Question 3.9: In most atoms, the radius of a neutron is about 10,000 times......
In most atoms, the radius of a neutron is about 10,000 times smaller than the radius of the nucleus. Using this fact and the results presented in the previous problem(s), derive an expression for the total scattering cross section of a neutron elastically scattering off of an atomic nucleus of radius R.
In the previous problem, we learned that the total elastic scattering cross section for the neutron was σ_s = π(r + R)^2. In the case when r ≪ R, the expression for the scattering cross section reduces to σ_s = πR^2, where R is the radius of the atomic nucleus. This scattering cross section is sometimes called the scattering cross section for potential scattering, and it is used extensively in other nuclear engineering textbooks (see, e.g., Reference 8) to calculate the scattering rate.