Moderating Ratio
In a moderator, there is competition between elastic scattering, which produces the desired reduction in energy, and capture, which means the loss of the neutron. The competition depends on the relative magnitudes of the elastic scattering cross section aei and the capture cross section ac. A figure of merit for a moderator is the moderating ratio, defined as
A good moderator is one in which £ and aei are high and ac is low. Properties of various moderators are presented in Table 7.2.10
9 Again, isotropy refers to the center-of-mass system.
10 The moderating ratio should be calculated as an average over the energies of the slowing neutrons.
|
Material" |
A |
£ |
nb |
MR |
|
H |
1 |
1.000 |
14 | |
|
D |
2 |
0.725 |
20 | |
|
H2O |
0.920 |
16 |
71 | |
|
D2 O |
0.509 |
29 |
5670 | |
|
Be |
9 |
0.209 |
69 |
143 |
|
C |
12 |
0.158 |
91 |
192 |
|
238 y |
238 |
0.008 |
1730 |
0.009 |
"Here, H denotes *H and D denotes 2H. bn is the number of collisions to reduce the energy by factor of 2 x 106 [see Eq. (7.9)]. Source : Data are from Ref. [7, p. 324].
"Here, H denotes *H and D denotes 2H. bn is the number of collisions to reduce the energy by factor of 2 x 106 [see Eq. (7.9)]. Source : Data are from Ref. [7, p. 324].
An obvious choice for use as a moderator is hydrogen, in the form of ordinary ("light") water (1H2O). The oxygen in the water is relatively inert, having a very low capture cross section and being much less effective than hydrogen as a moderator. However, ordinary hydrogen has the major drawback of having a large cross section (0.33 b at 0.0253 eV) for the capture reaction n+ 1H ^ 2H + 7.
The moderating ratio for light water, as defined in Eq. (7.11), is 71 (see Table 7.2).
The moderating ratio for heavy water, D2O (2H2O), is almost 100 times greater, despite the larger mass of deuterium.11 This is because the neutron-capture cross section is much less in deuterium than in hydrogen (0.0005 b at 0.0253 eV). It was recognized early in the nuclear weapons programs of World War II that heavy water would be a very valuable substance in reactor development, and considerable effort was devoted to attacking heavy water production facilities in Norway, which were then under German control. The choice between light and heavy water remains unclear, with the former having the advantage of being very easily obtainable and the latter making it possible to use natural uranium as the reactor fuel.
Carbon, in the form of pure graphite, is a more effective moderator than light water, with a moderating ratio of 192, despite the higher A and lower £ for 12C. The reason for this, again, is a low neutron-capture cross section (0.0035 b at 0.0253 eV). However, in contrast to light water and heavy water, graphite cannot be used as a coolant as well as a moderator.
11 The actual moderating ratio for a heavy water reactor depends on the magnitude of the light water impurity in the heavy water.
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