¯
¯
¯
eff
REACTOR KINETICS
DOE-HDBK-1019/2-93
Reactor Theory (Reactor Operations)
NP-04
Rev. 0
Page 12
TABLE 1
Delayed Neutron Fractions for Various Fuels
Group
Half-Life (sec)
Uranium-235
Uranium-238
Plutonium-239
1
55.6
0.00021
0.0002
0.00021
2
22.7
0.00141
0.0022
0.00182
3
6.22
0.00127
0.0025
0.00129
4
2.30
0.00255
0.0061
0.00199
5
0.61
0.00074
0.0035
0.00052
6
0.23
0.00027
0.0012
0.00027
TOTAL
-
0.00650
0.0157
0.00200
The term (pronounced beta-bar) is the average delayed neutron fraction. The value of is
the weighted average of the total delayed neutron fractions of the individual types of fuel. Each
total delayed neutron fraction value for each type of fuel is weighted by the percent of total
neutrons that the fuel contributes through fission. If the percentage of fissions occurring in the
different types of fuel in a reactor changes over the life of the core, the average delayed neutron
fraction will also change. For a light water reactor using low enriched fuel, the average delayed
neutron fraction can change from 0.0070 to 0.0055 as uranium-235 is burned out and
plutonium-239 is produced from uranium-238.
Delayed neutrons do not have the same properties as prompt neutrons released directly from
fission. The average energy of prompt neutrons is about 2 MeV. This is much greater than the
average energy of delayed neutrons (about 0.5 MeV). The fact that delayed neutrons are born
at lower energies has two significant impacts on the way they proceed through the neutron life
cycle. First, delayed neutrons have a much lower probability of causing fast fissions than
prompt neutrons because their average energy is less than the minimum required for fast fission
to occur. Second, delayed neutrons have a lower probability of leaking out of the core while
they are at fast energies, because they are born at lower energies and subsequently travel a
shorter distance as fast neutrons. These two considerations (lower fast fission factor and higher
fast non-leakage probability for delayed neutrons) are taken into account by a term called the
importance factor (I). The importance factor relates the average delayed neutron fraction to the
effective delayed neutron fraction.
The effective delayed neutron fraction
is defined as the fraction of neutrons at thermal
energies which were born delayed. The effective delayed neutron fraction is the product of the
average delayed neutron fraction and the importance factor.
