Which expression correctly defines the diffusion coefficient D in terms of the transport cross-section Σ_tr?

• A. D ≈ 3 Σ_tr
• B. D ≈ 1 / (3 Σ_tr), where Σ_tr = Σ_t - μ̄ Σ_s
• C. D equals Σ_tr
• D. D ≈ 3 Σ_t - Σ_s

Answer: (B)

The diffusion coefficient tells you how fast neutrons spread in the diffusion approximation, which depends on how effectively scattering randomizes their directions. This speed is governed by the transport cross section Σ_tr, not by the total scattering or total extinction alone. The diffusion coefficient is inversely proportional to Σ_tr, with the standard relation D ≈ 1/(3 Σ_tr). The transport cross section itself accounts for angular deflection through Σ_tr = Σ_t − μ̄ Σ_s, where μ̄ is the average cosine of the scattering angle. When scattering is isotropic, μ̄ = 0, so Σ_tr ≈ Σ_t and D ≈ 1/(3 Σ_t). The 3 in the denominator comes from averaging over the three spatial dimensions in the diffusion process. Expressions that make D depend directly on Σ_tr in a linear or different fashion, or mix Σ_t and Σ_s incorrectly, do not reflect how scattering angle deflection controls diffusion.