NEUTRON LIFE CYCLE
DOE-HDBK-1019/2-93
Reactor Theory (Nuclear Parameters)
Example:
Calculate the thermal utilization factor for a homogeneous reactor. The macroscopic
absorption cross section of the fuel is 0.3020 cm-1, the macroscopic absorption cross
section of the moderator is 0.0104 cm-1, and the macroscopic absorption cross section of
the poison is 0.0118 cm-1.
Solution:
f
S
U
a
S
U
a
S
m
a
S
p
a
0.3020 cm
1
0.3020 cm
1
0. 0104cm
1
0. 0118cm
1
0.
932
Reproduction Factor, (
h
)
Most of the neutrons absorbed in the fuel cause fission, but some do not. The reproduction factor
(h) is defined as the ratio of the number of fast neurtons produces by thermal fission to the number
of themal neutrons absorbed in the fuel. The reproduction factor is shown below.
h
number of fast neutrons produced by thermal fission
number of thermal neutrons absorbed in the fuel
The reproduction factor can also be stated as a ratio of rates as shown below.
h
rate of production of fast neutrons by thermal fission
rate of absorption of thermal neutrons by the fuel
The rate of production of fast neutrons by thermal fission can be determined by the product of the
fission reaction rate (Sf
u
fu) and the average number of neutrons produced per fission (n). The
average number of neutrons released in thermal fission of uranium-235 is 2.42. The rate of
absorption of thermal neutrons by the fuel is Sa
u
fu. Substituting these terms into the equation
above results in the following equation.
h S
U
f
f
U
n
S
U
a
f
U
Table 1 lists values of n and h for fission of several different materials by thermal neutrons and
fast neutrons.
NP-03
Rev. 0
Page 6
