The Greuling–Goertzel and Wigner approximations in the theory of neutron slowing down

The classic Greuling–Goertzel and Wigner approximations for neutron slowing-down problems are reappraised theoretically and numerically. We sketch the standard derivations of these approximations and show that, contrary to conventional wisdom, their theoretical bases are comparable. We also present a new derivation of these approximations, which clarifies the relationship between them and the Fermi age approximation. Finally, we compare numerical solutions of the exact, Greuling–Goertzel, and Wigner equations. These results show that for narrow absorption resonances described by the Breit–Wigner formula, the Wigner solution is significantly more accurate than the Greuling–Goertzel solution.