Все науки. №11, 2023. Международный научный журнал - страница 6

Further, when this value is determined, it is necessary in order to determine which part of all directed particles will actually pass through a nuclear reaction and be able to give a result, the following algorithm is used for this. Let N (x) particles hit the target, and after overcoming the target, the number of particles is N (x) -dN, from where dN is the number of all interactions that occurred in the target. Now, let’s determine that the coordinate at the beginning of the target is x, and at the moment of exit is x+dx, hence dx is the thickness of the target. Then the definition of the concept of the density of the target nuclei is introduced, in order to calculate it, it is necessary to use (20).

This is the number of nuclei present in one cubic meter of the substance used, therefore, based on the definitions and designations introduced, it can be concluded that there are (21) nuclei in the entire target, and if we take into account that the area where the particles enter into interaction, counting as the area of a single case, where it is enough to get one directed particle in order for the reaction to occur, take (14), then for the entire target, these values can be determined according to (22).

Now it is possible to determine the ratio of the entire area, getting to which, it is possible to cause the beginning of the reaction to the entire area of the target, which will be equal to the ratio of the particles that entered the reaction to all particles – functions expressing this value at the initial moment of time, directed initially in the beam (23).

Obtaining such an expression, it is possible to integrate both parts, indicating that the number of particles, as is known, is a function that, according to a certain integral, will take in itself the boundaries from the initial number of directed particles to the number of interactions in the target for the first integral. For the second side, this definite integral has boundaries from zero to the value of the extreme thickness of the target (24—25) [12—18].

For the second integral, the boundaries change, as does the sign of expression (26) with further transformation (27).

From this ratio, an equation can be obtained that would describe the number of particles entering the interaction (28) and from where the percentage efficiency of the nuclear reaction (29) could be calculated.