## Prompt and Delayed Neutrons

It is known the fission neutrons are of importance in any chain-reacting system. Neutrons trigger the nuclear fission of some nuclei (^{235}U, ^{238}U or even ^{232}Th). 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.

## Key Characteristics of Prompt Neutrons

- Prompt neutrons are emitted
**directly from fission**and they are emitted within very short time of about**10**.^{-14}second

- Most of the neutrons produced in fission are prompt neutrons –
**about 99.9%**.

- For example a fission of
^{235}U by thermal neutron yields**2.43 neutrons**, of which 2.42 neutrons are prompt neutrons and 0.01585 neutrons are the delayed neutrons.

- The production of prompt neutrons slightly increase with incident neutron energy.

- Almost all prompt fission neutrons have
**energies between 0.1 MeV and 10 MeV**.

- The mean neutron energy is about
**2 MeV**. The most probable neutron energy is about**0.7 MeV**.

- In reactor design
**the prompt neutron lifetime**(PNL) belongs to key neutron-physical characteristics of reactor core.

- Its value depends especially on the type of the moderator and on the energy of the neutrons causing fission.

- In an infinite reactor (without escape) prompt neutron lifetime is the sum of the
**slowing down time and the diffusion time**.

- In LWRs the
**PNL increases with the fuel burnup**.

- The typical prompt neutron lifetime in thermal reactors is on the order of
**10**second.^{-4}

- The typical prompt neutron lifetime in fast reactors is on the order of
**10**second.^{-7}

## Key Characteristics of Delayed Neutrons

- The presence of delayed neutrons is perhaps
**most important aspect of the fission process**from the viewpoint of reactor control.

- 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 emission of neutron happens orders
**of magnitude later**compared to the emission of the prompt neutrons.

- About
**240 n-emitters**are known between^{8}He and^{210}Tl, about 75 of them are in the non-fission region.

- In order to simplify reactor kinetic calculations it is suggested
**to group together the precursors**based on their half-lives.

- Therefore delayed neutrons are traditionally represented by
**six delayed neutron groups**.

- Neutrons can be produced also in
**(γ, n) reactions**(especially in reactors with heavy water moderator) and therefore they are usually referred to as**photoneutrons**.**Photoneutrons**are usually treated no differently than regular delayed neutrons in the kinetic calculations.

- The total yield of delayed neutrons per fission, v
_{d}, depends on:- Isotope, that is fissioned.
- Energy of a neutron that induces fission.

- Variation among individual group yields is much greater than variation among group periods.

- In reactor kinetic calculations it is convenient to use relative units usually referred to as
**delayed neutron fraction (DNF)**.

- At the steady state condition of criticality, with k
_{eff}= 1, the delayed neutron fraction is equal to the precursor yield fraction β.

- In LWRs the
**β decreases with fuel burnup**. This is due to isotopic changes in the fuel.

- Delayed neutrons have
**initial energy between 0.3 and 0.9 MeV**with an**average energy of 0.4 MeV**.

- Depending on the
**type of the reactor**, and their**spectrum**, the delayed neutrons may be more (in thermal reactors) or less effective than prompt neutrons (in fast reactors). In order to include this effect into the reactor kinetic calculations**the effective delayed neutron fraction – β**must be defined._{eff}

- The effective delayed neutron fraction is the product of the average delayed neutron fraction and the importance factor
**β**_{eff}= β . I.

- The weighted delayed generation time is given by
**τ = ∑**, therefore the weighted decay constant_{i}τ_{i}. β_{i}/ β = 13.05 s**λ = 1 / τ ≈ 0.08 s**.^{-1}

- The mean generation time with delayed neutrons is about
**~0.1 s**, rather than**~10**as in section Prompt Neutron Lifetime, where the delayed neutrons were omitted.^{-5}

- Their presence completely changes the dynamic time response of a reactor to some reactivity change,
**making it controllable by control systems**such as the control rods.