Concept

Mossbauer effect — where it appears

The emission and absorption of gamma rays by nuclei bound in a crystal without any loss of energy to recoil, because the whole crystal takes up the momentum. The lines are so narrow that they resolve shifts of a part in 10¹⁵.

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

$How much slower a warm atom ticks. The fraction by which a free atom's clock runs slow on average because of its thermal motion, (3/2)kT/mc², against temperature on logarithmic axes, for five atoms used in clocks or tests of relativity: hydrogen 4.1 × 10⁻¹¹ at 300 K, aluminium ion 1.5 × 10⁻¹² at 300 K, strontium 4.8 × 10⁻¹³ at 300 K, caesium 3.1 × 10⁻¹³ at 300 K, mercury ion 2.1 × 10⁻¹³ at 300 K. Every line falls in proportion to the temperature and to one over the mass. A clock aiming at one part in 10¹⁸ must hold strontium below 0.63 mK and hydrogen below 7.3 µK — or know their temperature well enough to correct for it. Pound and Rebka's gravitational shift across 22.5 m, 2.46 × 10⁻¹⁵, is marked for scale.$

The clock that runs slow because it is warm

Every atom in a gas is moving, and every moving clock runs slow. The first-order Doppler shifts of a hot gas cancel on average; the time dilation does not, because it has only one sign. A hydrogen maser at 40 °C runs slow by four parts in a hundred billion from this alone, a nucleus in a crystal runs slow even at absolute zero, and the first test of gravitational time dilation nearly drowned in a one-kelvin temperature difference.

relativity · Time dilation

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

Named alongside it

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

Atomic clock Debye model Doppler effect Gravitational redshift Heat capacity Mass-energy Maxwell–Boltzmann distribution Natural linewidth Recoil Recoil free fraction Resonant absorption Second-order doppler effect

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