---
title: "How a crystal takes the recoil of an emitting nucleus"
description: "Why can putting nuclei in a solid restore an extremely narrow gamma-ray resonance?"
canonical_url: "https://sandboxphysics.com/stories/quantum-evidence/mossbauer-recoil-free-resonance/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/quantum-evidence/mossbauer-recoil-free-resonance/"
last_modified: "2026-10-24"
---

[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# How a crystal takes the recoil of an emitting nucleus

Sandbox Physics · 2026-10-15

Why can putting nuclei in a solid restore an extremely narrow gamma-ray resonance?

## An emitting nucleus recoils

When a gun fires a bullet forwards, the gun recoils backwards. A free excited nucleus emitting a gamma-ray photon also has to recoil. The photon carries momentum, and the nucleus takes an opposite momentum and some kinetic energy. A free nucleus absorbing the photon needs recoil energy as well.

Nuclear resonance lines can be extremely narrow. The small loss of photon energy on emission and the extra energy needed on absorption can separate the two processes by many natural line widths. A source and absorber made from the same isotope may therefore show little resonant absorption.

Read the evidence: B. Fultz, Mössbauer Spectrometry — technical chapter hosted by the Advanced Photon Source

## Bind the nucleus into a crystal

In 1958, Mössbauer investigated iridium nuclei bound in solids. Changing the temperatures of the source and absorber, he found a marked enhancement of resonant absorption at low temperature. Binding had changed the opportunities for emission and absorption. This early work used iridium; the iron transitions common in later spectroscopy came afterwards.

Atoms in a crystal are connected to one another. In some nuclear events, no lattice-vibration excitation is created or removed, and the whole crystal receives the momentum. Its enormous mass makes the recoil energy negligible on the scale of the narrow line. These events form the recoil-free channel.

The crystal still receives momentum, and its atoms still vibrate. What matters is that the internal vibrational state stays unchanged in that event. The probability of this channel depends on the material, temperature and transition. Cooling often increases the recoil-free fraction; its low-temperature value still depends on the solid and transition.

Read the evidence: R. L. Mössbauer (1958), Kernresonanzfluoreszenz von Gammastrahlung in Ir191, Z. Phys. 151, 124–143 — publisher abstract B. Fultz, Mössbauer Spectrometry — technical chapter hosted by the Advanced Photon Source

## The mass receiving the momentum matters

For the same momentum, a heavier object takes less kinetic energy. The equation gives the approximate recoil energy of a free nucleus initially at rest. The photon energy is labelled with gamma, M is the nuclear mass, and c is the speed of light. It assumes a recoil speed much smaller than the speed of light. Recoil energy rises rapidly with photon energy and falls as the receiving mass grows.

This identifies what the crystal makes possible. In an event with no change of internal vibration, its large overall mass reduces the energy cost of receiving momentum. The narrow energy windows for emission and absorption can overlap again.

$$
E_{\mathrm R}\simeq\frac{E_\gamma^2}{2Mc^2}
$$

Read the evidence: B. Fultz, Mössbauer Spectrometry — technical chapter hosted by the Advanced Photon Source

## Move the source slowly to scan the resonance

Once the narrow resonance exists, it must be located. Moving a gamma-ray source slowly towards the absorber gives the photons a small Doppler energy increase; moving it away reduces their energy. At speeds far below light speed, the magnitude of the fractional energy change is approximately the line-of-sight speed divided by light speed. Counting transmitted photons at each speed produces a finely resolved absorption spectrum.

The electrons, electric fields and magnetic fields around a nucleus can shift or split its lines. Interpreting the structure also requires source-speed calibration, absorber thickness, nonresonant background and the recoil-free fraction. With suitable references and level assignments, the narrow nuclear resonance becomes a sensitive probe of the nucleus’s local environment inside a material.

Read the evidence: B. Fultz, Mössbauer Spectrometry — technical chapter hosted by the Advanced Photon Source

## Continue with the models

These teaching Labs produce simulated data, which are separate from the historical observations discussed above.

- [Move the simulated source and measure gamma-ray transmission](https://sandboxphysics.com/labs/mossbauer-doppler-resonance/)

## Sources and reading notes

The German abstract of the 1958 paper can be read on the publisher’s site. The Nobel PDF was blocked; it is listed for further reading, and we did not read it in full. Recoil-free fractions and Doppler scanning follow Fultz’s technical treatment, hosted by the Advanced Photon Source. No historical spectrum is reproduced.

1. [R. L. Mössbauer (1958), Kernresonanzfluoreszenz von Gammastrahlung in Ir191, Z. Phys. 151, 124–143 — publisher abstract](https://link.springer.com/article/10.1007/BF01344210)
2. [B. Fultz, Mössbauer Spectrometry — technical chapter hosted by the Advanced Photon Source](https://www.aps.anl.gov/files/APS-Uploads/SECTOR3/Conferences/NRS2016/PDF/MossbauerWileycom069.pdf)

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