Question 4.9: Suppose the volume ratio of coolant to fuel is increased in ......

Part a: The fast fission factor should show a slite decrease, since once neutrons escape the fuel rod in which they were born, the increase in moderator will be more effective in slowing the neutrons down below the energy threshold were fast fission can take place in uranium-238 before they enter another fuel rod. This effect is not included in the simple approximation given by Eq. (4.56)

Part b: The resonance escape probability should increase, since the additional moderator will more effectively slow down neutrons, causing decreased capture in the uranium-238 resonances. This can be seen in Eq. (4.40), since the volume ratio V_f / V_m will decrease, causing p to increase

Part c: The thermal utilization will decrease, since the added moderator will cause added thermal neutron absorption in the moderator. This is indicated in Eq. (4.55) by the increase in V_m / V_f , which causes ƒ to decrease

Part d: As indicated by Eq. (4.49), η_T depends only on fuel cross sections. Thus changes in moderator ratios will have only secondary effects, cause by shifts in the thermal neutron spectrum ,\varphi_f  (E)