Reactor Theory and Nuclear Physics
Domain 1 tests the neutron balance of a reactor: how multiplication, delayed neutrons, reactivity, poisons, and temperature feedback determine whether power rises, falls, or holds steady.
Core rules
- Criticality is k_eff = 1. The six-factor formula separates k∞ into fast fission (ε), resonance escape (p), thermal utilization (f), reproduction (η), fast non-leakage (P_FNL), and thermal non-leakage (P_TNL).
- Reactivity ρ = (k_eff − 1)/k_eff, usually in pcm (1 pcm = 10^-5 Δk/k). A positive ρ above the delayed-neutron fraction β (about 650 pcm for U-235) is prompt critical; normal operation stays far below it.
- Negative feedbacks stabilize: Doppler broadening of U-238 resonances responds in milliseconds, moderator temperature coefficient in seconds to minutes, and boron dilution or xenon burnout over hours.
- Xenon-135 is the dominant transient poison; it peaks after a power reduction because iodine-135 decay continues while burnout falls. Samarium-149 is a slower, largely permanent poison.
Worked example
A core has k_eff = 1.005. Then ρ = 0.005/1.005 = 0.004975 = 497.5 pcm, about 500 pcm. If a rod withdrawal adds +300 pcm and boron adds −120 pcm, net ρ ≈ 680 pcm. That is near, but below, a typical U-235 β; confirm the delayed-neutron margin before calling it safe.
Traps
Using ρ = k − 1 misstates reactivity and is wrong at large k. Forgetting to divide by k loses about 0.5% here. Treating xenon as prompt misses the iodine decay peak. Mixing pcm with %Δk/k (1% = 1000 pcm) causes order-of-magnitude errors.