Cross section, Mossbauer effect

It is much more difficult to observe the Mossbauer effect with the 130 keV transition than with the 99 keV transition because of the relatively high transition energy and the low transition probability of 130 keV transition, and thus the small cross section for resonance absorption. Therefore, most of the Mossbauer work with Pt, published so far, has been performed using the 99 keV transition. Unfortunately, its line width is about five times larger than that of the 130 keV transition, and hyperfine interactions in most cases are poorly resolved. However, isomer shifts in the order of one-tenth of the line width and magnetic dipole interaction, which manifests itself only in line broadening, may be extracted reliably from Pt (99 keV) spectra. 

The theoretical interpretation of the effect was done by R. L. Mossbauer himself, using the theory of W. E. Lamb, Jr. (8), for neutron capture by atoms in a crystal. According to this theory the resonance-absorption cross section is given by... 

Maximum cross-section resonant absorption, usually some orders of magnitude, exceeds another cross-sections of interaction of y-quanta with matter. That is why the Mossbauer effect is easy observable for Fe and Sn, despite their small content in natural isotope blend ( Fe 2.2%, Sn 8.5%). Cross-section of resonant interaction reaches a maximum value for the energy E = Eq- Dependence of o on E is given by the Wigner formula... 

The Mossbauer measurements makes it possible to study a variety of interesting effects that may be brought about by the introduction of impurity in the lattice as also the modifications brought about by imperfection in the crystal lattice, since the nuclei must be bound in a crystal for this study of resonant emission (or absorption) of y-rays. Three dynamical quantities of interest, which are possible in the Mossbauer studies, are (i) Zero-phonon absorption cross-section giving the Lamb-Mossbauer factor, (ii) One-phonon absorption cross section yielding the time information as well as the information of the localized modes and through this the information on the force constant between impurity and the host atom, (iii) the second order Doppler effect yielding information about the mean square velocity of the Mossbauer probe. 

As mentioned before, the first study of f(T) was carried out by Mossbauer (1958), and since then many systems have been studied. Mossbauer s results were theoretically analysed by Visscher (1960). The effective absorption cross-section for Ir as a function of temperature is shown in Figure 6.1, while in Figure 6.2 the temperature dependence of the Debye-Waller factor of tin metal is shown. Serious corrections to the Debye model are needed to fit the experimental observations. One correction is due to the expansion of the crystal, which causes the Debye temperature, to be temperature dependent. The other correction is due to the anharmonicity of the nuclear motion (Boyle, Bunbury, Edwards Hall, 1961). 

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