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| The four-factor formula, also known as Fermi's '''four factor formula''' is used in [[nuclear engineering]] to determine the multiplication of a [[nuclear chain reaction]] in an infinite medium. The formula is<ref name=Duderstadt>{{cite book |last=Duderstadt |first=James |coauthors=Hamilton, Louis |title=Nuclear Reactor Analysis |year=1976 |publisher=John Wiley & Sons, Inc |isbn=0-471-22363-8 }}</ref>
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| <center><math>k_{\infty} = \eta f p \varepsilon</math></center>
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| ! Symbol
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| ! Name
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| ! Meaning
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| ! Formula
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| |<math>\eta</math>
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| | Reproduction Factor (Eta)
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| | The number of fission [[neutron]]s produced per absorption in the fuel.
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| | <math> \eta = \frac{\nu \sigma_f^F}{\sigma_a^F} </math>
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| | <math>f</math>
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| | The thermal utilization factor
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| | Probability that a neutron that gets absorbed does so in the fuel material.
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| | <math>f = \frac{\Sigma_a^F}{\Sigma_a}</math>
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| | <math>p</math>
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| | The resonance escape probability
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| | Fraction of fission neutrons that manage to slow down from fission to thermal energies without being absorbed.
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| | <math>p \approx \mathrm{exp} \left( -\frac{\sum\limits_{i=1}^{N} N_i I_{r,A,i}}{\left( \overline{\xi} \Sigma_p \right)_{mod}} \right)</math>
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| | <math>\epsilon</math>
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| | The fast fission factor
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| | <center><math>\frac{\mbox{total number of fission neutrons}}{\mbox{number of fission neutrons from just thermal fissions}}</math></center>
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| | <math>\varepsilon \approx 1 + \frac{1-p}{p}\frac{u_f \nu_f P_{FAF}}{f \nu_t P_{TAF} P_{TNL}}</math>
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| The [[six factor formula]] defines each of these terms in much more detail.
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| ==Multiplication==
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| The multiplication factor, k, is defined as (see [[Nuclear chain reaction]]): <center><math>k = \frac{\mbox{number of neutrons in one generation}}{\mbox{number of neutrons in preceding generation}}</math></center>
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| If k is greater than 1, the chain reaction is ''supercritical,'' and the neutron population will grow exponentially. <br />
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| If k is less than 1, the chain reaction is ''subcritical,'' and the neutron population will exponentially decay. <br />
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| If k = 1, the chain reaction is ''critical'' and the neutron population will remain constant.
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| In an infinite medium, neutrons cannot leak out of the system and the multiplication factor becomes the infinite multiplication factor, <math>k = k_{\infty}</math>, which is approximated by the four-factor formula.
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| ==See also==
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| * [[Six factor formula]]
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| * [[Critical mass]]
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| * [[Nuclear chain reaction]]
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| * [[Nuclear reactor]]
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| ==References==
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| {{reflist}}
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| [[Category:Nuclear technology]]
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| [[Category:Radioactivity]]
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