Breit-Wigner Nuclear Resonance Cross-Section

Resonance Parameters

Preset reaction Resonance energy E₀ (keV)100 Total width Γ (keV)20 Partial width Γₙ/Γ0.50 Angular momentum ℓ0 Background σ_bg (mb)50

At Resonance E₀

σ_peak (mb)—

FWHM (keV)—

Γₙ (keV)—

Γ_reaction (keV)—

Resonance integral (mb·keV)—

Theory

The Breit-Wigner single-level resonance formula gives the cross-section for compound nucleus formation:

σ(E) = σ_bg + λ²(2ℓ+1)(Γₙ·Γᵣ) / [(E−E₀)² + (Γ/2)²]

The peak cross-section can reach 10⁶ × geometric cross-section. This formula, from quantum scattering theory (1936), describes compound nucleus resonances in nuclear reactions and explains why nuclear cross-sections vary wildly with energy.