Recoil-Free Emission and Absorption

The arguments seen in section 2.3 suggest that resonant y-absorption should decrease at very low temperatures because the Doppler broadening of the y-lines decreases and may even drop below the value of the recoil energy. In his experiments with solid sources and absorbers, however, R.L. Mossbauer ([1] in Chap. 1) observed on the 

Independent of specific theoretical models for the phonon spectrum of a solid matrix, the recoil-free fraction can be given in terms of the y-energy Ej and the mean local displacement of the nucleus from its equilibrium position ([2] in Chap. 1) [5]  

Appropriate approximations of the integral yield a dependence for/(T) in the low temperature limit (T d). 

The recoil-free fraction / is an important factor for determining the intensity of a Mossbauer spectrum. In summary, we notice from inspecting (2.14)-(2.17) and Fig. 2.5a that 

For a more detailed account of the recoil-free fraction and lattice dynamics, the reader is referred to relevant textbooks ([12-15] in Chap. 1). 

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Rudolf Mossbauer found during work on his PhD thesis in 1953 that, if Ir nuclei are embedded in a crystal lattice, there is a certain probability for recoil-free emission and absorption of y quanta. Later he received the Nobel prize because in the meantime it had been found that recoil-free emission and absorption of y quanta also worked for Fe and this boosted the application of the technique in physics, material science, and chemistry. A very instructive description of these investigations can be found in his Nobel lecture. ... 

Mossbauer spectroscopy is based on the observation that nuclei held rigidly in a lattice can undergo recoil-free emission and absorption of X-radiation the separation of nuclear energy levels can be measured with great accuracy, and it is possible to detect weak interactions between a nucleus and its electronic environment. This may reveal the chemical state of the atom or ion, but only a few nuclei are susceptible to the effect, most work having been done with iron ( Fe) and tin Sn) and a little with ruthenium... 

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. 

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. 

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. 

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...

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. 

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. 

Figure 1. Relation of line width, transition energy, and recoil energy, (a) Overlap (schematic) of emission and absorption lines in optical transitions, (b) Absence of overlap (schematic) of emission and absorption lines in nuclear transitions involving atoms free to recoil. Drawn to scale, separation between two lines would be about 4 X 10 the width of each line at half rriaximum...

If the free-atom recoil energy is much greater than the characteristic energy for phonon excitation ha>h where cor is the associated lattice vibration frequency, then phonon creation represents another mode of energy loss, which destroys resonance (29, 30, 32). For R° less than or of the order of tuo, a significant fraction of the nuclear events (emission and absorption)... 

Mossbauer effect was first reported by Rudolph Mossbauer in 1958. Three years later, he won the Nobel Prize with his discovery. Since then, it is believed that nuclear y-ray emission and absorption process can take place in recoil-free fashion. In reality, of course we have both recoil and recoil-free events. Mossbauer also utilized the Doppler (velocity) shift to modulate the y-ray energy so that Mossbauer effect could be developed into a spectroscope for material characterization. The emission of y-rays with natural or nearly natural line width allows for observing in the y-ray spectra the interaction between the nucleus and its atom in solids and viscous liquids. 

The source of the y-rays is the 119mSn isotope which is prepared by the (n,y) reaction of 118Sn. It decays with a half life of 245 days to give the nuclear excited 119Sn. This has a spin / of /2, and a half life of 1.84 x 10 x s, and emits ay-ray of 23.875 keV in its transition to the ground state with spin I of 1 /2. It is usually incorporated into barium or calcium stannate, which give a line-width of about 0.33 mm s 4. Measurements are usually carried out at 77 K, to increase the recoil-free fraction of the emission and absorption for BaSnC>3, this is 0.8 at 77 K, and 0.55 at 300 K. 

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. 

Fig. 4.2. y-ray energy distribution for emission and absorption lines in free atoms. The emission and absorption lines are separated by 2Er 10 y due to recoil effect. The overlap (extremely small) is not to scale... 

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