Mass

DOE-STD-1136-2004

Guide of Good Practices for Occupational Radiation Protection in Uranium Facilities

facilities because deliberate engineering efforts, such as moderation with heavy water, reactor-grade

graphite, etc., are required to create a critical mass with natural uranium. However, safe-handling

measures should always be observed when handling uranium of any enrichment.

7.2.1.2 Mass

The minimum mass of uranium that will sustain a chain reaction under specified conditions is called

the minimum critical mass. The minimum critical mass depends on 235U enrichment and other factors, such

as the amount of moderator. For example, the minimum critical mass of an aqueous mixture of 235U with

full water reflection is approximately 800 grams. The single parameter subcritical limit for this condition is

700 grams of 235U (ANSI/ANS 1983b).

7.2.1.3 Density or Concentration

Density or concentration is defined as mass per unit volume (grams/liter, etc.). A uniform solution or

slurry less than 10.8 gm 235U /l will be subcritical at any volume, while a concentration four or five times

greater could result in the minimum critical mass (ANSI/ANS 1983b).

7.2.1.4 Moderation and Reflection

A moderator is a material that slows down fast neutrons. The most effective moderators are those

materials having a low atomic weight, such as hydrogen, deuterium, beryllium and carbon. The moderator

concentration is usually expressed as the ratio of the number of hydrogen atoms to the number of

fissionable atoms of the isotope; thus, the extent of moderation in an aqueous solution of 235U may be

expressed as the H/235U ratio. The ratio H/235U may range from zero for metal, or a dry unhydrated salt, to

several thousands for a dilute aqueous solution. Over this concentration range and with the assumed

spherical geometry, the critical mass may vary from a few tens of kilograms (with little hydrogen) through

a minimum of a few hundred grams (at optimum moderation) to infinity in a very dilute solution where the

neutron absorption by hydrogen makes a chain reaction impossible. A moderated and/or reflected system

allows a smaller mass of 235U to become critical.

A reflected system is an assembly where the fissionable material is partly or wholly surrounded by

another material having a greater neutron scattering cross-section than air. (Technically, air is a reflector,

but its effect is usually negligible). In a reflected system, a fraction of the neutrons leaving the fissionable

material (core) is reflected back into the fissionable material where they may induce additional fissions.

The effect of a reflection is to reduce the minimum critical mass. A good reflector is a material that has a

low neutron absorption cross-section. Water, concrete, graphite, and stainless steel are typically "good"

reflectors, although any material will serve as a reflector. A "fully reflected" system is one where the

fissionable material is totally surrounded by a reflector such that increasing the reflector thickness results in

little or no decrease in the critical mass. For example, experiments at various laboratories have shown that

increasing the thickness of water surrounding the fissionable material beyond 8 inches does not

significantly decrease the critical mass (Paxton et. al.1986).

7.2.1.5 Geometry or Shape

Leakage of neutrons from a system depends on the shape of the system and on the

neutron-reflecting properties of surrounding materials. The shape and size of containers are determined by

considering the ratio of surface area (S) to volume (V). The ratio S/V is maintained at a value that

prevents a chain reaction regardless of the quantity of material contained.

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