Calculator Inputs
Use microscopic or macroscopic cross sections, then estimate mean free path, attenuation, and shielding behavior in one place.
Example Data Table
These illustrative examples help compare trends. Exact values depend on neutron energy, isotope composition, temperature, and the selected interaction cross section.
| Material Target | Density (g/cm³) | Target Atoms | Cross Section (barns) | Approx. Mean Free Path (cm) |
|---|---|---|---|---|
| Hydrogen in Light Water | 1.00 | 2 per H₂O | 20.4 | 0.73 |
| Carbon in Graphite | 1.70 | 1 per C | 4.74 | 2.48 |
| Iron | 7.87 | 1 per Fe | 11.2 | 1.05 |
| Boron-10 in Boron Carbide | 2.52 | 4 per B₄C | 3835 | 0.012 |
| Hydrogen in Polyethylene | 0.94 | 2 per CH₂ | 20.4 | 0.61 |
| Lithium-6 in LiF | 2.64 | 1 per LiF | 940 | 0.17 |
Formula Used
Formula Unit Density: Nf = (ρ × NA) / M
Target Number Density: N = Nf × n × f × p
Macroscopic Cross Section: Σ = N × σ
Mean Free Path: λ = 1 / Σ
Transmission Through Thickness x: T(x) = e-Σx = e-x/λ
Here, ρ is density, M is molar mass, NA is Avogadro’s number, n is target atoms per formula unit, f is isotopic abundance fraction, and p is packing fraction.
If you already know the macroscopic cross section, the calculator skips microscopic conversion and uses λ = 1/Σ directly.
How to Use This Calculator
- Select a preset or type your own material and target isotope details.
- Choose whether you want to enter microscopic or macroscopic cross section data.
- Enter density, molar mass, target atoms per formula unit, isotopic abundance, and packing fraction.
- Enter the sample thickness and choose thickness and output units.
- Press Calculate Mean Free Path to show the result above the form, view the graph, and download CSV or PDF outputs.
FAQs
1) What is neutron mean free path?
It is the average distance a neutron travels before an interaction occurs in a material. A shorter mean free path means interactions are more likely within a smaller thickness.
2) What is the difference between microscopic and macroscopic cross section?
Microscopic cross section describes one target nucleus and is usually given in barns. Macroscopic cross section includes the number density of targets and is given in inverse length units.
3) Why does density affect mean free path?
Higher density usually means more target nuclei per unit volume. That increases the macroscopic cross section and decreases the average distance between neutron interactions.
4) Can I use scattering or absorption data?
Yes. The calculator works with whichever interaction cross section you choose. Just make sure the selected value matches the physical question you want to study.
5) What does isotopic abundance change?
It scales the effective number of target nuclei. Lower abundance means fewer relevant nuclei are present, so the macroscopic cross section becomes smaller and mean free path becomes longer.
6) Why is neutron energy included as a label?
Cross sections often depend strongly on neutron energy. The label helps document whether your chosen value represents thermal, epithermal, fast, or custom conditions.
7) What does transmission through thickness mean?
Transmission is the probability that a neutron passes through the specified slab without the selected interaction. It follows an exponential attenuation model for a uniform material.
8) Is this enough for final shielding design?
No. It is a strong first estimate, but full shielding design also needs spectra, geometry, buildup, secondary radiation, temperature effects, and validated transport calculations.