Class CrossSection

java.lang.Object
org.episteme.natural.physics.nuclear.CrossSection
public class CrossSection extends Object
Nuclear reaction cross-section models. Cross-section measures probability of nuclear reactions. Units: barns (1 barn = 10⁻²⁴ cm²)
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Field Details

    • BARN

      public static final Real BARN
      1 barn in m²

    • U235_FISSION

      public static final Real U235_FISSION
      Uranium-235 fission σ_f = 584 barns

    • U238_CAPTURE

      public static final Real U238_CAPTURE
      Uranium-238 capture σ_c = 2.68 barns

    • CD113_CAPTURE

      public static final Real CD113_CAPTURE
      Cadmium-113 capture σ_c = 20,600 barns

    • B10_ALPHA

      public static final Real B10_ALPHA
      Boron-10 (n,α) σ = 3840 barns

    • H1_CAPTURE

      public static final Real H1_CAPTURE
      Hydrogen capture σ = 0.332 barns

  • Constructor Details

    • CrossSection

      public CrossSection()

  • Method Details

    • geometric

      public static Real geometric(int massNumber)
      Geometric cross-section for a nucleus. σ = π r² where r = r₀ A^(1/3)
      Parameters:
      massNumber - A = Z + N
      Returns:
      Cross-section in m²

    • breitWigner

      public static Real breitWigner(Real energy, Real resonanceEnergy, Real width, Real peakCrossSection)
      Breit-Wigner resonance cross-section for compound nucleus formation. σ(E) = σ₀ * (Γ/2)² / [(E - E₀)² + (Γ/2)²]
      Parameters:
      energy - Incident energy
      resonanceEnergy - Eâ‚€ - Resonance peak energy
      width - Γ - Resonance width (FWHM)
      peakCrossSection - σ₀ - Peak cross-section
      Returns:
      Cross-section at given energy

    • oneOverV

      public static Real oneOverV(Real thermalCrossSection, Real energy)
      1/v law for thermal neutron capture. σ(E) = σ₀ * sqrt(E₀/E)
      Parameters:
      thermalCrossSection - σ₀ at thermal energy (E₀ = 0.0253 eV)
      energy - Neutron energy in eV
      Returns:
      Cross-section at given energy

    • reactionRate

      public static Real reactionRate(Real crossSection, Real flux)
      Calculates reaction rate per target nucleus. R = n * v * σ where n is projectile density, v is velocity
      Parameters:
      crossSection - σ in m²
      flux - φ = n*v in particles/(m²·s)
      Returns:
      Reaction rate per target nucleus per second

    • meanFreePath

      public static Real meanFreePath(Real crossSection, Real numberDensity)
      Mean free path for neutron in material. λ = 1 / (n * σ) where n is number density of targets
      Parameters:
      crossSection - σ in m²
      numberDensity - n in atoms/m³
      Returns:
      Mean free path in meters