// Workers AI · dad joke modeWhy did the delayed neutron go to therapy? It was feeling a little behind.
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
[edit]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 two to three free neutrons (2.43 on average), called "prompt" neutrons.[1] 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.
The longest-lived groups can be traced to specific decay chains. In about 70% of 87Br beta decays (half-life 55 s), the 87Kr daughter is left in a nuclear state above the 5.4 MeV needed to eject its last neutron; it promptly releases a neutron, ending as stable 86Kr. The neutron emission rate is set by the rate of formation of 87Kr, so the group carries the 55 s half-life of the precursor. The 23 s group is attributed mainly to 137I (half-life 24.5 s[2]), which beta decays to excited states of 137Xe that promptly emit a neutron to form stable 136Xe. In both cases the number of neutrons in the emitter exceeds a magic number (50 and 82, respectively) by exactly one neutron, so the last neutron is weakly bound and easily emitted; the other, shorter-lived groups are produced in analogous chains.[3]
Delayed Neutron Data for Thermal Fission of U-233, U-235 and Pu-239[4][5][6]
| Group | Half-Life (s) | Decay Constant (s−1) | Energy (keV) | Yield, Neutrons per Fission | Fraction | ||||
|---|---|---|---|---|---|---|---|---|---|
| U-233 | U-235 | Pu-239 | U-233 | U-235 | Pu-239 | ||||
| 1 | 55.72 | 0.0124 | 250 | 0.00057 | 0.00052 | 0.00021 | 0.000225 | 0.000215 | 0.0000689 |
| 2 | 22.72 | 0.0305 | 560 | 0.00197 | 0.00346 | 0.00182 | 0.000776 | 0.001424 | 0.000597 |
| 3 | 6.22 | 0.111 | 405 | 0.00166 | 0.00310 | 0.00129 | 0.000654 | 0.001274 | 0.000423 |
| 4 | 2.30 | 0.301 | 450 | 0.00184 | 0.00624 | 0.00199 | 0.000725 | 0.002568 | 0.000652 |
| 5 | 0.610 | 1.14 | – | 0.00034 | 0.00182 | 0.00052 | 0.000134 | 0.000748 | 0.000170 |
| 6 | 0.230 | 3.01 | – | 0.00022 | 0.00066 | 0.00027 | 0.0000867 | 0.000273 | 0.0000885 |
There are at least 45 precursor isotopes. In reactor analysis they are conventionally combined into six effective groups, each with an effective half-life (about 55, 22, 6, 2, 0.5, and 0.2 seconds) and an effective yield. The 55-second group is dominated by 87Br, the 22-second group by 88Br and 137I, and the shorter-lived groups have many contributors. The group parameters depend on the fuel isotope, since fission product yields vary with the fissile material.[7][8]
An eight-group structure has also been defined, which uses the same set of half-lives for all fissioning systems, with the three longest-lived groups corresponding to the three dominant long-lived precursors 87Br, 137I and 88Br.[9] The International Atomic Energy Agency (IAEA) publishes eight-group parameters for several actinides; for thermal fission of U-235 they are:[10]
| Group | Half-Life (s) | Decay Constant (s−1) | Fraction of delayed neutrons | Fraction of all neutrons (%) |
|---|---|---|---|---|
| 1 | 55.6 | 0.012467 | 0.0328 | 0.0218 |
| 2 | 24.5 | 0.028292 | 0.1539 | 0.1023 |
| 3 | 16.3 | 0.042524 | 0.091 | 0.0605 |
| 4 | 5.21 | 0.133042 | 0.197 | 0.131 |
| 5 | 2.37 | 0.292467 | 0.3308 | 0.2200 |
| 6 | 1.04 | 0.666488 | 0.0902 | 0.0600 |
| 7 | 0.424 | 1.634781 | 0.0812 | 0.0540 |
| 8 | 0.195 | 3.554600 | 0.0229 | 0.0152 |
The last column sums to 0.665%, a delayed neutron fraction of 0.00665 for thermal fission of U-235.
