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3.18
There are three approaches which can be employed to estimate allowable enrichnent
criteria for 233U in 238U corresponding to the statutory 20% limit set for 235U in 238U.
These three criteria are: (1) critical mass, (2) infinite multiplication factor, and
(3) yield.
Critical Mass
These can be employed singularly or in combination as discussed below.
As stated above, the bare-sphere critical mass of metallic 20% 235U and 80% 238U is
about 850 kg. This amount can be reduced by a factor of two to three by the use of a
neutron reflector.
fissile material will not be substantially less than that of the bare sphere, and may
even be greater. In addition, for a nuclear explosive, an assembly scheme must be added
which will increase the size and weight substantially. Concentrations of 235U, 233U, or
plutonium in mixtures with 238U such that they have bare-sphere metallic critical masses
of about 850 kg represent one possible reasonably conservative criterion for arriving at
concentrations below which the material is not usable in practical nuclear weapons. This
850 kg bare-sphere critical mass criterion can also be used for other materials which are
or might be in nuclear fuel cycles. Although this criterion provides a basis for consistent
safeguards requirements for 233U or 235U embedded in 238U, it leans to rather
low limits.
Infinite Mu1 tip1 ication Factor
However, the size and weight of the combination of reflector and
hother possible criterion is the one associated with the infinite multiplication
factor k,. For a weapon to be successful, a certain degree of supercriticality must be
attained. D. P. Smith of Los Alamos Scientific Laboratory has adopted this approach. He
takes k, = 1.658 for 20% 235U-enriched uranium, which implies k, = 1.5346 for the oxide.
He then performs a search calculation on enrichment for the other systems so as to obtain
the same k, value. His results are shown in Table 3.3-1. We note that for 233U the limits
are 11.65% 233U for the oxide and 11.12% 233U for the metal.
Fuel
Table 3.3-1 Equivalent Enrichment Limits
Hateri a1 kco
Metal 20% 235U, 80% 238U 1.658
11.12% 233U, 88.88% 238U 1.658
11.11% 239Pu, 88.89% 238U 1.658
Oxide (20% 235U, 80% 238U)02 1 5346
(11.65% 233U, 88.35% 238U)02 1.5346
(13.76% 239P~, 86.24% 238U)02 1.5346
(14.5% 239Pu, 1.5% 240Pu, 85% 238u)02 1.5344
~ ~ ~~~ ~~~ ~
These numbers were obtained by D. P. Smith of Los Alamos
Scientific Laboratory from DTF IV calculations using
Hansen-Roach cross sections.