Find the ratio $$\frac{E_i}{E_f}$$, where $$E_i$$ and $$E_f$$ are the energies of a neutron before and after interaction with the nuclei of the moderator in a nuclear reactor.

PLACEHOLDER ANSWER - the answer is an expression. For a head-on elastic collision of a neutron with a stationary nucleus of mass $$A$$ times the neutron's, the neutron's speed becomes $$\frac{A - 1}{A + 1}$$ of its initial value. So $$\frac{E_i}{E_f} = \left(\frac{A + 1}{A - 1}\right)^2$$; for example 9 for deuterium ($$A = 2$$) and $$\left(\frac{13}{11}\right)^2 \approx 1.4$$ for carbon ($$A = 12$$). The paper does not say which moderator is used.