NUC-14

Reaction cross section

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

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NuclearCross section

Governing equation

\sigma=R/(n\varphi)

where

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

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: $R$ , $n$ , $\varphi$ $\rightarrow$ $\sigma$ . A barn is 10⁻²⁸ m². Macroscopic Σ = n σ, mean free path 1/Σ.

Purpose

Purpose: compute

\sigma

from

R

n

\varphi

in Nuclear physics via

\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\,\mathrm{1/m^{3}/s}

n = 1.000e+28\,\mathrm{1/m^{3}}

\varphi = 1.000e+16\,\mathrm{1/m^{2}/s}

, the governing relation

\sigma=R/(n\varphi)

yields

\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.

Calculator

Inputs

Reaction rate density R1000000000000000000 1/m³/sTarget density n1e+28 1/m³Flux \varphi10000000000000000 1/m²/s

Outputs

Cross section \sigma100.000 b

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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.

Reading speed

Watch on YouTube