Illustrated Physics
physics, drawn
Concept

Klein nishina — where it appears

The cross-section for a photon scattering off a free electron, derived from quantum electrodynamics in 1929. It equals the Thomson value at low energy and falls roughly as the inverse of the photon energy above the electron's rest energy, so energetic photons scatter less and mostly forward.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The photon a fast electron throws back. The highest energy of a laser photon scattered straight back by an electron it meets head-on, against the electron's energy, for a carbon-dioxide laser, an infrared and a green one, on logarithmic axes: dashed, 4γ² times the laser photon's energy, the double Doppler shift of a mirror moving at the electron's speed; solid, the exact edge with the electron's recoil, E·x/(1 + x) with x = 4γε/mc²; dotted, the electron's own energy, which no scattered photon reaches. A 1 GeV electron turns 1.17-eV infrared photons into gamma rays of 17.6 MeV, within 1.8 per cent of the mirror's figure. At 46.6 GeV and 2.35 eV the mirror's figure is 78.2 GeV, more than the electron has to give; the photon actually comes back with 29.2 GeV.

The photon a fast electron throws back

Shine an infrared laser at a beam of gigaelectronvolt electrons and gamma rays come back out of the collision, each carrying seventeen million times the energy of the laser photon it started as. The electron acts as a mirror moving at nearly the speed of light, and a moving mirror multiplies the energy of light by two Doppler factors. Push the electron's energy far enough and the mirror arithmetic promises photons more energetic than the electron itself — and the photon's own momentum, which the mirror ignored, steps in to stop it.

relativity · Length contraction What one scattering does to a photon's energy. The average fractional change in a photon's energy when it scatters off an electron in a gas at temperature T, against the photon's energy: (4kT − ε)/mc², for gases at 10⁶, 10⁷ and 10⁸ K. A photon below 4kT gains energy, taking it from the electrons' motion; one above loses it, as recoil, to the electrons. The crossing sits at ε = 4kT: 0.34 keV at 10⁶ K, 3.45 keV at 10⁷ K, 34.47 keV at 10⁸ K. The changes per scattering are small, a few per cent at most here, but a gas whose electrons scatter each photon many times, or that is bathed in light for long enough, is heated or cooled until the gains and losses balance over the whole spectrum.

The temperature a gas takes from the light around it

A thin, ionised gas bathed in light settles at a temperature that has nothing to do with how much light there is and everything to do with its colour. Every time a photon scatters off an electron, the two exchange a little energy: a photon softer than four times the electrons' thermal energy gains, a harder one loses by recoil. Balanced over a spectrum, the rule sets the gas at a quarter of the light's mean photon energy. That puts gas near a quasar at tens of millions of kelvin, and it caps the heating once photons approach the electron's own rest energy. For blackbody light the rule falls four per cent short, and the shortfall is the photon being a boson.

relativity · Relativistic thermodynamics

Named alongside it

The objects these essays reach for when they reach for this one.

Compton scatteringThomson scatteringAccretionBlackbodyCompton temperatureDoppler effectInverse compton scatteringThe Lorentz factorPair productionStimulated emissionThermal equilibriumUndulator

All concepts