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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 –
λ1Σλ1Σ, 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=ΣTϕdxdϕ=ΣTϕdx,

with the solution –
ϕ(x)=ϕ0eΣTxϕ(x)=ϕ0eΣTx if ϕ(0)=ϕ0ϕ(0)=ϕ0.

Additional notes

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Principles of nuclear engineering Copyright © 2015 by R.A. Borrelli is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.