The traditional theory of neutron moderation is based on the law of probability of the energy distribution of elastically scattered neutrons in the laboratory coordinate system ("L"--system) (neutron scattering law, for example, [4, 6]), which is based on solving the problem of the kinematic elastic scattering of neutrons by nuclei of the reactor active zone [1 - 6].

resting laboratory coordinate system, which we call the laboratory coordinate system "L";

moving laboratory coordinate system with respect to a constant rate equal to the rate of the thermal motion of the nucleus moderating medium at the neutron scattering, which will be called the laboratory frame "L'".

It should be noted that we consider the special case when the spatial orientation of the coordinate axes of the laboratory coordinate system "L" and "L'" is the same, as well as the radius vector of the start of the laboratory coordinate system "L'" in the laboratory coordinate system "L" coincides with the radius vector of the moderating medium nucleus, at which the neutron scattering in the laboratory coordinate system "L" (that is the moderating medium nucleus in the laboratory frame "L'") is at rest.

2] - the kinetic energy of the neutron, respectively before and after the collision in the laboratory coordinate system "L ",

Now, using the relation between the neutron velocity in the laboratory coordinate system "L'" and the laboratory coordinate system "L" and the ratio (1), the ratio (2) can be given as follows:

From (3) after algebraic manipulations we can find the ratio of the neutron velocity squares before and after interaction with the nucleus in the laboratory coordinate system "L", which is also equal to the ratio of the kinetic energy of the neutrons before and after the interaction:

10] before scattering on a nucleus in the laboratory coordinate system "L", after scattering will have a kinetic energy in the range from [E.

Let x axis, y axis and z axis be parallel to the X axis, Y axis and Z axis of the

laboratory coordinate system respectively (Figure 3), the constant velocity v =([v.

To be explicit, starting from the principal-axis frame, we rotate the coordinate system coincides about the z axis by [alpha], then about the new y axis by [beta], and then about the new z axis by [gamma] so that the rotated coordinate system coincides with the

laboratory coordinate system.