An increase in the moderator temperature TM leads to a reduction in thermal neutron absorption due to moderator expansion and an increase in resonance absorption due to the moderating power decrease as well. They are described through f and p, respectively. Because the thermal neutron spectrum changes depending on the moderator temperature (spectral shift), there is a variation in the thermal cross sections averaged by the thermal neutron spectrum. This is discussed with n and f.

(1) Moderator temperature coefficient of resonance escape probability

In Eq. (1.58), an increase in the moderator temperature causes a reduction in the moderator atomic density (the moderator volume fraction is constant) and results in a reduction in the resonance escape probability. This means that the resonance absorption of neutrons rises due to the reduction in the neutron moderating power. The moderator temperature coefficient of the resonance escape probability is given by

which shows a negative value. An expansion of the moderator in liquid or gas is described by the relation between the temperature coefficient of atomic density and the linear expansion coefficient as

where the volume expansion coefficient (= 30M) can be used instead of the linear expansion coefficient.

Figure 1.12 shows the volume expansion coefficients of liquid modera­tors. The moderator temperature coefficient of the resonance escape prob­ability is about 10_4Ak/k/K and has a large negative reactivity effect.