Free Nuclear Cross Section Calculator
Calculate the macroscopic cross section from microscopic cross section and atom number density for nuclear reactions.
Macroscopic Cross Section (Sigma)
28.3880 1/cm
Macroscopic Cross Section (Sigma) vs Microscopic Cross Section (sigma)
Nuclear Reaction Cross Section
The macroscopic cross section combines the probability of a single nucleus interacting (microscopic cross section) with the number of target nuclei per volume.
Formulas
N = rho × NA / A (atom number density)
Sigma = N × sigma (macroscopic cross section)
Lambda = 1 / Sigma (mean free path)
where sigma is in barns (1 barn = 10⁻²⁴ cm²), NA = 6.022 × 10²³/mol.
Example Calculation
U-235 (sigma_f = 580 barns, density 19.1 g/cm³, A = 235).
- 01N = 19.1 × 6.022 × 10²³ / 235 = 4.89 × 10²² atoms/cm³
- 02Sigma = 4.89 × 10²² × 580 × 10⁻²⁴ = 28.38 cm⁻¹
- 03Mean free path = 1 / 28.38 = 0.0352 cm
Frequently Asked Questions
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