Mössbauer effect

The Mößbauer effect (after the discoverer Rudolf Mößbauer , also written Mössbauer effect ) is understood as the recoil-free nuclear resonance absorption of gamma radiation by atomic nuclei . If you combine the emission of the gamma quanta and their renewed absorption , Mössbauer spectroscopy is an extremely sensitive measurement method for the change in energy in the gamma quanta. To do this, the atomic nucleus must be in a crystal lattice that can take over the recoil and, due to its large mass, hardly withdraws any energy from the gamma quantum (see also elastic impact ). Rudolf Mößbauer received the Nobel Prize in Physics for his discovery in 1961 .

Properties of gamma radiation

Physicists have known gamma radiation as a phenomenon of radioactivity since the beginning of the 20th century . Antoine Henri Becquerel and Paul Villard are considered to be the discoverers , the latter being able to prove around 1900 that gamma radiation is extremely high-energy electromagnetic waves. Gamma radiation occurs u. a. as a result of a preceding alpha or beta decay , since the atomic nucleus is in an excited state after this decay.

In contrast to an α or β decay, the emission of the gamma quantum does not materially change the nucleus; there is no conversion into another nuclide . Only the excitation energy stored in the nucleus is emitted as one or more radiation quanta, just like excited electrons emit their energy in the form of light quanta. Atomic nuclei can also absorb gamma quanta, as a result of which they pass into an excited state relative to the previous state.

From theoretical considerations, it was concluded early on that the gamma radiation emitted by most nuclei is characterized by very sharp energy levels and must therefore have an extremely narrow line width. Atomic nuclei can also be compared to an oscillating crystal, which can only be excited at a certain frequency. In fact, the energy constancy (and thus the frequency accuracy) of many gamma radiation transitions is comparable to the accuracy of atomic clocks .

The initial situation in front of Mößbauer

The theoretically predicted spectral purity of the gamma radiation was practically undetectable before the discovery made by Mössbauer. Due to the high energy of the gamma quanta, their frequency can only be roughly determined using calorimetric methods. An electronic frequency counter no longer works in the frequency range of gamma radiation.

In addition, when a gamma quantum is emitted, the core experiences a recoil that cannot be neglected. This is due to the high energy of the quanta, which as photons have no mass , but have an impulse . The recoil acting on the core causes a reduction in the energy of the gamma quantum: If the core loses its energy with the mass due to the emission of the photon , it experiences a recoil of the energy due to energy and momentum conservation . The emitted photon then has the reduced energy . ${\ displaystyle M}$ ${\ displaystyle E_ {0}}$ ${\ displaystyle E_ {R}}$ ${\ displaystyle \ Delta E}$ ${\ displaystyle E _ {\ gamma} = E_ {0} - \ Delta E}$

{\ displaystyle E_ {R} = \ Delta E = {\ frac {E _ {\ mathrm {\ gamma}} ^ {2}} {2Mc ^ {2}}}}

This results from (with the nuclear mass ) and the relativistic energy-momentum relationship for the photon . ${\ displaystyle E_ {R} = {\ tfrac {({\ vec {p}}) ^ {2}} {2M}}}$ ${\ displaystyle M}$ ${\ displaystyle E _ {\ mathrm {\ gamma}} = pc = | {\ vec {p}} | \, c}$

Equivalent to this description is a consideration from the point of view of the now moving core, taking into account the Doppler frequency shift . Will now absorb the light emitted from another core gamma ray again a core, so this is really only possible if previously both cores are flown exactly twice the recoil velocity each other (twice, because even at the absorption an equally strong rebound occurs) . The required speed can be generated experimentally, for example, by placing the source or absorber on the edge of a rapidly rotating centrifuge or a turntable or by heating the source in order to increase the thermal line broadening. Mössbauer followed both methods. The use of a centrifuge or a turntable (as it was first used by PB Moon in 1951 for nuclear magnetic resonance fluorescence) was not feasible with the iridium source he used , since it would have required supersonic speed without the effect he later discovered.

Mössbauer's experiment

As part of his dissertation, which was carried out in 1958 at the Technical University of Munich with Heinz Maier-Leibnitz and for which he previously experimented at the Max Planck Institute for Medical Research in Heidelberg, Mößbauer wanted the probability of such an emission and subsequent absorption of a gamma quantum determine. The requirement that the two nuclei involved move towards each other at the correct speed should be fulfilled by the thermal movement of the atoms.

Here is the schematic set-up of his experiment:

On the left is a radioactive source for gamma rays. Some of the rays hit an absorber on the right that contains the same atoms as the source, but these are not inherently radioactive. If a core in the absorber is hit by a gamma photon, the gamma photon can be scattered towards the detector if the above requirement is met. The direct path of the radiation to the detector is blocked by a lead shield.

The temperature of solids , liquids and gases is correlated with the speed of the particles ( atoms , molecules ) in them. The higher the temperature, the faster the particles move on average. However, the speed of all particles is not the same, but is statistically distributed, as is the direction of movement of the particles.

