This factor is determined by the probability that fission reaction will occur times the average number of neutrons produced per one fission reaction. In the case of fresh uranium fuel we consider only one fissile isotope 235U and the numerical value of η is given by following equation:
in which ν is the average neutrons production of 235U, N5 and N8 are the atomic number densities of the isotopes 235U and 238U (when using other uranium isotopes or plutonium the equation is modified in a trivial way). This equation can be also written in terms of uranium enrichment:
Reproduction factor as a function of the uranium enrichment
where e is the atomic degree of enrichment e = N5/(N5+N8). The reproduction factor is determined by the composition of the nuclear fuel and strongly depends on the neutron flux spectrum in the core. For natural uranium in the thermal reactor η = 1.34. As a result of the ratios of the microscopic cross sections, η increases strongly in the region of low enrichment fuels. This dependency is shown on the picture. It can be seen there is the limit value about η = 2.08.
Table of key prompt and delayed neutrons characteristics.
Most of the neutrons produced in fission are prompt neutrons. Usually more than 99 percent of the fission neutrons are the prompt neutrons, but the exact fraction is dependent on certain nuclide to be fissioned and is also dependent on an incident neutron energy (usually increases with energy).
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library
It is known the fission neutrons are of importance in any chain-reacting system. Neutrons
trigger the nuclear fission
of some nuclei (235U
or even 232Th
). What is crucial the fission of such nuclei produces 2, 3 or more free neutrons
But not all neutrons are released at the same time following fission. Even the nature of creation of these neutrons is different. From this point of view we usually divide the fission neutrons into two following groups:
- Prompt Neutrons. Prompt neutrons are emitted directly from fission and they are emitted within very short time of about 10-14 second.
- Delayed Neutrons. Delayed neutrons are emitted by neutron rich fission fragments that are called the delayed neutron precursors. These precursors usually undergo beta decay but a small fraction of them are excited enough to undergo neutron emission. The fact the neutron is produced via this type of decay and this happens orders of magnitude later compared to the emission of the prompt neutrons, plays an extremely important role in the control of the reactor.
See also: Prompt Neutrons
See also: Delayed Neutrons
See also: Reactor control with and without delayed neutrons – Interactive chart
The numerical value of η
does not change with core temperature over the range considered for most thermal reactors. There is essentially small change in η
over the lifetime of the reactor core (decreases).This is due to the fact there is a continuous decrease in ΣfU
, but on the other hand this decrease is partially offset by the increase in ΣfPu
. As the fuel burnup increases, the 239Pu
begins to contribute to the neutron economy of the core.
See also: Nuclear Breeding
There are significant differences in reproduction factors between fast reactors and thermal reactors. The differences are in both the number of neutrons produced per one fission and, of course, in neutron cross-sections, that exhibit significant energy dependency. The differences in cross-sections can be characterized by capture-to-fission ratio, which is lower in fast reactors. Furthermore, the number of neutrons produced per one fission is also higher in fast reactors than in thermal reactors. These two features are of importance in the neutron economy and contributes to the fact the fast reactors have a large excess of neutrons in the core.