## Prompt and Delayed Neutrons

^{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.

## Prompt Neutrons

**Prompt fission neutrons**and

**prompt gamma rays**are emitted when excited primary fission fragments release their energy to reach a more stable configuration. This happens shortly after the fission of the nucleus on two fission fragments. Studying prompt neutrons and gamma rays is of importance not only for deepening our understanding of the nuclear fission process, but also in

**core design calculations**or in

**radiation shielding calculations**.

Most of the neutrons produced in fission are prompt neutrons. Usually **more than 99 percent** of the fission neutrons are the prompt neutrons, but the exact fraction is dependent on the nuclide to be fissioned and is also dependent on an incident neutron energy (usually increases with energy). For example a fission of ^{235}U by thermal neutron yields **2.43 neutrons**, of which **2.42 neutrons are the prompt neutrons** and 0.01585 neutrons **(0.01585/2.43=0.0065=ß)** are **the delayed neutrons**. The production of prompt neutrons slightly increase with incident neutron energy.

Prompt neutrons are emitted **within 10 ^{-14} second**. This is very important, because

**it is very very fast**and causes very very fast response of the reactor power in case of prompt criticality. Therefore nuclear reactors must operate

**in a prompt subcritical, delayed critical condition**. All power reactors are designed to operate in a delayed critical conditions and are provided with safety systems to prevent them from ever achieving prompt criticality.

It must be noted the response of the reactor on the reactivity insertion is determined by **a neutron generation time** (not by emission time), which is the average time from a prompt neutron emission to a capture that results only in fission.

## 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}

## Prompt Gamma Rays

**~7 MeV in prompt gamma rays**and additional ~7 MeV (for

^{235}U) in delayed gamma rays. This is a significant portion of energy (~7 % of fission energy released) and it must be considered in many fields of reactor design or in the design of nuclear reactor shields. A particular challenge is the calculation of the gamma heat deposition in core baffles (reflectors), pressure vessels or excore detector channels.

In past the comparisons of various benchmarks experiments with calculated gamma heating showed a systematic underestimation for the main fuel isotopes ^{235}U and ^{239}Pu. Discrepancies observed for C/E ratios in various benchmarks range from 10 to 28%, while required accuracy is 7.5%. Therefore requests for new measurements of prompt gamma rays in the reactions 235U(n,f) and 239Pu(n,f) have been formulated in the Nuclear Data High Priority Request List of the Nuclear Energy Agency.

## Prompt Neutron Lifetime

**Prompt neutron lifetime, l**, is the

**average time from a prompt neutron emission**to either

**its absorbtion**(fission or radiative capture) or to

**its escape**from the system. This parameter is defined in multiplying or also in nonmultiplying systems. In both systems the prompt neutron lifetimes depend strongly on:

- material composition of the system
- multiplying – nonmultiplying system
- system with or without thermalization
- isotopic composition of the system

- geometric configuration of the system
- homogeneous or heterogeneous system
- shape of entire system

- size of the system

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

**l=t _{s} + t_{d}**

In an infinite thermal reactor **t _{s} << t_{d}** and therefore

**l ≈ t**. The typical prompt neutron lifetime

_{d}**in thermal reactors**is on the order of

**10**. Generally, the longer neutron lifetimes take place in systems in which the neutrons must be thermalized in order to be absorbed.

^{−4}secondSystems in which most of the neutrons are absorbed at higher energies and the neutron thermalization is suppressed (e.g. in fast reactors), have much shorter prompt neutron lifetimes . The typical prompt neutron lifetime **in fast reactors** is on the order of **10 ^{−7} second**.

Slowing Down and Diffision Times for Thermal Neutrons in an Infinite Medium

Source: Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.

## Prompt Generation Time – Mean Generation Time

_{eff}=1). This time is known as the

**prompt neutron generation time**.

**Prompt Neutron Generation Time** (or **Mean Generation Time**), **Λ**, is the average time **from a prompt neutron emission** **to a capture that results only in fission**. The prompt neutron generation time is designated as:

**Λ = l/k _{eff}**

In power reactors **the prompt generation time** changes with the fuel burnup. In LWRs increases with the fuel burnup. It is simple, fresh uranium fuel contains much fissile material (in case of uranium fuel about 4% of ^{235}U). This causes significant excess of reactivity and this **excess must be compensated** via chemical shim (in case of PWRs) or via burnable absorbers.

Owing to these factors (high probability of absorption in fuel and high probability of absorption in moderator) the prompt neutron lives much shorter and prompt neutron lifetime is low. With fuel burnup the amount of fissile material as well as the absorption in moderator decreases and therefore the prompt neutron is able to “live”much longer.