Importance in nuclear reactors
[edit]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). For example, with a neutron lifetime of 10−3 s and a reactivity step of 0.0022, the reactor period would be 0.45 s without delayed neutrons, but is 14 s with them.[11] 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[12] of delayed neutrons makes the use of large percentages of plutonium in nuclear reactors more challenging.
Fraction definitions
[edit]The precursor yield fraction β is defined as:
and it is equal to 0.0065 for U-235.[13]
The value of β depends on the fissioning isotope and on the energy of the fissioning neutrons, so it is not a universal constant. Thermal fission of Pu-239 gives β ≈ 0.0021, about a third of the U-235 value, while fast fission of U-238 gives 0.0148, so the values differ by more than a factor of seven across the actinides.[14] In a reactor, the effective β must be averaged over the fuel isotope mixture, which changes with core life. Since the bred fuels Pu-239 and U-233 have somewhat lower delayed neutron yields than U-235, in most thermal reactors the effective delayed neutron fraction decreases as the core ages.[15]
The delayed neutron fraction (DNF) is defined as:
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 βeff, 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.[16]
See also
[edit]References
[edit]- ↑ Brown, D. A.; et al. (2018). "ENDF/B-VIII.0: The 8th Major Release of the Nuclear Reaction Data Library with CIELO-project Cross Sections, New Standards and Thermal Scattering Data". Nuclear Data Sheets. 148: 76. doi:10.1016/j.nds.2018.02.001.
- ↑ Delayed Neutron Data for the Major Actinides (PDF) (Report). OECD Nuclear Energy Agency. 2002. p. 23.
- ↑ Glasstone, Samuel; Sesonske, Alexander (1994). Nuclear Reactor Engineering (4th ed.). Chapman & Hall. pp. 110–111. ISBN 0-412-98521-7.
- ↑ J. R. Lamarsh, Introduction to Nuclear Engineering, Addison-Wesley, 2nd Edition, 1983, page 76.
- ↑ G. R. Keepin, Physics of Nuclear Kinetics, Addison-Wesley, 1965.
- ↑ Glasstone, Samuel; Sesonske, Alexander (1994). Nuclear Reactor Engineering (4th ed.). Chapman & Hall. p. 110. ISBN 0-412-98521-7.
- ↑ Duderstadt, James J.; Hamilton, Louis J. (1976). Nuclear Reactor Analysis. Wiley. pp. 62–63. ISBN 0-471-22363-8.
- ↑ Stacey, Weston M. (2018). Nuclear Reactor Physics (3rd revised ed.). Wiley-VCH. p. 141. ISBN 978-3-527-41366-9.
- ↑ Delayed Neutron Data for the Major Actinides (PDF) (Report). OECD Nuclear Energy Agency. 2002. p. 41.
- ↑ "Nuclear Data for Safeguards, Appendix A-7: Delayed-neutron eight-group parameters". International Atomic Energy Agency.
- ↑ Glasstone, Samuel; Sesonske, Alexander (1994). Nuclear Reactor Engineering (4th ed.). Chapman & Hall. pp. 249–250. ISBN 0-412-98521-7.
- ↑ "Nuclear Data for Safeguards".
- ↑ Lamarsh, John R.; Baratta, Anthony J. (2014). Introduction to Nuclear Engineering (3rd ed.). Pearson. p. 88. ISBN 978-1-292-02581-0.
- ↑ Lamarsh, John R.; Baratta, Anthony J. (2014). Introduction to Nuclear Engineering (3rd ed.). Pearson. p. 343. ISBN 978-1-292-02581-0.
- ↑ Duderstadt, James J.; Hamilton, Louis J. (1976). Nuclear Reactor Analysis. Wiley. p. 240. ISBN 0-471-22363-8.
- ↑ Talamo, A.; Gohar, Y.; Nuclear Engineering Division (29 July 2010). Deterministic and Monte Carlo Modeling and Analyses of Yalina-Thermal Subcritical Assembly (ANL-NE-10/17). Argonne National Laboratory. doi:10.2172/991100. OSTI 991100.