NUC-13

Neutron moderation (head-on)

E′/E = ((A−1)/(A+1))² for a head-on elastic scatter on a nucleus of mass A.

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NuclearNeutron moderation

Governing equation

\dfrac{E'}{E}=\left(\dfrac{A-1}{A+1}\right)^2

$A \in \left[1, 238\right]$

where

A: Moderator A (u)
E: Incident energy (MeV)
\alpha: Energy ratio (—)
E': After scatter (MeV)

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

\dfrac{E'}{E}=\left(\dfrac{A-1}{A+1}\right)^2

$A \in \left[1, 238\right]$

$A = 1$ $\alpha = 0$

Along the curve

②

Domain of the variable — blue

A_{\min} = 1,\quad A_{\max} = 238

$A \in \left[1, 238\right]$

$A = 1$ $A = 1$

Along the curve

③

Response curve — green

\dfrac{E'}{E}=\left(\dfrac{A-1}{A+1}\right)^2

$A \in \left[1, 238\right]$

$A = 1$ $\alpha = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\alpha}{\mathrm{d}A}

$A \in \left[1, 238\right]$

$A = 2.491$ $\alpha^{\prime} = 0.12$

Along the curve

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-13 — Neutron moderation (head-on)) is the form associated with Neutron moderation. Working symbols: $A$ , $E$ $\rightarrow$ $\alpha$ , $E'$ . Hydrogen (A=1) can stop a neutron in one collision. Uranium barely ticks the energy.

Purpose

Purpose: compute

\alpha

E'

from

A

E

in Nuclear physics via

\dfrac{E'}{E}=\left(\dfrac{A-1}{A+1}\right)^2

E′/E = ((A−1)/(A+1))² for a head-on elastic scatter on a nucleus of mass A. 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

A = 1.000\,\mathrm{u}

E = 2.000\,\mathrm{MeV}

, the governing relation

\dfrac{E'}{E}=\left(\dfrac{A-1}{A+1}\right)^2

yields

\alpha = 0.0000\,\mathrm{—}

E' = 0.0000\,\mathrm{MeV}

. A neutron, a nucleus, a smaller E′. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Moderator A A1 uIncident energy E2 MeV

Outputs

Energy ratio \alpha0.0000 —
After scatter E'0.0000 MeV

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Narration of this film

A neutron, a nucleus, a smaller E′.

Hydrogen (A=1) can stop a neutron in one collision. Uranium barely ticks the energy.

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