Fermi Age Theory and Elementary Solutions

The slowing-down diffusion relations which are to be reduced are given by (6.5) and (6.6). The corresponding relations for the time-dependent one-velocity flux distribution are 

The neutron-absorption cross section Sa and the diffusion coefficient D are defined for the one-velocity v specified by the problem. The function n(Tyi) is the corresponding neutron density and is expressed in neutrons per unit volume. The two differential equations (6.5) and (6.7) may be written in terms of a single function by applying the coupling relations (6.6) and (6.8). If we omit the source term, the results are 

Note that q(r,u) is the slowing-down density for a system which includes absorption represented by the cross section 2a and that the exponential 

These equations reduce to the standard form of the heat-conduction equa- 

The calculation to be performed first is the determination of the slow-ing- lown density of neutrons that originate from a plane isotropic source. We specify that the source emits neutrons of lethargy zero (corresponding to some high energy) at the rate go neutrons per unit area per unit time. This problem is clearly one-dimensional, and, for convenience, we place the source plane at the origin of the x axis. The appropriate differential equation is obtained from (6.17). 

---