# Prompt and Delayed Neutrons

The neutrons emitted within a short interval of 10^{-17} s of the fission process are called 'prompt neutrons', which is about 99% of the fission neutrons. The remaining neutrons are delayed in their emission in the fission process itself and are known as 'delayed neutrons' (Hetrick 1971, Lamarsh 1983, Stacey Weston 2007).

For an example, we can consider the delayed neutron emission from the fission product, isotope Br^{87}, which has a half-life of 55.6 s. The beta decay of Br^{87}, through its two main branches of 2.6 and 8 MeV electrons, leads to the formation of Kr^{87} in its ground state, and it subsequently decays through two successive beta emissions into the stable isotope of Sr^{87}, whereas it is possible for the delayed neutron precursor Br^{87} nucleus to beta decay into an excited state of the Kr^{87} nucleus at an energy of 5.5 MeV, which is larger than the binding energy of a neutron in the Kr^{87} nucleus. In this case, the beta emission is followed by a neutron emission leading to the stable Kr^{87} isotope.

The fraction of delayed neutrons from U^{235} is only p = 0.0065. But it is smaller for Pu^{239} at P = 0.0021. The occurrence of delayed neutrons is crucial for the control of nuclear reactors. Even though the fraction of delayed neutrons is small, their presence provides a long time constant. Hence, it slows down the dynamic time response of a nuclear reactor to make it controllable by the withdrawal and insertion of control rods, containing nuclear absorbing materials such as boron.

The weighted average of the mean lifetime of the delayed neutrons is much larger than that of the prompt neutrons.

## Delayed Neutron Parameters

Consider *N* number of delayed neutron groups (usually taken as 6), then the number of delayed neutrons produced per unit volume in the steady state is (Ghoshal 2010)

where Q *(r*) and are the ith concentration of the beta emitter, which is a precursor of a delayed neutron emitter and a decay constant for the neutron emitter of the *i*th type, respectively.

For steady state, the generated fission products from the fission process are equal to those decaying through radioactive decay, which can be written as

where *w _{{}* is the fraction of fissions, which yields precursors of the ith type.

The total number of prompt and delayed neutrons produced per unit volume per unit time is represented as

where p is the delayed neutrons fraction from fissions.

This p is related to the fraction of neutrons from the fission that is produced by the ith delayed neutron precursor group given by