7. Consider a slab cell composed of fuel and moderator, as shown in Figure 5.9, and assume that the net leakage of neutrons is zero at the outer surfaces of the cell, that is, at X = +(4, + Am). Assume that, at some energy E, the diffusion-theory model is valid. a. At that energy, and using the flat-source approximation (5.6.2), find analytical expressions for the escape probabilities Pr(E) and P_(E). b. Show that, in the homogeneous limit where A, and A. go to 0 but A,/J. remains constant, P.(E) = Jim)(E) E.(E) ' P.(E) = Inn( E) E. (E) ' where Enmm)(E) is the total moderator interaction cross section averaged over the entire cell volume, Eur( E) is the analogous total fuel cross section, and E.(E) = ((my(E) - [in( E). fuel moderator zone zone X Figure 5.9 c. For this limiting condition Pr - Pm = 1. Explain physically why Pr - Pm # 1 when A, and Am are large