Pixel-art crystal lattice with one lime nucleus emitting a cyan 14.4 keV gamma ray while the lattice stays still, captioned no recoil, no miss

The Mössbauer Effect: Recoil-Free Gamma Rays and Gravity

Nuclei can emit and absorb gamma rays with astonishingly sharp energies. In principle, a gamma ray from one iron-57 nucleus should be swallowed eagerly by another iron-57 nucleus. In practice, for free atoms, it almost never is. Rudolf Mössbauer found the way round this in 1958, and the trick, recoil-free emission from nuclei bound in a solid, became the Mössbauer effect Mössbauer effect, Wikipedia[1]. It is the physics behind our Mossbra Mössbauer effect tee.

Formula plate in Pixelated Physics pixel style: ER = Eγ²/(2Mc²); Δf/f = gh/c² ≈ 2.46 × 10⁻¹⁵; v = gh/c ≈ 0.74 μm/s

Why does recoil spoil nuclear resonance?

When a nucleus at rest emits a photon of energy Eγ, momentum conservation forces the nucleus to recoil with momentum Eγ/c. The kinetic energy carried off by the recoil is

ER = Eγ2/(2Mc2)

where M is the mass of the emitting atom in kg and c is the speed of light in m/s Mössbauer spectroscopy, Wikipedia[2]. The emitted photon therefore comes out short by ER, and an absorbing nucleus needs a photon with ER extra to make up for its own recoil. The emission and absorption lines are separated by 2ER Mössbauer effect, Wikipedia[1].

For iron-57, the gamma ray used in almost all Mössbauer work has 14.4 keV Pound–Rebka experiment, Wikipedia[3]. Our own arithmetic with a mass of about 57 atomic mass units gives ER ≈ 1.96 × 10⁻³ eV, a fractional shift of about 1.4 × 10⁻⁷. That sounds tiny, but the recoil-free line is far narrower: its half-width is about 1.13 × 10⁻¹² of the photon energy Pound–Rebka experiment, Wikipedia[3]. The recoil shift is about a hundred thousand line half-widths. Free nuclei simply cannot hit the resonance.

What did Mössbauer discover?

Working on iridium-191 for his doctoral thesis, Mössbauer found that nuclei bound in a crystal can sometimes emit and absorb without any recoil at all Mössbauer 1958[4] Mössbauer effect, Wikipedia[1]. The reason is quantum. A nucleus in a solid cannot recoil freely; it can only hand energy to lattice vibrations, which are quantised as phonons. There is a finite probability that a decay excites no phonon at all. In that fraction of events, the whole crystal takes up the momentum, and because the crystal’s mass is enormous the recoil energy is effectively zero Mössbauer effect, Wikipedia[1].

The probability of a zero-phonon event is the recoil-free fraction, or Lamb–Mössbauer factor Mössbauer effect, Wikipedia[1]. Mössbauer published his results with his thesis in 1958, then used the Doppler effect, by moving the source on a turntable, to scan the resonance and record a full spectrum. That was the birth of Mössbauer spectroscopy Mössbauer effect, Wikipedia[1]. He received half of the 1961 Nobel Prize in Physics; the other half went to Robert Hofstadter Nobel Prize in Physics 1961[5].

Pixel-style physics bar chart on a log scale comparing the iron-57 recoil shift 1.36 × 10⁻⁷, line half-width 1.13 × 10⁻¹² and gravitational shift 2.46 × 10⁻¹⁵

How did the Mössbauer effect measure gravitational redshift?

General relativity, and even Einstein’s earlier equivalence-principle argument, predicts that light falling through a height h in a gravitational field g gains energy, with a fractional frequency change

Δf/f = gh/c2 ≈ 2.46 × 10−15

Here g is in m s⁻² and h in metres Pound–Rebka experiment, Wikipedia[3]. Robert Pound and Glen Rebka used the tower of Harvard’s Jefferson Laboratory, with a source and absorber 22.5 m apart Pound–Rebka experiment, Wikipedia[3] Pound and Rebka 1960[6]. Using the standard value gn = 9.80665 m s⁻² NIST CODATA: standard acceleration of gravity[7], our own arithmetic gives gh/c² ≈ 2.46 × 10⁻¹⁵, in line with the 2.5 × 10⁻¹⁵ Pound and Rebka anticipated Pound–Rebka experiment, Wikipedia[3].

That shift is about 500 times smaller than the line half-width Pound–Rebka experiment, Wikipedia[3]. To measure it, they moved the source slowly to Doppler-shift the gamma ray back onto resonance and used careful slope detection, reversing source and absorber every few days so that rising and falling photons were both measured Pound–Rebka experiment, Wikipedia[3]. The absorber was a 38 cm array of iron foils enriched to 32% iron-57, against a natural abundance of about 2% Pound–Rebka experiment, Wikipedia[3] Isotopes of iron, Wikipedia[8]. The equivalent Doppler speed, by our arithmetic, is

v = gh/c ≈ 0.74 μm/s

less than a micrometre per second. They reported a shift of (2.56 ± 0.25) × 10⁻¹⁵, matching the prediction within 10% Pound–Rebka experiment, Wikipedia[3] Pound and Rebka 1960[6]. Pound and Snider later reached the 1% level Pound and Snider 1964[9] Pound–Rebka experiment, Wikipedia[3]. Clocks in orbit feel the same effect, scaled up to a measurable daily drift, which we cover in how GPS corrects for relativity; our Orbitick GPS clock sticker draws it.

