= Solution
\b[One energy group and a nearly isotropic local neutron distribution are the main approximations.] The <one-group neutron diffusion equation> replaces the full energy-dependent transport problem by one scalar <neutron flux> and averaged coefficients. A single group cannot resolve spectral changes, resonance absorption or differences between rapidly moving and <thermal neutrons>; its effective parameters depend on the spectrum used for averaging.
The <diffusion approximation> also replaces angular transport by a current proportional to the negative <neutron flux> gradient. It works best where repeated scattering makes the angular distribution nearly isotropic over distances comparable to the field's variation length. It is less reliable close to a sharply localized source, a vacuum boundary, a strong absorber or an abrupt material interface, and in weakly scattering regions. Approximate boundary extrapolation does not restore the lost angular information.
Thus an apparently smooth solution of the <one-group neutron diffusion equation> need not accurately represent a transport field outside the assumptions that produced its coefficients and <boundary conditions>.
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