Elementary Source in Infinite Media

The appropriate differential equations for the neutron-diffusion problem in rectilinear coordinates is obtained from (5.51) and takes the form 

The constant B is evaluated by applying the special boundary condition (5.59). In the present situation, the source is isotropic therefore, exactly one-half the neutrons must be released to each side. Thus, 

We compute J x) from (5.10) and note that this is the specialization of (5.516) to the present problem. Substitution of this result into (5.77) yields, in taking the limit as x —+ 0, 5 = Lgo/2Z). The solution t=o 

This expression gives the spatial distribution of neutrons in an infinite medium with a plane isotropic source (see Fig. 5.11). 

As before, it is required that A s 0 so as to satisfy boundary condition (5.72a). The constant B is determined by the condition on the source strength. If denotes the rate of neutron emission from the origin (neutrons per unit time), then the total net outflow of neutrons from the source is given by the limit of the product of the net current in the radial direction and the area of a sphere as the radius r — 0. Thus 

---