Recoil-free resonant emission/absorption

The term Mossbauer effect describes the recoil-free resonant absorption of y quanta by nuclei of the same kind as the emitters. If a free nucleus undergoes a transition from an excited state by emission of a y quantum, it suffers a recoil. The energy of this quantum in the laboratory frame is given as = E — E/j, where E is the nuclear transition energy and Er is the recoil energy of the nucleus after the emission of the y quantum. It can be expressed as... 

Mossbauer effect is the recoilless (also called recoil-free) nuclear resonance emission/ absorption of y rays (see O Pig. 25.1). In the case of a nuclear transition, the de-excited nucleus is normally recoiled by the momentum of the y photon emitted, which makes its resonance absorption impossible by another ground-state nucleus of the same type. In solids, however, recoilless photons can be emitted (and reabsorbed by another ground-state nucleus) with some probability. 

The Mossbauer effect, discovered by Rudolf L. Mossbauer in 1957, can in short be described as the recoil-free emission and resonant absorption of gamma radiation by nuclei. In the case of iron, the source consists of Co, which decays with a half-life of 270 days to an excited state of Fe (natural abundance in iron 2%). The latter, in turn, decays rapidly to the first excited state of this isotope. The final decay generates a 14.4 keV photon and a very narrow natural linewidth of the order of nano eV. 

However, in contrast, the resonance effect increased by cooling both the source and the absorber. Mdssbauer not only observed this striking experimental effect that was not consistent with the prediction, but also presented an explanation that is based on zero-phonon processes associated with emission and absorption of y-rays in solids. Such events occur with a certain probability/, the recoil-free fraction of the nuclear transition (Sect. 2.4). Thus, the factor/is a measure of the recoilless nuclear absorption of y-radiation - the Mdssbauer effect. 

Figure 5.1 Resonant absorption of y-radiation by a nucleus can only take place in the solid state because of recoil effects. The excited nucleus of a free atom emits a y-photon with an energy EirER, whereas the nucleus in the ground slate of a free atom can only absorb a photon if it has an energy equal to Eo+ER. As the linewidth of nuclear transitions is extremely narrow, the emission spectrum does not overlap with the absorption spectrum. In a solid, a considerable fraction of events occurs recoil free (ER=0), and here the emission spectrum overlaps completely with the absorption spectrum (provided source and absorber have the same chemical environment).

The Mossbauer effect involves the resonance fluorescence of nuclear gamma radiation and can be observed during recoilless emission and absorption of radiation in solids. It can be exploited as a spectroscopic method by observing chemically dependent hyperfine interactions. The recent determination of the nuclear radius term in the isomer shift equation for shows that the isomer shift becomes more positive with increasing s electron density at the nucleus. Detailed studies of the temperature dependence of the recoil-free fraction in and labeled Sn/ show that the characteristic Mossbauer temperatures Om, are different for the two atoms. These results are typical of the kind of chemical information which can be obtained from Mossbauer spectra. 

The observation of resonance is governed by the probability of emission (in the source) and absorption (in the absorber) of the gamma photons. This probability (Eq. (2)) is named the Lamb-Mossbauer or recoil-free factor. The probability of the interaction of a photon with a nucleus that is at the basis of the absorption is proportional to the square of the matrix element of the interaction Hamiltonian which excites the initial state i to the final state f ... 

Mossbauer effect. A nuclear phenomenon discovered in 1957. Defined as the elastic (recoil-free) emission of a 7-particle by the nucleus of a radioactive isotope and the subsequent absorption (resonance scattering) of the particle by another atomic nucleus. Occurs in crystalline solids and glasses but not in liquids. Examples of y-emitting isotopes are iron-57, nickel-61, zinc-67, tin-119. The Mossbauer effect is used to obtain information on isomer shift, on vibrational properties and atomic motions in a sohd, and on location of atoms within a complex molecule. 

Mossbauer spectroscopy is specialized, but it can be invaluable when it is available. The technique relies on the recoil-free emission and resonant absorption of y-rays by nuclei that are bound in the solid state. (If it is not in a solid, the free nucleus recoils and no resonance is detected.) To see this resonance, we have to match the energy of the y-ray emitter to the energy of the absorber (the sample), which means that only a small number of elements can be studied. Two that can be studied are tin and iron. The technique gives information on the bonding and coordination, and on the valence (oxidation) state. Since the technique relies on Z, it works for particular isotopes, Fe for iron with Co as the radioactive source of y-rays. (Natural Fe contains -2.19 wt% Fe.)... 

A Mossbauer spectrum arises from the recoil-free emission and resonant absorption of a 7-ray by a nuclide. The intensity of the radiation emitted by a source containing the radioactive Mossbauer precursor nuclide, and transmitted through a solid absorber containing the Mossbauer nuclides in... 

The recoil-free emission and resonant absorption processes necessary to observe the Mossbauer spectrum can only occur for nuclei bound into a solid. The fraction of such events depends on the 7-ray energy and the vibrational properties of the crystal. Hence, in principle from temperature-dependent measurements of the absorption area, information about crystal dynamics, such as the Debye temperature, can be obtained. 

Unfortunately, the requirements of recoil-free emission and resonant absorption and transmission through the absorber limit the useable energy range of the Mossbauer effect 7-ray to approximately 10-100 keV. Further, in order to obtain rather sharp absorption lines and a reasonable spectral resolution, the mean lifetime of the Mossbauer 7-ray precursor state should be between 1 ns and 100 ns. Further, the Mossbauer nuclide must have a sufficiently high isotopic abundance in the element to yield a usable signal-to-noise ratio over a reasonable acquisition time. Finally, the radioactive source containing the Mossbauer 7-ray precursor state must be easily prepared and have a mean lifetime of several weeks to be practical. These various requirements limit the number of nuclides available for typical Mossbauer spectral studies. 

In the X-ray region the recoil energy can be so large that the frequency of y quanta emitted by free nuclei is shifted out of resonance with the absorption profile of the same transition in absorbing nuclei of the same kind. The recoil can be avoided by implanting the nuclei into the rigid lattice of a bulk crystal below its Debye temperature. This recoil-free emission and absorption of Y quanta is called the mGhauer effect. 

A free atom interacting with a laser field experience two different kinds of forces. The first is due to the photon recoil during resonance absorption with subsequent spontaneous emission. This force is often called resonanoe radiation pressure. The second force arises from nonresonant stimulated scattering of photons by atoms and occurs only in fields with a nonvanishing field gradient. Let us at first consider how the spontaneous reooil foroe can be utilized to cool atoms [13.13a]. 

Fig. 2.4 Energy separation of y-emission and absorption lines caused by recoil of resting free nuclei (2 r lO T, note the three separate sections of the energy scale). Since there is virtually no overlap between emission and absorption line, resonant absorption is not possible...

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