Question 3.10: A common expression for the radius of an atomic nucleus is R......
A common expression for the radius of an atomic nucleus is R = 1.25 A^{1/3} × 10^{−13} cm, where A is the atomic mass number (i.e., the number of protons and neutrons the nucleus contains). Use this equation to derive the potential scattering cross section for a neutron from the nucleus of a carbon-12 atom.
In the previous problem, we learned that the total elastic scattering cross section can be found from σ_s = πR^2, where R is the radius of the atomic nucleus. Since R = 1.25 A^{1/3} × 10^{−13} cm, another expression for the elastic scattering cross section is
\sigma_{s}=\pi\mathrm{R}^{2}=4.9~~\mathrm{A}^{2/3}\times10^{-26}\mathrm{cm^{2}}.
In the case of Carbon-12, A = 12, so σ_s = πR^2 = 4.9 A^{2/3} × 10^{−26} cm^2 = 0.259 × 10^{−24} cm^2 = 0.259 barns, where 1 barn = 1 × 10^{−24} cm^2. The use of the barn as a unit of neutron scattering is discussed in more detail in the next chapter.