Calculator Inputs
Example Data Table
The following example is illustrative. Replace it with material-specific reference data for real design or safety work.
| Material | Energy label | σs (barns) | σγ (barns) | σf (barns) | σo (barns) | ρ (g/cm³) | A (g/mol) | Abundance % | x (cm) | Flux (n/cm²·s) | Area (cm²) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Graphite sample | Thermal example | 4.8 | 0.0035 | 0 | 0 | 2.20 | 12.0 | 100 | 2.0 | 1.00e12 | 10 |
| Boron-rich shield | Thermal example | 5.0 | 1200 | 0 | 0 | 2.34 | 10.0 | 100 | 0.5 | 5.00e11 | 12 |
| Fissile fuel case | Thermal example | 10 | 98 | 585 | 3 | 18.9 | 235.0 | 100 | 0.25 | 2.00e13 | 8 |
Formula Used
1) Microscopic totals
σa = σγ + σf and σt = σs + σγ + σf + σo
2) Number density
N = (ρ × NA / A) × abundance fraction
3) Macroscopic cross section
Σ = N × σ × 10⁻²⁴, because one barn equals 10⁻²⁴ cm².
4) Attenuation and transmission
I = I0 × e^(−Σt x), Transmission = I / I0 = e^(−Σt x), and Pinteraction = 1 − e^(−Σt x).
5) Mean free path and rates
λ = 1 / Σt, HVL = ln(2) / Σt, and Rvol = φ × Σ.
This calculator uses a one-speed, narrow-beam attenuation model. It is excellent for teaching, screening, and fast comparisons, but not a replacement for evaluated nuclear data libraries or full transport simulations.
How to Use This Calculator
- Enter a material or isotope name and an energy label so your exported results stay organized.
- Type microscopic scattering, capture, fission, and other cross sections in barns.
- Provide density, atomic mass, isotopic abundance, slab thickness, neutron flux, and exposed area.
- Press Calculate Now to generate macroscopic cross sections, transmission, event probabilities, and reaction rates.
- Use the CSV and PDF buttons above the form to save the displayed result set.
- Load the example values first if you want to learn the workflow before entering real material data.
FAQs
What is a neutron cross section?
It is an effective interaction area that represents the likelihood of a neutron reaction with a nucleus. Larger values mean higher interaction probability for the selected energy and reaction channel.
Why are barns used?
Barns are convenient nuclear units for tiny microscopic areas. One barn equals 10⁻²⁴ square centimeters, which keeps cross-section values readable without long decimal strings.
What is the difference between microscopic and macroscopic cross section?
Microscopic cross section belongs to a single nucleus. Macroscopic cross section scales that value by number density, giving the bulk interaction probability per unit path length inside a material.
Why does neutron energy matter?
Cross sections can change dramatically with neutron energy. Thermal, resonance, and fast neutrons may produce very different reaction probabilities for the same isotope.
What does mean free path tell me?
Mean free path estimates the average distance a neutron travels before interacting. Smaller values indicate stronger attenuation and more frequent collisions within the material.
Can I use this for shielding checks?
Yes, for early comparisons and educational attenuation estimates. Final shielding design should still use evaluated data, buildup treatment, geometry effects, and transport modeling.
Why is isotopic abundance included?
Real materials often contain mixtures of isotopes. Abundance adjusts number density participation for the selected isotope, which changes bulk macroscopic behavior.
Does this calculator replace reactor physics software?
No. It is a compact analytical tool for fast estimates. Detailed reactor or shielding work requires energy-group methods, resonance treatment, geometry modeling, and verified libraries.
Notes for Practical Use
Use cross sections that match the same neutron energy and material state. Mixed temperatures, inconsistent libraries, or mismatched isotopic assumptions can distort the output.