Reactor Theory (Nuclear Parameters)
DOE-HDBK-1019/2-93
NEUTRON LIFE CYCLE
TABLE 1
Average Number of Neutrons Liberated in Fission
Fissile Nucleus
Thermal Neutrons
Fast Neutrons
n
h
n
h
Uranium-233
2.49
2.29
2.58
2.40
Uranium-235
2.42
2.07
2.51
2.35
Plutonium-239
2.93
2.15
3.04
2.90
In the case where the fuel contains several fissionable materials, it is necessary to account for
each material. In the case of a reactor core containing both uranium-235 and uranium-238, the
reproduction factor would be calculated as shown below.
(3-2)
h
N
U 235
s
U 235
f
n
U 235
N
U 235
s
U 235
a
N
U 238
s
U 238
a
Example:
Calculate the reproduction factor for a reactor that uses 10% enriched uranium fuel. The
microscopic absorption cross section for uranium-235 is 694 barns. The cross section
for uranium-238 is 2.71 barns. The microscopic fission cross section for uranium-235 is
582 barns. The atom density of uranium-235 is 4.83 x 1021 atoms/cm3. The atom density
of uranium-238 is 4.35 x 1022 atoms/cm3. n is 2.42.
Solution:
Use Equation (3-2) to calculate the reproduction factor.
h
N
U 235
s
U 235
f
n
U 235
N
U 235
s
U 235
a
N
U 238
s
U 238
a
4.83 x 1021
atoms
cm3
582 x 10
24cm2
2.42
4.83 x 1021
atoms
cm3
694 x 10
24cm2
4.35 x 1022
atoms
cm3
2.71 x 10
24cm2
1.96
Rev. 0
NP-03
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