Mössbauer expected that as the temperature rises, the probability of emission and subsequent absorption of a gamma quantum should increase, since statistically more atoms are moving towards one another at the correct speed. Conversely, at very low temperatures the probability of this process should be reduced to almost zero, since the atoms are on average so slow that the required speed difference is hardly ever reached.

The initially surprising result

The first measurements near room temperature and above seemed to confirm Mössbauer's expectations. However, when he began to cool the source and absorber out of curiosity, he surprisingly found that the probabilities for gamma emission and absorption suddenly rose sharply again at low temperatures, beyond what had been measured at higher temperatures.

Mößbauer carried out his experiments on solids. In these, the atoms oscillate around their positions of rest in the crystal lattice (with increasing temperature with increasing amplitude). However, due to quantum mechanics, not all oscillation states are allowed, but only discrete energy states ( phonons ). For this reason, when a gamma quantum is emitted and absorbed, the core cannot emit any strong impulse in the form of vibrational energy. Since the absorption and release of the oscillation energy is quantized, there is a certain probability (given by the so-called Debye-Waller factor ) that the atom does not generate any oscillation energy and can transfer its recoil impulse to the entire crystal lattice. Since its mass significantly exceeds that of the core, gamma emission and absorption occur almost without recoil in this case.

Mössbauer then checked the result more precisely by attaching the source to a turntable and thus using the Doppler effect to vary the energy and measure the resonance.

For the isotope Iridium-191 used by Mössbauer, the gamma ray energy was 129 keV and the natural line width was in the order of magnitude of eV. The energy resolution was thus never reached before . Soon afterwards, other Mössbauer lines were discovered, especially Fe-57 with recoil-free emission at room temperature, a gamma ray energy of 14.4 keV and a natural line width of eV. ${\ displaystyle 10 ^ {- 5}}$ ${\ displaystyle 10 ^ {- 10}}$ ${\ displaystyle \ approx 5 \ cdot 10 ^ {- 9}}$

Applications

The recoil-free nuclear resonance absorption results in completely new measurement methods in the fields of solid-state physics, materials research and chemistry. Furthermore, predictions of the general theory of relativity can also be examined with this effect. In 1960, in a Mössbauer experiment by Robert Pound and Glen Rebka, it was found that if the source and absorber are vertically spaced around 20 meters apart, the earth's gravitational potential leads to a measurable change in the energy of the light quanta when passing through the height difference ( Pound Rebka experiment ).

The Mössbauer effect is used in the most varied of areas today in chemistry. Since the development of the electron shell of a molecule has a slight effect on the energy levels of the excited states of its atomic nuclei, the Mössbauer effect has developed into an irreplaceable instrument in chemical analysis (see: Mössbauer spectroscopy ).

literature

Rudolf Mößbauer: Gamma radiation in Ir191 . In: Journal of Physics . tape 151 , 1958, pp. 124-143 , doi : 10.1007 / BF01344210 .
Rudolf Mößbauer: Recoilless Nuclear Resonance Absorption of Gamma Radiation , Nobel Lecture 1961, Online
Hans Frauenfelder : The Mössbauer Effect , WA Benjamin, New York, 1962
Leonard Eyges: Physics of the Mössbauer Effect . In: American Journal of Physics . tape 33 , 1965, pp. 790-802 , doi : 10.1119 / 1.1970986 .
Philipp Gütlich: Physical methods in chemistry: Mössbauer spectroscopy I . In: Chemistry in Our Time . tape 4 , 1970, pp. 133-144 , doi : 10.1002 / ciuz.19700040502 .
Horst Wegener : The Mössbauer effect and its application in physics and chemistry , BI Wissenschaftsverlag 1965

Web links

Mössbauer Effect ( LEIFI )

Remarks

^ PB Moon: Resonant Nuclear Scattering of Gamma-Rays: Theory and Preliminary Experiments . In: Proceedings of the Physical Society. Section A . tape 64 , no. 1 , January 1951, p. 76-82 , doi : 10.1088 / 0370-1298 / 64/1/311 (quoted in Mößbauer's Nobel Lecture).
↑ The area of the crystal lattice that can absorb recoil energy results roughly from the volume of the sphere, the radius of which corresponds to the distance that the sound can travel in this lattice during the mean life of the gamma transition.
^ Hans Kuzmany: Solid-State Spectroscopy: An Introduction . Springer Science & Business Media, 1998, p. 300 ( limited preview in Google Book Search).

[1] PB Moon: Resonant Nuclear Scattering of Gamma-Rays: Theory and Preliminary Experiments . In: Proceedings of the Physical Society. Section A . tape 64 , no. 1 , January 1951, p. 76-82 , doi : 10.1088 / 0370-1298 / 64/1/311 (quoted in Mößbauer's Nobel Lecture).

[2] The area of the crystal lattice that can absorb recoil energy results roughly from the volume of the sphere, the radius of which corresponds to the distance that the sound can travel in this lattice during the mean life of the gamma transition.

[3] Hans Kuzmany: Solid-State Spectroscopy: An Introduction . Springer Science & Business Media, 1998, p. 300 ( limited preview in Google Book Search).