Applications of the Kernel Method

Consider, therefore, an isotropic point source of fast neutrons in an infinite medium. If denotes the macroscopic scattering cross section of the fast source neutrons, and the source releases go neutrons per unit time, then the density of first-scattering collisions at radial distance r from the source is given by 

Number of neutrons available at surface of sphere of radius r 

We use this quantity as the source term in the diffusion equation thus, for a spherically symmetric system, 

The solution to this equation may be obtained by the application of the kernel method. The general solution is given by (5.97). In the present case the source distribution S(t) is given by the right-hand term of 

It is difficult to compare (5.259) with (5.84) directly. However, a measure of the relative spread of the two functions may be obtained by comparing in the two cases the mean square distance from the source point to the point of absorption (as thermal neutrons) that is, we calculate in the two cases 

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