Illustrated Physics
physics, drawn
Concept

Natural linewidth — where it appears

The spread of frequencies of light emitted in a transition, set by the lifetime of the excited state through the energy–time relation. It is the narrowest a spectral line can be, and in a vapour it is usually hidden beneath far wider Doppler broadening.

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

An atom's line and a nucleus's, on one scale. Three energies, in electronvolts on a logarithmic scale, for an atomic transition, sodium's yellow line, and a nuclear one, the 14.4 keV gamma ray of iron-57: the amount by which emission and absorption by free atoms miss each other because of recoil, E²/Mc²; the natural width of the line, ħ over the excited state's lifetime; and the Doppler width from thermal motion at room temperature. For sodium the recoil miss is 2.1·10⁻¹⁰ eV, 197 times smaller than the natural width, so an atom absorbs its neighbour's light. For iron-57 it is 0.00392 eV, 839,015 times its natural width of 4.67·10⁻⁹ eV. The recoil grows as the square of the transition energy and the width does not, so a gamma ray emitted by a free nucleus misses an identical nucleus by nearly a million line widths.

The gamma ray its own kind cannot absorb

An atom can absorb the light another atom of its kind emits; that is how a sodium flame casts a shadow in sodium light. A nucleus cannot. When it emits a gamma ray it loses the photon's energy as mass, and the photon's momentum kicks it backward, taking a small share of the energy with it; to absorb the same gamma ray, an identical nucleus would need that share added rather than removed. For iron-57's 14.4 keV line the shortfall is nearly a million times the line's own width. In 1958 Rudolf Mössbauer found that a nucleus held in a crystal can hand its recoil to the whole crystal and lose almost nothing — and the resulting line is so sharp that it could weigh the fall of light down a twenty-two metre tower.

relativity · Mass-energy The hyperfine structure, read off a room-temperature cell. The difference between the probe's absorption with the pump off and on, which removes the Doppler hump and leaves only the Doppler-free features, against detuning. The three transitions, labelled by the excited level F′, sit at −423.6, −266.65 and 0 MHz, and the three crossovers midway between them at −345.1, −211.8, −133.3 MHz. In this model, which empties the ground level only by exciting it, the crossover between F′ = 2 and 3 is the second strongest feature and the weak transitions to F′ = 1 and 2 are small. In real rubidium spectra the crossovers are often the strongest of all, because excited atoms can fall to the other ground level and be lost to the transition altogether — optical pumping, which the model leaves out and which deepens every hole the pump burns. The positions do not depend on any of that: the separations between the features are the hyperfine splittings of rubidium's excited state, read to a fraction of a megahertz in a glass cell on a bench.

The lines a warm vapour hides

Shine a tunable laser through a cell of rubidium vapour and the absorption is one smooth hump half a gigahertz wide, though the atoms' own lines are eighty times narrower and three of them lie inside it. The atoms are moving, each sees the light Doppler-shifted by its own speed, and their lines are smeared together. Send a second, stronger beam back the other way and narrow dips appear in the hump at exactly the frequencies of the hidden lines — because only atoms standing still can be talked to by both beams at once. The vapour stays at room temperature and the motion is not removed; it is selected against.

quantum · Atomic spectra

Named alongside it

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

Doppler broadeningDoppler effectGravitational redshiftHyperfine structureLaserMass-energyMossbauer effectRecoilRecoil free fractionResonant absorptionSaturationSpectral line

All concepts