Four different methods are used to study the neutron slowing down and
to evaluate the neutron resonance escape probability in an infinite ho
mogeneous medium containing a heavy resonant nuclide [U238] and a ligh
t moderator nuclide [H]. Two statistical methods use the Monte Carlo s
imulation and two deterministic methods are based on the numerical sol
utions of the neutron slowing down equation and a corresponding adjoin
t equation with an appropriate adjoint source. This study has been don
e for several dilutions and for two neutron source energies (E-s = 676
.45 eV and E-s = 2 MeV). The cut-off energy is placed at 2.77 eV. We h
ave found that the direct numerical solution of the neutron slowing do
wn equation does not agree with the other three methods. In order to e
liminate this disagreement, we have taken account of some corrections
concerning the hydrogen cross-section in the thermal region. (C) 1997
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