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22.101 Applied Nuclear Physics (Fall 2004) Due: Oct. 6, 2004 Problem Set No. 4 Problem 1 (a) Using a sketch explain the physical meaning of the angular differential neutron scattering cross section σ (θ ) ≡ dσ / dΩ . (b) Let P(Ω) be the probability distribution defined as P(Ω)dΩ = probability that the scattered neutron goes in the direction dΩ about Ω How would you express σ (θ ) in terms of P(Ω) ? (c) If you were told that the scattering distribution is spherically symmetric, what would you write for σ (θ ) ? Problem 2 Derive the expression for the angular differential scattering cross section σ (θ ) for swave scattering, then obtain the expression for the scattering cross section σ . Problem 3 Calculate the neutron scattering cross section of C12 for thermal neutrons. Assume a potential well with depth Vo = 36 Mev and range ro = 1.4xA1/3 F and consider only the swave contribution. Compare your result with the experimental value ( σ = 5 barns) and discuss any significance.