Neutron Flux in a sub-critical reactor

[Oxlade]

Hi everyone,

I am supposed to derive the neutron flux equation provided for region A of my reactor. Just wondering if anyone can help me out since I stuck on the derivation for [1/r - 1/R2]; S/4πD aspect is very similar to a solving the constant for a point source spherical reactor

Here is my reactor diagram consisting of nested spheres (sorry, this is my first time posting):

Sphere 1 --> Lead target with radius of R0 (Target-region)
Sphere 2 --> Actinide Fuel surrounding lead target; has outer radius of R1 (A-region)
Sphere 3 --> Reflector surrounding the fuel with outer radius of R2 (E-region)

Neutron Flux vanished at R2 and the flux at A-region is given as:

Φ(r) = S/4πD [1/r - 1/R2]My attempts at deriving this equation always leaves me with exponential terms if I'm assuming I'm solving the diffusion equation for a finite spherical reactor with a point source. Can anyone help me?

 

[Astronuc]

Assuming symmetry, the current at the center of the Pb is zero. The current at the boundaries/interfaces on one side must equal that on the other side.