Neutron Mean Free Path Calculations
The Mean Free Path (λ) of a neutron in a material is given by this equation:
| λ | = 1 / Σ | where Σ is the macroscopic cross section |
| = 1 / Nσ | where N is the atomic density and σ is the microscopic cross section of the material | |
| = 1 / (ρA/m)σ | where ρ is the density, A is Avogadro’s number, and m is the atomic mass of the material | |
| = m / ρAσ |
The microscopic cross sections can be obtained from Los Alamos National Laboratory t2.lanl.gov/nis/data/endf/endfvii.1-n.html or the Korean Atomic Energy Research Institute (KAERI) atom.kaeri.re.kr:8080/ton).
Avogadro’s number is ~6.022 × 1023. A barn is 10−24cm2.
| λ for 14.64 MeV neutrons | ||||
|---|---|---|---|---|
| Material | m | ρ | σ [1] | λ |
| g/cm3 | barns | cm | ||
| Lead | 207.2 | 11.34 | 5.35 | 5.65 |
| Beryllium | 9.01 | 1.85 | 1.49 | 5.43 |
| Lithium | 6.94 | 0.535 | 1.47 | 14.7 |
| Iron | 55.8 | 7.87 | 2.57 | 4.58 |
It’s important to realize that less than half the neutrons will go as far as the mean free path before interacting, because the mean is skewed by the small number that go much further. It is in fact ~36.8% (that is, 1/e) that go at least as far as the mean free path. ~13.5% (1/e2) go at least twice that far, ~5.0% (1/e3) go at least three times that far, and so on.
(e is a mathematical constant, with the value ~2.718.)
[1] See Mean X-section Calculations for sources and calculations.