NEUTRON LIFE CYCLE
DOE-HDBK-1019/2-93
Reactor Theory (Nuclear Parameters)
Six Factor Formula
With the inclusion of these last two factors it is possible to determine the fraction of neutrons that
remain after every possible process in a nuclear reactor. The effective multiplication factor (keff)
can then be determined by the product of six terms.
keff = f p t f h
(3-3)
Equation (3-3) is called the six factor formula. Using this six factor formula, it is possible to
trace the entire neutron life cycle from production by fission to the initiation of subsequent
fissions. Figure 1 illustrates a neutron life cycle with nominal values provided for each of the
six factors. Refer to Figure 1 for the remainder of the discussion on the neutron life cycle and
sample calculations. The generation begins with 1000 neutrons. This initial number is
represented by No. The first process is fast fission and the population has been increased by the
neutrons from this fast fission process. From the definition of the fast fission factor it is
possible to calculate its value based on the number of neutrons before and after fast fission
occur.
number of fast neutrons produced by all fissions
number of fast neutrons produced by thermal fissions
1040
1000
1.04
The total number of fast neutrons produced by thermal and fast fission is represented by the
quantity No .
Next, it can be seen that 140 neutrons leak from the core before reaching the thermal energy
range. The fast non-leakage probability is calculated from its definition, as shown below.
f
number of fast neutrons that do not leak from reactor
number of fast neutrons produced by all fissions
1040 140
1040
0.865
The number of neutrons that remain in the core during the slowing down process is represented
by the quantity No
f.
NP-03
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