# σ θ

```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.
```