Slowing-down length, neutron

While 8 is somewhat greater than 1, both p and / are somewhat smaller than 1. Therefore, for approximate calculations, epf can be set 1. The fission factor rj varies appreciably with the energy of the neutrons, as shown in Fig. 11.4 for The neutron losses in a reactor of finite dimensions can be taken into account approximately by the sum L +1 , where Ls is the mean slowing-down length of the fission neutrons in the moderator and L the mean diffusion length in the fuel-moderator mixture. For a spherical reactor of radius R the approximate relation is... 

The linear dependence of the average r u) on r u) is a general result. The constant of proportionality is determined by the source distribution. Thus, in general, the square root of the Fermi age is a measure of the slowing-down length of a neutron. 

Slowing-down length is proportional to the straight-line distance that a neutron covers between the time it is emitted from the source at high energy to the time it reaches a much lower energy (Ellis et al., 2003). 

These effects are illustrated in the sketch on p. 4.46 which is based on some (XINL experiments. Fission neutrons enter the iron from the left. The observed relaxation length of about 9 cm in the iron is probably due to slowing down and absorption of neutrons in the low-energy part of the spectrum. The neutrons which emerge from the iron are predominantly grouped near the "window in the iron cross-section which occurs around 1 Mev. 

There are two particularly simple problems in connection with the energy distribution of neutrons which are present in a medium of finite temperature. In the first problem the slowing down is uniform throughout the entire space which is itself uniformly filled with the slowing down material. In this case the neutron distribution is evidently the same all over space. In the second problem the neutrons enter a half space from one side with uniform intensity and diffuse into it. The question in this case is the density distribution of neutrons at large distances from the boundary plane of the half space and the exponential relaxation length of the neutron density. We shall be interested only in the first problem. 

In these Ut is the density of thermal neutrons multiplied by their velocity, q t) is proportional to the slowing down density t is the age of neutrons, to the age of thermal neutrons, k the multiplication constant, Kf the reciprocal diffusion length of thermal neutrons in the mixture. The above equations were derived by Fermi on the assumption that the number of collisions which a fission neutron suffers before it becomes thermal is the same for all neutrons and that the distance between two collisions is also a well-defined quantity depending only on the energy. 

Migration length is the straight line distance that a neutron travels in its lifetime, that is, while slowing down and diffusing. 

FIGURE 5.14 Slowing-down and diffusion lengths in sandstone, limestone and dolomite for neutrons from an Am-Be-source. Gilchrist (2009). 

To give a more precise physical significance to this "age," we may calculate the second spatial moment of the slowing-down density (see Section II. 3 of "Measurement of Thermal Neutron Diffusion Length in H2O") denoted by... 

---