An approximate but sensibly accurate formula is developed for estimating the minimum possible critical radius for a sphere of fissile material surrounded by a thick tamper of material of neutron transport mean free path λtamp. The minimum critical radius is approximately proportional to λtamp0.4; results are given for uranium-235 and plutonium-239 cores surrounded by several commonly used tamper materials.

1.
R.
Serber
,
The Los Alamos Primer: The First Lectures on How To Build An Atomic Bomb
(
University of California
,
Berkeley
,
1992
).
2.
Reactor Physics Constants Center, United States Atomic Energy Commission
,
Division of Technical Information: Reactor Physics Constants
(
United States Government Printing Office
,
Washington
,
1963
), see pp.
582
and
585
.
3.
B. C.
Reed
,
The Physics of the Manhattan Project
(
Springer
,
Berlin
,
2015
), chap. 2.
4.
B. C.
Reed
, “
Arthur Compton's 1941 report on explosive fission of U-235: A look at the physics
,”
Am. J. Phys.
75
(
12
),
1065
1072
(
2007
).
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