After averaging the expression (9) over the Maxwell distribution of the thermal motion of nuclei moderating medium (10), considering that [[bar.E].sup.(L).sub.10] = [E.sup.(L).sub.10] and using the well-known result [mathematical expression not reproducible] , we obtain the following expression:
According to the above it is clear that the nature of this peak is associated with the process of slowing down of non-equilibrium system of neutrons, that are emitted by an isotropic source of neutrons on the thermalized system of nuclei of a moderating medium and could not be explained only by a thermalized part of neutron system, i.e., by a thermal equilibrium part of the neutron system and therefore could not be described by Maxwell distribution.
Given that pressure, temperature, and all the other thermodynamic state variables are related to the speed of the gas molecules, recent studies in thermodynamics accent the search of the correct formulation of relativistic Maxwell distribution. At low temperature (low speed), a dilute gas in equilibrium has a velocity distribution that follows the Maxwellian probability density function (PDF):
Interpretations of the heavy ion collision described by the relativistic Langevin equation, the cosmic microwave background radiation caused by hot electron thermalization of inverse Compton scattering (Sunyaev-Zeldovich effect) (Itoh, Kohyama, & Nozawa, 1998), and many other astrophysical phenomena all rely on the relativistic Maxwell distribution function.