Criticality Safety

A "critical" nuclear system is one where exactly one of the neutrons produced in a fission reaction survives escape or absorption to continue the nuclear chain reaction. Such a system is said to have a neutron multiplication of one, or keff=1. The fission process will continue in a stable way as long as the conditions don't change. This is the condition in an operating nuclear power reactor. In a "subcritical" system, fewer than one neutrons survive on the average, for example, keff=0.8, and the fission chain reaction will rapidly die away. A subcritical system will remain safely turned off as long as the conditions around it remain stable. If the multiplication factor is greater than one, the system is "supercritical." The fission rate will rapidly increase until things get hot enough to disperse the system (it requires very specific conditions to turn such a runaway reaction into a bomb). This supercritical system will produce large amounts of dangerous radiation and persistant radioactive contamination.

It is the role of the Criticality Safety Engineer to evaluate the conditions that must be met to avoid a runaway fission process, or "criticality accident," wherever nuclear materials are stored, transported, or processed.


A large variety of nuclear materials are being stored at sites all around our nation and throughout the world. Examples include spent nuclear reactor fuel in storage ponds at power reactors, wastes from processing plutonium out of irradiated fuel elements from reactors, new fuel rods for reactors, and the "pits" removed from decomissioned nuclear weapons here and in Russia.

As an example, a particular nuclear site may contain a concrete storage bunker where drums of waste material are kept. How closely can these drums be positioned to one another? Is it safe to stack two drums on top of each other? What would happen if the storage area should be flooded with water? These types of questions are answered by doing detailed calculations of the transport of neutrons inside the drums and between the drums using sophisticated radiation transport codes like MCNP from Los Alamos or the SCALE system from Oak Ridge. These transport codes depend on having accurate nuclear data to make reliable calculations, and providing these data is one of the roles of our Group.


It is occasionally necessary to transport nuclear materials from one site to another. For example, new reactor fuel rods have to be transported from the manufacturer to the power reactor, and used fuel rods must be shipped from the power reactor site to a reprocessing center or to a permanent storage site. Waste from fabrication facilities, laboratories, reprocessing centers, or decomissioned reactors must be shipped to storage centers. Such shipments pass over our highways, through our towns, and along our railroads. It is vitally important that there is no possibility of a criticality accident during transportation. However, we also want to minimize the number of such shipments. Thus, we want to put as much nuclear material as possible into each shipment without violating criticality safety.

As an example of the type of thought put into the transportation process, consider "burnup credit." A used reactor fuel rod contains less fissile material (U-235) than a new one because part of the fuel has been consumed to produce electricity. It also contains some new fissile material (Pu-239) produced during its exposure, and it contains large amount of "fission products," the fragments of the uranium nuclei remaining after fission. Many of these fission products are strong neutron absorbers and act to damp down the fission process. However, the regulations that govern the transportation of fuel rods normally require that the criticality analyst only consider the fissile fuel loading without taking "credit" for the additional absorptive effect of the fission products. This is a conservative regulation, but if we could predict the burnup credit with great reliability, we could increase the number of fuel rods in a shipment.

In order to justify changing the regulations, we must obtain the best possible nuclear data for these fission products and attempt to quantify the uncertainty of our knowledge of their cross sections. In addition, we must thoroughly validate the computer codes used for the transportation cask designs. A number of Groups throughout the world are attacking these problems, and our Group at Los Alamos is among them.

Fabrication and Processing

During the fabrication and processing of nuclear materials, there may be several steps involved. Examples include machining of metallic forms and dissolving radioactive materials in acids for chemical separation. During these steps, it is possible for the fissionable materials to accumulate in glove boxes, piping, or filters. If too much material were to accumulate, it might become supercritical, causing dangereous levels of radiation to personnel and seriously contaminating the facility. The equipment and operating procedures for such a facility must be designed and maintained using the advice of criticality safety engineers supported by advanced computer models (because of the very complex geometries involved) and the best available nuclear data.

Criticality Experiments

As in all scientific disciplines, theoretical calculations are not sufficient; it is always necessary to go back to nature and ask our questions using well designed experiments. There is now only one site left in the US where experiments in nuclear criticality are carried out, the Los Alamos Critical Experiments Facility (LACEF). The scientists at this facility design, construct, and operate a variety of critical assemblies. A particular assembly might be in the nature of a prototype for some intended application, or it might be a simpler design intended to provide the data needed to validate the radiation transport codes and the nuclear data that they use. In addition, LACEF operates hands-on training courses for criticality safety engineers, facility managers, and other people who contribute to the safe use of nuclear materials.

There is a large body of criticality data available from experiments done in the past, and there are other criticality facilities still operating in other countries. Therefore, it is important to gather together old and new experimental results, give the data a careful review, and publish them. See the International Criticality Safety Benchmark Evaluation Project. These standardized experiments can then be used by criticality safety engineers all over the world to validate their methods. And when we can't quite make the calculations match the experiments, nuclear data specialists like those in our Group can go to work to try to resolve the problem.

