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NUC-25

Four-factor k∞

k∞ = η ε p f. Infinite-medium multiplication.

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NuclearFour-factor

Governing equation

k∞=η ε p fk_\infty=\eta\,\varepsilon\, p\, f

p∈[0.5,1]p \in \left[0.5, 1\right]

where

\eta
Reproduction η (—)
\varepsilon
Fast fission ε (—)
p
Resonance escape (—)
f
Thermal utilisation (—)
k_\infty
Multiplication (—)

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NUC-25 · reactor
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①

Governing law — red

k∞=η ε p fk_\infty=\eta\,\varepsilon\, p\, f

p∈[0.5,1]p \in \left[0.5, 1\right]

p=0.5p = 0.5k∞=0.822k_\infty = 0.822

②

Domain of the variable — blue

pmin⁡=0.5,pmax⁡=1p_{\min} = 0.5,\quad p_{\max} = 1

p∈[0.5,1]p \in \left[0.5, 1\right]

p=0.5p = 0.5p=0.5p = 0.5

③

Response curve — green

k∞=η ε p fk_\infty=\eta\,\varepsilon\, p\, f

p∈[0.5,1]p \in \left[0.5, 1\right]

p=0.5p = 0.5k∞=0.822k_\infty = 0.822

④

Rate of change — amber

dk∞dp\frac{\mathrm{d}k_\infty}{\mathrm{d}p}

p∈[0.5,1]p \in \left[0.5, 1\right]

p=0.503p = 0.503k∞′=1.644k_\infty^{\prime} = 1.644

Lecture brief

Historical brief

Rutherford, Chadwick, the semi-empirical mass formula, fission (Hahn–Strassmann 1938) and fusion Q-values, then Compton and Bethe–Bloch stopping, are the nuclear toolkit. Decay, binding and dose start here. This sheet (NUC-25 — Four-factor k∞) is the form associated with Four-factor. Working symbols: η\eta, ε\varepsilon, pp, ff →\rightarrow k∞k_\infty. η reproduction, ε fast fission, p resonance escape, f thermal utilisation.

Purpose

Purpose: compute k∞k_\infty from η\eta, ε\varepsilon, pp, ff in Nuclear physics via k∞=η ε p fk_\infty=\eta\,\varepsilon\, p\, f k∞ = η ε p f. Infinite-medium multiplication. Use it when a real nuclear physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given η=2.020 —\eta = 2.020\,\mathrm{—}, ε=1.030 —\varepsilon = 1.030\,\mathrm{—}, p=0.870 —p = 0.870\,\mathrm{—}, f=0.790 —f = 0.790\,\mathrm{—}, the governing relation k∞=η ε p fk_\infty=\eta\,\varepsilon\, p\, f yields k∞=1.4300 —k_\infty = 1.4300\,\mathrm{—}. Four bars whose product is k. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • Multiplication k_\infty1.4300 —
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NUC-25 · reactor
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Narration of this film

Four bars whose product is k.

η reproduction, ε fast fission, p resonance escape, f thermal utilisation.

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