SIX- AND FOUR-FACTOR FORMULAS
We shall develop here a formula for the multiplication factor keff in a thermal reactor. We do so by considering the life history of a neutron from birth to death, and describing each fork in the road via a mathematical statement of probability. First, we define:
We now sketch a neutron's history in a thermal reactor. You will need to identify what physical process takes place provided that the neutron does not leak out of the system. Drag the symbols on the left to their proper place on the graph. You will receive immediate feedback.
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It follows that the multiplication factor must be:
It is customary to define
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This gives us the six-factor formula:
In an infinite medium nothing leaks, and we have the four-factor formula for the infinite-medium multiplication factor, 
:
is an upper bound for Keff
The six- and four-factor formulas provide insight into how a system's physical characteristics affect the multiplication factor.
REFERENCES
D.J. Bennet & J.R. Thomson, The Elements of Nuclear Power, John Wiley & Sons (1988).
J.J. Duderstadt & L.J. Hamilton, Nuclear Reactor Analysis, John Wiley & Sons (1976).
J.R. Lamarsh & A.J. Baratta, Induction to Nuclear Engineering, Prentice Hall (2001).
W.M. Stacey, Nuclear Reactor Physics, John Wiley & Sons (2001).
Parrington, J.R.; Knox, H.D.; Breneman, S.L.; Baum, E.M.; and Feiner, F. 1996. Nuclides and Isotopes, Chart of the Nuclides. 15th Edition. San Jose, California : General Electric Company and KAPL, Inc.
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