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 (235U, 238U 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.
Neutron Production - Prompt Neutrons
Neutron Production – Prompt Neutrons.Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library
Energy from Uranium Fission
Energy release from 235U fission.
Table of key prompt and delayed neutrons characteristics
Table of key prompt and delayed neutrons characteristics.

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 235U 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 10-4 second.
  • The typical prompt neutron lifetime in fast reactors is on the order of 10-7 second.

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 8He and 210Tl, 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, vd, 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 keff = 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 – βeff must be defined.
  • The effective delayed neutron fraction is the product of the average delayed neutron fraction and the importance factor βeff = β . I.
  • The weighted delayed generation time is given by τ = ∑iτi . βi / β = 13.05 s, therefore the weighted decay constant λ = 1 / τ ≈ 0.08 s-1.
  • The mean generation time with delayed neutrons is about ~0.1 s, rather than ~10-5 as in section Prompt Neutron Lifetime, where the delayed neutrons were omitted.
  • 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.
Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above: