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60 CHAPTER 6 Fission product poisoning

10 8
Ratio of lodine to Xenon 6 4

0 2
10 12 10 13 10 14
–2
Neutron flux (#/ cm s)
FIG. 6.1
Ratio of steady-state I-135 to Xe-135.

6.2.5 Xe-135 poisoning
Fission products increase non-fission absorptions. The six-factor formula of reactor
physics permits evaluation of the reactivity loss due to increased non-fission absorp-
tions. The six-factor formula is:

k eff ¼ ηε pf L f L s (6.11)
where

η¼neutrons produced per absorption in fuel
ε¼fast fission factor
p¼resonance escape probability
f¼thermal utilization factor
L f ¼fast neutron non-leakage probability
L s ¼thermal neutron non-leakage probability

The thermal utilization (f), is the term affected by an increase in fission product quan-
tities as follows:

Σ af
f ¼ (6.12)
Σ af + Σ aO
where

Σ af ¼macroscopic cross section for absorptions in fissile material
Σ aO ¼macroscopic cross section for absorptions in all non-fissile material

The presence of fission products alters the thermal utilization as follows:
Σ af
0
f ¼ (6.13)
Σ af + Σ aO + Σ ap
where Σ ap ¼macroscopic cross section for absorptions in fission products.