Consider a uniform flux of neutrons neutrons $[\frac{\text{:}}{eV*c{m}^2*s}\}$ in an infinite sea of hydrogen, with macroscopic scattering cross section ${}_s(E^{\text{'}})=E^{\text{'}-\frac{1}{2}}.$ Experimental data has shown that the differential scattering probability for neutrons interacting with ${?}^{1}H$ nuclei is given by the formula:

$p(E^{\text{'}}E)=\{\begin{array}{ccc}\frac{1}{E^{\text{'}}}& if& E{E}^{\text{'}}\\ 0& if& E>E^{\text{'}}\end{array}$