Nuclear Data for Criticality Safety

Many kinds of neutron data are important for criticality safety calculations. We will consider especially the following:
  • Fission-product capture cross sections,
  • Fission-product scattering cross sections and distributions,
  • Cross sections for reactor calculations, and
  • Fission-product yields.
The capture cross section for one of the important fission products, Sm-151 with a half life of 90 years, is shown below:


In a moderated system (e.g., water is present), there is a strong peak in the flux near .025 eV caused by neutrons in thermal equilibrium with water at room temperature. Note that the cross section is very large here for this isotope. The cross section is often represented by its value at .0253 eV. At higher energies, strong resonances show up, and the cross section is often represented by giving the "resonance integral" with respect to a simple 1/E spectrum. Thus, the thermal parameters for Sm-151 from ENDF/B-VI are as follows:

  • Thermal capture cross section (.0253 eV) -- 15,189 b (exp. 15,200 b)
  • Capture resonance integral -- 3364.8 b (exp. 3300.0 b)
In a collaboration with Oak Ridge, our Group is comparing different evaluations for the fission-product cross sections and their integral measures in an attempt to evaluate the uncertainty in these values and motivate improvements expected to improve criticality safety.

Wet or Dry?

Fission neutrons are born at fairly high energies (in the MeV region). They then slow down ("moderate") by collisions with nuclei in the material. Hydrogen is the most effective moderator material, and if water is present in the system, the neutrons slow down very rapidly to thermal energies where the cross sections for more fissions are very large. However, in dry assemblies, the moderation is not as effective and the equilibrium neutron flux is more energetic. The following figure shows typical "wet" and "dry" neutron spectra:


It is clear that the important cross sections for dry nuclear assemblies are those at higher energies, such as inelastic scattering and the "unresolved resonance" range.

Inelastic scattering can take place when the energy of the incident neutron is large enough to excite the target nucleus to a higher energy state. The scattered neutron then loses this excitation energy, resulting in fairly effective moderation. The excited target nucleus will then emit gamma rays to return to its normal ground-state configuration. Inelastic scattering is difficult to measure experimentally and difficult to model theoretically. As an example, the following figure shows the spectrum of secondary neutrons produced from 1 MeV incident neutrons on Zr-96 from three different evaluation data libraries:

Zr-96 Inelastic Spectrum

Our Group is working to improve the modeling of such inelastic scattering processes in order to provide better data for simulating the moderation in nuclear criticality safety problems.

Unresolved Resonances

As illustrated by the cross section for Sm-151 shown above, the resonance range contains many sharp peaks. As the energy increases, these peaks eventually get so close together that they are hard to distinguish experimentally and begin to overlap (e.g., at 300 eV in the Sm-151 illustration). For some evaluations, one can define an "unresolved energy range," where resonances are described by their average widths and spacings and the probability distributions that these widths and spacings obey. Unresolved ranges typically extend to energies from 10 to 100 keV. These statistical properties can then be used to calculate expected values for the cross sections in various configurations.

One hig-quality method for handling the unresolved resonance range in continuous-energy Monte Carlo transport codes is the "Probability Table Method." The NJOY Nuclear Data Processing System is used to prepare tables giving the probability of observing particular values of the total cross section at given neutron energies and material temperatures. The Monte Carlo code can then randomly sample these tables for each reaction to produce values of the total cross section that behave correctly on the average. Auxilliary tables are used to define how much of the total cross section results in scattering, capture, or fission.

Cross Sections for Reactor Calculations

If you are trying to store or transport some material that has been exposed in a nuclear reactor, you have to have a pretty good inventory of the various fuel, fission product, and structural isotopes that are in the material. In most cases, it is impractical to extract a sample from the material and do a complete analysis of its nuclear constituents. Therefore, we often have to rely on detailed reactor calculations to produce the inventories. These calculations require the best nuclear data that we can provide, and the codes and their data libraries have to be benchmarked against criticality experiments. When discrepancies between calculation and experiment are observed, we have to try to improve the data. The current results from this process of improvement are in the ENDF/V-VII.1 library.

Fission-Product Yields

When a nucleus fissions, it usually divides into two not quite equal fission fragments. When you average over many possible fission paths, you get a fission yield curve that shows two peaks:

Fission Yields

This figure is for fission induced by thermal neutrons. It is clear that a good knowledge of this curve is important for criticality safety calculations. The fission-product yields for the ENDF/B libraries in the US were evaluated in our Group, and the tables of values are available in our Publications Area under "Fission Product Yields."

Our work on data for criticality safety is currently supported under the Nuclear Criticality Predictability Program (NCPP), which is operated by the Environmental Management office of the US Department of Energy (DOE/EM).

Start the schoolbus tour
4 May 1998