Delayed neutron

In nuclear engineering, a delayed neutron is a neutron released not immediately during a nuclear fission event, but shortly afterward—ranging from milliseconds to several minutes later. These neutrons are emitted by excited daughter nuclei of certain beta-decaying fission products. In contrast, prompt neutrons are emitted almost instantaneously—within about 10⁻¹⁴ seconds—at the moment of fission.

During fission, a heavy nucleus splits into two smaller, neutron-rich fragments (fission products), releasing several free neutrons known as prompt neutrons. Many of these fission products are radioactive and typically undergo beta decay to reach more stable configurations. In a small subset of cases, the beta decay of a fission product results in a daughter nucleus in an excited state with enough energy to emit a neutron. This neutron, emitted shortly after fission but delayed due to the beta decay process, is called a delayed neutron.

The delay in neutron emission arises from the time required for the precursor nuclide (the beta-decaying fission product) to undergo beta decay—a process that takes orders of magnitude longer than the prompt emission of neutrons during fission. While the delayed neutron is emitted almost immediately after beta decay, it is actually released by the excited daughter nucleus produced in that decay. Therefore, the overall timing of delayed neutron emission is governed by the beta decay half-life of the precursor.

Delayed neutrons are critically important for controlling nuclear reactors. Their delayed appearance allows for a slower, more manageable response in reactor power changes, significantly enhancing both operational stability and safety.

Principle

Delayed neutrons are associated with the beta decay of the fission products. After prompt fission neutron emission the residual fragments are still neutron rich and undergo a beta decay chain. The more neutron rich the fragment, the more energetic and faster the beta decay. In some cases the available energy in the beta decay is high enough to leave the residual nucleus in such a highly excited state that neutron emission instead of gamma emission occurs.

Using U-235 as an example, this nucleus absorbs thermal neutrons, and the immediate mass products of a fission event are two large fission fragments, which are remnants of the formed U-236 nucleus. These fragments emit, on average, two or three free neutrons (in average 2.47), called "prompt" neutrons. A subsequent fission fragment occasionally undergoes a stage of radioactive decay (which is a beta minus decay) that yields a new nucleus (the emitter nucleus) in an excited state that emits an additional neutron, called a "delayed" neutron, to get to ground state. These neutron-emitting fission fragments are called delayed neutron precursor atoms.

Delayed Neutron Data for Thermal Fission in U-235^[1][2]

Group	Half-Life (s)	Decay Constant (s−1)	Energy (keV)	Yield, Neutrons per Fission	Fraction
1	55.72	0.0124	250	0.00052	0.000215
2	22.72	0.0305	560	0.00346	0.001424
3	6.22	0.111	405	0.00310	0.001274
4	2.30	0.301	450	0.00624	0.002568
5	0.610	1.14	–	0.00182	0.000748
6	0.230	3.01	–	0.00066	0.000273

Importance in nuclear reactors

If a nuclear reactor happened to be prompt critical – even very slightly – the number of neutrons would increase exponentially at a high rate, and very quickly the reactor would become uncontrollable by means of external mechanisms. The control of the power rise would then be left to its intrinsic physical stability factors, like the thermal dilatation of the core, or the increased resonance absorptions of neutrons, that usually tend to decrease the reactor's reactivity when temperature rises; but the reactor would run the risk of being damaged or destroyed by heat.

However, thanks to the delayed neutrons, it is possible to leave the reactor in a subcritical state as far as only prompt neutrons are concerned: the delayed neutrons come a moment later, just in time to sustain the chain reaction when it is going to die out. In that regime, neutron production overall still grows exponentially, but on a time scale that is governed by the delayed neutron production, which is slow enough to be controlled (just as an otherwise unstable bicycle can be balanced because human reflexes are quick enough on the time scale of its instability). Thus, by widening the margins of non-operation and supercriticality and allowing more time to regulate the reactor, the delayed neutrons are essential to inherent reactor safety, even in reactors requiring active control.

The lower percentage^[3] of delayed neutrons makes the use of large percentages of plutonium in nuclear reactors more challenging.

Fraction definitions

The precursor yield fraction β is defined as:

${\displaystyle \beta ={\frac {\mbox{precursor atoms}}{{\mbox{prompt neutrons}}+{\mbox{precursor atoms}}}}.}$

and it is equal to 0.0064 for U-235.

The delayed neutron fraction (DNF) is defined as:

${\displaystyle DNF={\frac {\mbox{delayed neutrons}}{{\mbox{prompt neutrons}}+{\mbox{delayed neutrons}}}}.}$

These two factors, β and DNF, are almost the same thing, but not quite; they differ in the case a rapid (faster than the decay time of the precursor atoms) change in the number of neutrons in the reactor.

Another concept, is the effective fraction of delayed neutrons β_eff, which is the fraction of delayed neutrons weighted (over space, energy, and angle) on the adjoint neutron flux. This concept arises because delayed neutrons are emitted with an energy spectrum more thermalized relative to prompt neutrons. For low enriched uranium fuel working on a thermal neutron spectrum, the difference between the average and effective delayed neutron fractions can reach 50 pcm.^[4]

See also

• Prompt critical
• Critical mass
• Nuclear chain reaction
• Dollar (reactivity)