9 Neutron attenuation
If a flux of neutrons (ϕ0ϕ0) is impinged on a target, some neutrons will interact with the medium, but many will pass through with a resultant flux (ϕϕ) on the other side.
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The probability that the neutrons interact with the medium is the cross section (σσ).
If the macroscopic cross section is defined as –
Σ=ρNAAΣ=ρNAA, the units of the quantity are in 1cm1cm.
Then, the mean free path can be defined as –
λ≡1Σλ≡1Σ, which are in units of cmcm.
The mean free path then can be considered as the expected value of the distance a neutron travels between interactions.
To solve for flux, it should be intuitive that the resultant flux will be less than the initial flux –
−dϕ=ΣTϕdx−dϕ=ΣTϕdx,
with the solution –
ϕ(x)=ϕ0e−ΣTxϕ(x)=ϕ0e−ΣTx if ϕ(0)=ϕ0ϕ(0)=ϕ0.
Additional notes