RAD-34

Collision stopping snapshot

Bethe log term.

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Radiationstopping

Governing equation

S_{\mathrm{col}}\propto Z/(\beta^2 A)\ln(2m_e c^2\beta^2/I)

$\beta \in \left[0.05, 0.95\right]$

where

Z: Z (—)
A: A (—)
\beta: β (—)
I: I (eV)
S: S/ρ (MeV cm²/g)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

S_{\mathrm{col}}\propto Z/(\beta^2 A)\ln(2m_e c^2\beta^2/I)

$\beta \in \left[0.05, 0.95\right]$

$\beta = 0.05$ $S = 212.8$

Along the curve

②

Domain of the variable — blue

\beta_{\min} = 0.05,\quad \beta_{\max} = 0.95

$\beta \in \left[0.05, 0.95\right]$

$\beta = 0.05$ $\beta = 0.05$

Along the curve

③

Response curve — green

S_{\mathrm{col}}\propto Z/(\beta^2 A)\ln(2m_e c^2\beta^2/I)

$\beta \in \left[0.05, 0.95\right]$

$\beta = 0.05$ $S = 212.8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S}{\mathrm{d}\beta}

$\beta \in \left[0.05, 0.95\right]$

$\beta = 0.056$ $S^{\prime} = -4824.3$

Along the curve

Lecture brief

Historical brief

Beer attenuation, Compton (1923), Klein–Nishina, Bragg–Gray cavity and KERMA are the transport of photons and charged particles in matter. The sheets compute fluence, kerma and stopping. This sheet (RAD-34 — Collision stopping snapshot) is the form associated with stopping. Working symbols: $Z$ , $A$ , $\beta$ , $I$ $\rightarrow$ $S$ . Bethe log term.

Purpose

Purpose: compute

S

from

Z

A

\beta

I

in Radiation physics via

S_{\mathrm{col}}\propto Z/(\beta^2 A)\ln(2m_e c^2\beta^2/I)

Bethe log term. Use it when a real radiation physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Z = 6.000\,\mathrm{—}

A = 12.000\,\mathrm{—}

\beta = 0.500\,\mathrm{—}

I = 80.000\,\mathrm{eV}

, the governing relation

S_{\mathrm{col}}\propto Z/(\beta^2 A)\ln(2m_e c^2\beta^2/I)

yields

S = 5.131\,\mathrm{MeV cm^{2}/g}

. Bethe log term. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Z Z6 —A A12 —β \beta0.5 —I I80 eV

Outputs

S/ρ S5.131 MeV cm²/g

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Narration of this film

Bethe log term.

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