Fick's Law Diffusion HW

1. Nov 19, 2013

afung

The problem of the hw states:

Mono-energetic sources of neutrons emitting S neutrons/cm3 are distributed throughout an infinite moderator with diffusion coefficient, D (cm), and absorption cross section Ʃa (cm-1)

Show that the neutron flux in the moderator is given by:

$\Phi$ = S/Ʃa

I know that the Diffusion equation is

dn/dt = S - Ʃa$\Phi$ + D$\nabla$2$\Phi$

For Steady-State the equation becomes

0= S - Ʃa$\Phi$ + D$\nabla$2$\Phi$

and $\nabla$J =0 if space independent thus giving the following equation as

dn/dt = S - Ʃa$\Phi$

So, my question to this problem is can you assume the following diffusion equation to be steady state and space independent to get this:

$\Phi$ = S/Ʃa ? or do I need to consider other variables?