Abstract
Exact solutions have been obtained for several problems in one-velocity neutron transport theory by means of the Wiener-Hopf technique. The basic problem concerns the calculation of the neutron flux and angular distribution at the surface of an infinite, purely absorbing foil or control plate embedded in a moderator. Solutions are obtained for the cases of isotropic and linear anisotropic scattering in the moderator. An approximate solution has been obtained for an infinite lattice of such absorbers by the `end-point method'. Numerical results are compared with those from approximate theories such as P13, double P3 and variational methods. It is found that the double P3 and variational methods are very accurate indeed, whereas the P13 method, which although adequate, shows some unexpected errors for such a high order polynomial approximation. An approximate formula has been developed which allows a certain amount of scattering in the foil; the limitations of this are discussed.
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