reactions, in turn, is divided into exa-energetic, that is, reactions with a positive reaction yield and endo-energetic, that is, with a negative reaction yield. There are also decay reactions for heavy nuclei. It is also worth agreeing that each of these reactions is considered on the scale of atomic nuclei, since for smaller elementary particles or larger atomic and molecular measures, other special types of reactions take place with lines of interaction between each of the reaction components.
However, in practice, collision reactions on a stationary target of directed particles are most common, which led to a large number of results, however, there are cases when the result of such a collision became nuclei, in turn, disintegrating into component parts. Or, a similar result was observed in a collider collision, that is, when one beam became a target relative to the second and the second became a target relative to the first. This factor led to the fact that these reactions with particle bombardment were also subdivided into instantaneous and composite reactions in addition to the exa-energy and endo-energy types. The thing is that this is determined already from the energy of directed particles, and if it is comparatively large for a particular reaction, along with other constituent moments, from which the time of the reaction itself is determined, then it can pass instantly, forming reaction products, then directed particles literally knock out parts of the products of the nuclear reaction from the composite core [7—10].
For compound reactions, there is an algorithm by which the target merges for a certain time with a directed particle, after which it begins to disintegrate, starting a new formation without taking into account previous impulses. In this case, the decay reaction is included in the reaction of directed particles alone, from which it can be concluded that these two types of nuclear reactions are inextricably linked. But now it is worth moving on to a complete analysis of a definitely given reaction, with appropriate conditions, namely, the reaction (1) itself, its main channel, the masses of all the components of this reaction – M
