Mossbra: Mössbauer Effect
Nuclear & Particle Physics arc, page 178 of 193. Back to The Pixelated Physics Universe
Who they are
Mossbra, armoured in crystal, looses a gamma arrow and does not rock back at all. The whole lattice takes the kick for her.
Mossbra is a character of the Nuclear & Particle Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
A free nucleus that emits a gamma ray recoils and steals a little energy, so the photon misses the absorber's resonance. For iron-57's 14.4 keV line the recoil is about 2.0 × 10⁻³ eV, while the natural linewidth is only about 4.6 × 10⁻⁹ eV: the miss is roughly 400 000 linewidths. Rudolf Mössbauer found in 1958, working with iridium-191, that a nucleus bound in a crystal can emit and absorb without recoil. The whole lattice takes the momentum, and with some probability no phonon is created. That gives a line of fractional width about 3 × 10⁻¹³, which made Mössbauer spectroscopy possible.
$$ \begin{gathered} E_R = \frac{E_\gamma^{2}}{2Mc^{2}} \\ {}^{57}\mathrm{Fe}:\ E_R \approx 2.0\times10^{-3}\ \mathrm{eV}, \quad \Gamma \approx 4.6\times10^{-9}\ \mathrm{eV} \\ \Gamma / E_\gamma \approx 3\times10^{-13} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $E_R$ | recoil energy of a free nucleus | eV |
| $E_\gamma$ | gamma-ray energy (14.4 keV for ⁵⁷Fe) | eV |
| $M$ | mass of the nucleus | kg |
| $c$ | speed of light, 299 792 458 m/s (exact) | m/s |
| $\Gamma$ | natural linewidth of the transition | eV |
Honest caveat: Only a fraction of the gammas are recoil-free, not all of them. Even then, the crystal does recoil, just by a negligible amount, because it is so heavy.
Sources
- Mössbauer (1958) Kernresonanzfluoreszenz von Gammastrahlung in Ir191, Z. Phys. 151, 124
- Nobel Prize in Physics 1961, NobelPrize.org
Crossovers
Mossbra meets Jetlagga (Clocks Around the World 1971). Mossbra's recoil-free gamma rays are sharp enough to measure gravitational redshift over a tower about 22 m tall, as Pound and Rebka did. Jetlagga measured relativity with clocks instead.
Mossbra meets Recoilwyn (Radioactive Recoil). Recoilwyn studied the recoil of a nucleus after it emits. Mossbra avoids recoil entirely: the whole crystal lattice takes the kick, so the gamma ray loses almost no energy.
Wear the lore
Concept keywords: Mössbauer Effect, Mossbra, Nuclear & Particle Physics, physics lore, Pixelated Physics