## Example – Infinite Multiplying System Without Source and Delayed Neutrons

**the point kinetics equation**(in certain form). This equation states that the time change of the neutron population is equal to the

**excess of neutron production**(by fission)

**minus neutron loss**by absorption

**in one prompt neutron lifetime**. The role of prompt neutron lifetime is evident. Shorter lifetimes give simply faster responses of multiplying systems.

If there are neutrons in the system at t=0, that is, if n(0) > 0, the solution of this equation gives the simplest form of point kinetics equation (without source and without delayed neutrons):

Let us consider that **the prompt neutron lifetime is ~2 x 10 ^{-5}** and k (k

_{∞}– neutron multiplication factor) will be step increased

**by only 0.01%**(

**i.e. 10pcm or ~1.5 cents**), that is k

_{∞}=1.0000 will increase to k

_{∞}=1.0001.

It must be noted such reactivity insertion (10pcm)** is very small** in case of LWRs. The reactivity insertions **of the order of one pcm** are for LWRs **practically unrealizable**. In this case the reactor period will be:

**T = l / (k _{∞ }- 1) = 2 x 10^{-5 }/ (1.0001 – 1) = 0.2s**

**This is a very short period.** In one second the neutron flux (and power) in the reactor would increase by a factor of e^{5} = 2.718^{5}, in 10 seconds the reactor would pass through 50 periods and the power would increase by e^{50} = ……

Furthermore in case of fast reactors in which prompt neutron lifetimes are **of the order of 10 ^{-7} second**, the response of such a small reactivity insertion will be even more unimaginable. In case of 10

^{-7}the period will be:

**T = l / (k _{∞ }- 1) = 10-7 / (1.0001 – 1) = 0.001s**

**Reactors with such a kinetics would be very difficult to control.** **Fortunately this behaviour is not observed** in any multiplying system. Actual reactor periods are observed to be considerably longer than computed above and therefore the nuclear chain reaction can be **controlled more easily**. The longer periods are observed due to the presence of **the delayed neutrons.**

## Interactive chart – Infinite Multiplying System Without Source and Delayed Neutrons

**clear and run**” button and try to stabilize the power at 90%.

Look at the reactivity insertion you need to insert in order to stabilize the system (of the order to tenth of pcm).

Do you think that such a system is controlable?

## Effect of Prompt Neutron Lifetime on Nuclear Safety

**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. Its importance for nuclear reactor safety is well known for a long time.

The longer prompt neutron lifetimes can substantially improve kinetic response of reactor (**the longer prompt neutron lifetime gives simply slower power increase**). For example under RIA conditions (**Reactivity-Initiated Accidents**) reactors should withstand a jump-like insertion of relatively large (~1 $ or even more) positive reactivity and the PNL (prompt neutron lifetime) plays here the key role. Therefore the PNL should be verified in a reload safety evaluation process.

In some cases (especially in some fast reactors) reactor cores or can be modified in order to increase the PNL and in order to improve nuclear safety.

See also: Improving Nuclear Safety of Fast Reactors by Slowing Down Fission Chain Reaction

## Prompt Neutron Energy Spectrum

Basic features of prompt neutron energy spectra are summarized below:

- The neutrons produced by fission are high energy neutrons.
- Almost all fission neutrons have
**energies between 0.1 MeV and 10 MeV.** - The prompt neutron energy distribution, or spectrum, may be best described by dependence of the fraction of neutrons per MeV on neutron energy.
- The most probable neutron energy is about
**0.7 MeV**.

The mean neutron energy is about**2 MeV**. - These values are for thermal fission of
^{235}U, but these values vary only slightly for other nuclides.

Prompt neutron fission spectra evaluation is one of the most interesting aspects of evaluation of actinides. Many experimental and theoretical researches have been carried out for the determination of prompt neutron spectra. There are several representations of prompt fission neutron spectra. Two early models of the prompt fission neutron spectrum, which are still used today, are **the Maxwellian and Watt spectrum**.

The modern spectrum representation of the prompt fission neutron spectrum and average prompt neutron multiplicity is called **the Madland-Nix Spectrum** (Los Alamos Model). This model is based upon the standard nuclear evaporation theory and utilizes an isospin-dependent optical potential for the inverse process of compound nucleus formation in neutron-rich fission fragments.

Source: Madland, David G., New Fission-Neutron-Spectrum Representation for ENDF, LA-9285-MS, April 1982.

Source: Madland, David G., New Fission-Neutron-Spectrum Representation for ENDF, LA-9285-MS, April 1982.

**Nuclear and Reactor Physics:**

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

**Advanced Reactor Physics:**

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