 Solution

The production rate is ${\sigma }_{c\mathrm{Th}}\varphi N_{\mathrm{Th}}$, while depletion includes both capture and fission of the fissile population, ${\sigma }_{a\mathrm{U}}\varphi N_{\mathrm{U}}$. Thus the conversion ratio in this stipulated model isAt zero instantaneous flux this expression describes the limiting ratio of the two reaction rates. The total absorption coefficients are $a=3.08+0.02=3.10\mathrm{b}$ and $b=7.10+57.10=64.20\mathrm{b}$, soIt is below one: fissile nuclei are initially removed slightly faster than this simplified chain replaces them. Consequently this model is not initially self-replacing in fissile inventory. Inventory replacement is distinct from the instantaneous neutron balance that determines criticality.