Pixel-style diagram of the Pound–Rebka experiment: a cobalt-57 source above an iron-57 absorber 22.5 m below, with Δf/f = gh/c² ≈ 2.46 × 10⁻¹⁵

What is Mössbauer spectroscopy used for?

With a source moving at a few millimetres per second, the gamma energy can be scanned across tiny nuclear energy differences. For iron-57, a typical velocity range is ±11 mm/s, and 1 mm/s corresponds to 48.075 neV Mössbauer spectroscopy, Wikipedia[2]. The technique can detect changes of a few parts in 10¹¹ Mössbauer spectroscopy, Wikipedia[2]. Three effects show up in a spectrum Mössbauer spectroscopy, Wikipedia[2]:

  • Isomer shift: a shift of the whole spectrum caused by the electron density at the nucleus, which reports on the chemical environment of the atom.
  • Quadrupole splitting: a doublet produced when an electric field gradient splits the excited nuclear level.
  • Magnetic hyperfine splitting: a six-line pattern in magnetically ordered iron, such as metallic iron foil.

A miniature spectrometer, MIMOS II, flew on both NASA Mars Exploration Rovers Mössbauer spectroscopy, Wikipedia[2]. On Opportunity it identified jarosite in the outcrop at Meridiani Planum. Because jarosite is a hydroxide sulfate, its presence is mineralogical evidence for water-driven processes on Mars Klingelhöfer et al. 2004[10].

Pixel-style schematic Mössbauer spectrum of magnetic iron showing six absorption dips across source velocities from −11 to +11 mm/s

Quick FAQ

Why does the Mössbauer effect work only in solids?

Recoil-free events need the nucleus to be bound in a lattice, so that the momentum can be taken up by the whole crystal with a chance of exciting no phonon Mössbauer effect, Wikipedia[1]. In liquids and gases there is no such rigid lattice.

Why iron-57?

It combines a low-energy gamma ray, which keeps recoil small, with a convenient parent, cobalt-57, which decays to the right excited state Mössbauer spectroscopy, Wikipedia[2].

Is the Pound–Rebka result the same as clocks running slower?

Yes. The experiment is read as showing that clocks at different heights in a gravitational field run at different rates Pound–Rebka experiment, Wikipedia[3]. Gravity also bends the path of light, which we explain in our post on Einstein rings and lensing. For a flying-clock version, see the Jetlagga clocks-around-the-world tee, or browse the Relativity & Cosmos collection.

References

  1. Wikipedia, “Mössbauer effect”. https://en.wikipedia.org/wiki/M%C3%B6ssbauer_effect
  2. Wikipedia, “Mössbauer spectroscopy”. https://en.wikipedia.org/wiki/M%C3%B6ssbauer_spectroscopy
  3. Wikipedia, “Pound–Rebka experiment”. https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment
  4. Rudolf L. Mössbauer (1958), “Kernresonanzfluoreszenz von Gammastrahlung in Ir191,” Zeitschrift für Physik 151, 124–143 (DOI 10.1007/BF01344210; metadata verified via Crossref). https://doi.org/10.1007/BF01344210
  5. NobelPrize.org, “The Nobel Prize in Physics 1961” (summary page: Robert Hofstadter and Rudolf Mössbauer). https://www.nobelprize.org/prizes/physics/1961/summary/
  6. R. V. Pound and G. A. Rebka (1960), “Apparent Weight of Photons,” Physical Review Letters 4, 337–341 (DOI 10.1103/PhysRevLett.4.337; metadata verified via Crossref). https://doi.org/10.1103/PhysRevLett.4.337
  7. NIST Reference on Constants, Units and Uncertainty, “standard acceleration of gravity g_n” (exact, 9.80665 m s⁻²). https://physics.nist.gov/cgi-bin/cuu/Value?gn
  8. Wikipedia, “Isotopes of iron”. https://en.wikipedia.org/wiki/Isotopes_of_iron
  9. R. V. Pound and J. L. Snider (1964), “Effect of Gravity on Nuclear Resonance,” Physical Review Letters 13, 539–540 (DOI 10.1103/PhysRevLett.13.539; metadata verified via Crossref). https://doi.org/10.1103/PhysRevLett.13.539
  10. G. Klingelhöfer et al. (2004), “Jarosite and Hematite at Meridiani Planum from Opportunity's Mössbauer Spectrometer,” Science 306, 1740–1745 (DOI 10.1126/science.1104653; metadata verified via Crossref). https://doi.org/10.1126/science.1104653

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.

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