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Moderon

Neutron Moderation / Elastic Scattering Physics

\[\alpha = \left(\frac{A-1}{A+1}\right)^2\]
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Moderon is a Pixelated Physics law character, one of our forces designs. Neutron moderation: a neutron hitting a proton of equal mass can stop dead, which is why water slows reactor neutrons so well. This is a 3" × 3" pixel-art sticker. The physics panel below gives the equation, what each symbol means and the sources.

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Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Shipping calculated at checkout by destination. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

A neutron loses the largest share of its energy when it hits a nucleus of about its own mass. The average logarithmic energy loss per collision tells you how many collisions a moderator needs to slow fission neutrons down to thermal energies.

Moderon is a pool hustler, a proton with almost exactly the neutron’s mass, and he waits on the table.

A neutron fresh from fission flies at about 2 MeV. To keep a chain reaction going in a thermal reactor it has to be slowed to about 0.025 eV, roughly 2200 m/s, where uranium-235 catches it far more readily. The neutron has no charge, so the only way to slow it is to let it bump into nuclei.

The physics is the pool table. When a moving ball hits a resting ball of the same mass head-on, it stops dead and the other rolls off with all its energy. That is the first line on this page with A equal to one. Glancing hits take less; on average a collision with hydrogen takes away half the energy, so getting from 2 MeV to thermal takes about 18 hits. Heavier targets do worse. Deuterium needs about 25, carbon about 115, and uranium-238 about 2172, because a light ball bouncing off a heavy one keeps almost all its speed. That is why reactors use water and graphite.

In October 1934 Enrico Fermi’s group in Rome found that neutrons made their samples far more radioactive after passing through paraffin wax, which is rich in hydrogen. Fermi realised that the hydrogen was slowing the neutrons, and that slow neutrons are captured more easily. Edoardo Amaldi, Oscar D’Agostino, Fermi, Bruno Pontecorvo, Franco Rasetti and Emilio Segrè published the work in 1935, and Fermi received the 1938 Nobel Prize.

So Moderon doesn’t shoot. The neutron rolls in, and the hustle is nothing but conservation of momentum and energy.

Same mass. You stop. I roll.

Equations

\[\alpha = \left(\frac{A-1}{A+1}\right)^2\]
\[\xi = 1 + \frac{\alpha\ln\alpha}{1-\alpha}\]
\[n_{\text{coll}} \approx \frac{\ln(E_0/E_{\text{th}})}{\xi}\]
Symbols
SymbolMeaningUnit
\(A\) mass of the target nucleus in neutron masses (hydrogen: 1) \(\mathrm{1}\)
\(\alpha\) smallest possible ratio of neutron energy after to before one collision (a head-on hit) \(\mathrm{1}\)
\(\xi\) average loss of ln E per collision (hydrogen: 1) \(\mathrm{1}\)
\(n_{\text{coll}}\) average number of collisions to slow a neutron to thermal \(\mathrm{1}\)
\(E_0\) starting neutron energy, about 2 MeV from fission \(\mathrm{MeV}\)
\(E_{\text{th}}\) thermal neutron energy, about 0.025 eV \(\mathrm{eV}\)

Source Amaldi, E. et al. (1935). Artificial radioactivity produced by neutron bombardment—II. Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences 149, 522–558.doi.org/10.1098/rspa.1935.0080 (opens in a new tab)