Kostenloser Nuclear Cross Section Rechner
Berechnen Sie macroscopic cross section und mean free path aus microscopic cross section und material properties.
Macroscopic Cross Section (Sigma)
28.3880 1/cm
Macroscopic Cross Section (Sigma) vs Microscopic Cross Section (sigma)
Formel
## 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.
Lösungsbeispiel
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
Häufig Gestellte Fragen
What is a barn?
A barn (b) = 10⁻²⁴ cm² is the standard unit for nuclear cross sections. The name comes from the phrase "as big as a barn" because early nuclear physicists found certain cross sections surprisingly large.
Why does cross section vary with neutron energy?
Nuclear interactions depend on the relative energy between neutron and nucleus. At thermal energies, many fissile isotopes have large cross sections that follow a 1/v law. At higher energies, resonances create sharp peaks and valleys.
What is mean free path?
The average distance a neutron travels between interactions. Short mean free path means high reaction probability. In U-235 fuel, the fission mean free path is only fractions of a centimeter.
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