Flux attenuation, given interaction cross section

[thefury]

It strikes me that this may well be fairly easy, but i can't quite get my head round the correct way to lay this problem out (at least in a mathematical sense).

If you are considering a neutron flux onto a fully understood material, and you also know the neutron interaction cross section of the target object and the flux of the incoming neutrons, should it be possible to calculate the out going flux (i.e. on the reverse side of the target) ?

I'm guessing that the cross section and the number density of the atoms in the target will give you an effective target size, from which you could calculate a probability of interaction (i think?). Then this may be a simple task to apply to a given flux through a material of selectable thickness to give a final flux and/or number of neutrons that should have interacted with the material.

any help would be appreciated, i think i just need a good nudge in the right direction.

 

[Bob S]

Here is an example.

10 MeV neutrons on aluminum target. Cross section (n,total) is ~ 2 barns per atom.

σ = 2 barns per atom = 2 x 10^-24 cm² per atom
N₀ = 6 x 10²³ atoms per mole (Avagradro's number)
A = 27 grams per mole (atomic weight)
D = 2.7 grams/cm³ (density)
μ = attenuation coefficient (cm^-1)

μ = σN₀D/A = 0.12 cm^-1

If the incident neutron flux is F₀, the flux at penetration x is

F(x) = F₀ e^-μx

Bob S