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NUC-14

Reaction cross section

σ = R / (n φ). Rate per target nucleus per flux.

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NuclearCross section

Governing equation

σ=R/(nφ)\sigma=R/(n\varphi)

φ∈[1×1010,1×1020]\varphi \in \left[1\times 10^{10}, 1\times 10^{20}\right]

where

R
Reaction rate density (1/m³/s)
n
Target density (1/m³)
\varphi
Flux (1/m²/s)
\sigma
Cross section (b)

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NUC-14 · reactor
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①

Governing law — red

σ=R/(nφ)\sigma=R/(n\varphi)

φ∈[1×1010,1×1020]\varphi \in \left[1\times 10^{10}, 1\times 10^{20}\right]

φ=1×1010\varphi = 1\times 10^{10}σ=1×108\sigma = 1\times 10^{8}

②

Domain of the variable — blue

φmin⁡=1×1010,φmax⁡=1×1020\varphi_{\min} = 1\times 10^{10},\quad \varphi_{\max} = 1\times 10^{20}

φ∈[1×1010,1×1020]\varphi \in \left[1\times 10^{10}, 1\times 10^{20}\right]

φ=1×1010\varphi = 1\times 10^{10}φ=1×1010\varphi = 1\times 10^{10}

③

Response curve — green

σ=R/(nφ)\sigma=R/(n\varphi)

φ∈[1×1010,1×1020]\varphi \in \left[1\times 10^{10}, 1\times 10^{20}\right]

φ=1×1010\varphi = 1\times 10^{10}σ=1×108\sigma = 1\times 10^{8}

④

Rate of change — amber

dσdφ\frac{\mathrm{d}\sigma}{\mathrm{d}\varphi}

φ∈[1×1010,1×1020]\varphi \in \left[1\times 10^{10}, 1\times 10^{20}\right]

φ=6.29×1017\varphi = 6.29\times 10^{17}σ′=−7.95×10−11\sigma^{\prime} = -7.95\times 10^{-11}

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-14 — Reaction cross section) is the form associated with Cross section. Working symbols: RR, nn, φ\varphi →\rightarrow σ\sigma. A barn is 10⁻²⁸ m². Macroscopic Σ = n σ, mean free path 1/Σ.

Purpose

Purpose: compute σ\sigma from RR, nn, φ\varphi in Nuclear physics via σ=R/(nφ)\sigma=R/(n\varphi) σ = R / (n φ). Rate per target nucleus per flux. 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 R=1.000e+18 1/m3/sR = 1.000e+18\,\mathrm{1/m^{3}/s}, n=1.000e+28 1/m3n = 1.000e+28\,\mathrm{1/m^{3}}, φ=1.000e+16 1/m2/s\varphi = 1.000e+16\,\mathrm{1/m^{2}/s}, the governing relation σ=R/(nφ)\sigma=R/(n\varphi) yields σ=100.000 b\sigma = 100.000\,\mathrm{b}. A beam, a thin target, a count rate. Move a slider: the numbers are this situation, not a canned story.

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  • Cross section \sigma100.000 b
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NUC-14 · reactor
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Narration of this film

A beam, a thin target, a count rate.

A barn is 10⁻²⁸ m². Macroscopic Σ = n σ, mean free path 1/Σ.

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