Neutron flux Maxwell-Boltzmann distribution

The so-called cold source neutrons emerge from a small volume ( 20 liters) of liquid deuterium maintained at around 25 K. Thermal neutrons are those moderated usually with heavy water D2O at around 330 K. A block of hot graphite at T 2000 K functions as a source of hot neutrons. The Maxwell-Boltzmann distributions for T = 25, 330, and 2000 K are illustrated in Figure 1.1. The flux, that is, the number of neutrons of velocity v that emerge from the moderator per second is proportional to v times f(v), and therefore in terms of the neutron flux that is available for scattering measurement the distribution is a little skewed in favor of higher v in comparison to that shown in Figure 1.1. 

To specify completely the neutron activity and to choose the proper cross sections for calculating the reaction rate constant, it is necessary to know the distribution of neutron concentration, or neutron flux, with respect to energy. In a thermal reactor the distribution of neutrons in thermal equilibrium with nuclei at an absolute temperature T is similar to the distribution of gas molecules in thermal equilibrium and can be approximated by the Maxwell-Boltzmann distribution... 

Thus, if V is known, the reaction rate is proportional to the total neutron flux (f>. For example, for the commonly encountered Maxwell-Boltzmann distribution of thermal neutrons, v = Iv / fir, where Vp is the most probable neutron speed. 

A useful measure of the flux distortion is provided by the concept of the effective neutron temperature Tn- We define this temperature as that number which when used in (4.197) gives the best least-squares fit of a Maxwell-Boltzmann distribution to the computed flux (solid-line curve) in the range 0 < x < 35. The ratio of the effective neutron temperature to the moderator temperature Tn/Ts is indicated in the figure for the first two cases. The ratio has been omitted from the last case (A = 9, = 2 ) because the flux was so severely distorted from a... 

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