Nuclear transitions, Mossbauer spectra

Most Mossbauer spectra are split because of the hyperfine interaction of the absorber (or source) nuclei with their electron shell and chemical environment which lifts the degeneracy of the nuclear states. If the hyperfine interaction is static with respect to the nuclear lifetime, the Mossbauer spectrum is a superposition of separate lines (i), according to the number of possible transitions. Each line has its own effective thickness t i), which is a fraction of the total thickness, determined by the relative intensity W of the lines, such that t i) = Wit. 

Nuclear absorption of incident X-rays (from the synchrotron beam) occurs elastically, provided their energy, y, coincides precisely with the energy of the nuclear transition, Eq, of the Mossbauer isotope (elastic or zero-phonon peak at = E m Fig. 9.34). Nuclear absorption may also proceed inelasticaUy, by creation or annihilation of a phonon. This process causes inelastic sidebands in the energy spectrum around the central elastic peak (Fig. 9.34) and is termed nuclear inelastic scattering (NIS). 

Another parameter that one can extract from a Mossbauer spectrum is the quadrupole splitting. The 3/2 state in either iron or tin is degenerate with respect to an asymmetric electrostatic field, and in such a field these levels will be split into dz 3/2 and 1/2 levels. One can observe transitions either to or from these two levels to the ground state, and this is the quadrupole splitting. It is actually e qQ, where eq is the electrostatic field gradient—i,e., the second derivative of the potential with respect to the coordinate—and eQ is the nuclear quadrupole moment. The typical quadrupole split spectrum for iron is shown in Figure 6, in which the cubic (octahedral) symmetry around the iron atom is de-... 

The electronic environment about the sample s nucleus influences the energy of the y ray necessary to cause the nuclear transition from the ground to the excited state. The energies of the y rays from the source can be varied by moving the source relative to the sample. In order to obtain the Mossbauer spectrum, the source is moved relative to the fixed sample, and the source... 

A possible modification of this expression is presented elsewhere (82). The value of t, can be related to a diffusion coefficient (e.g., tj = l2/6D, where / is the jump distance), thereby making the Ar expressions qualitatively similar for continuous and jump diffusion. A point of major contrast, however, is the inclusion of anisotropic effects in the jump diffusion model (85). That is, jumps perpendicular to the y-ray direction do not broaden the y-ray resonance. This diffusive anisotropy will be reflected in the Mossbauer effect in a manner analogous to that for the anisotropic recoil-free fraction, i.e., for single-crystal systems and for randomly oriented samples through the angular dependence of the nuclear transition probabilities (78). In this case, the various components of the Mossbauer spectrum are broadened to different extents, while for an anisotropic recoil-free fraction the relative intensities of these peaks were affected. 

Beff interacts with the magnetic moment of the nucleus, /< = —g P BI, yielding the magnetic hyperfine splitting of the nuclear ground and excited states that we infer from the Mossbauer spectrum by measuring the transition energies. 

Fig. 10.20. Hyperfine interactions shift and split the nuclear levels of iron (see text) and thus make the state of the nucleus dependent on the state of the atom. Each transition corresponds to a peak in the Mossbauer spectrum, see e.g. Fig. 10.21.

Figure 14 shows three Fe case studies of the time behavior of the photons reemitted in the forward direction and a comparison with the typical spectra obtained in Mossbauer spectroscopy. Figure 14a corresponds to the case for which there is no hyperfine interaction. The nuclear levels are not split, and only one transition between ground and excited state is possible. In that case, the Mossbauer spectrum shows a single-absorption line and contains only y-quanta of equal energy. In the presence of an electric field gradient (Fig. 14b), the splitting of the excited state is... 

Fig. 4.7. Six allowed transitions in the Mossbauer spectrum of the 14.4 keV transition in Fe. The internal/external magnetic field results in Zeeman splitting of the nuclear levels while an EFG interacts with the excited state level producing further shifts. The insets show the schematic of resultant spectra in both cases.

To analyze the recorded spectra, the spectrometer needs to be calibrated. The three main calibration parameters are the velocity scale, the center point of the spectrum and the nonlinearity of the velocity/time profile of the oscillation compared to a standard reference. The calibration is performed using a spectrum recorded from an a-iron foil at room temperature using the well defined line positions of the sextet from a-iron, which occur at 5.312mms , 3.076mms , and 0.840mms The center of this a-iron spectrum at room temperature is taken as the reference point (0.0 nun s ) for isomer shift values of sample spectra. The typical Mossbauer spectrum of the 14.4 keV transition of Fe in natural iron (Fig. 4.10) represents a simple example of pure nuclear Zeeman effect. Because of the cubic symmetry of the iron lattice, there is no quadrupole shift of the nuclear energy levels. The relative intensities of the six magnetic dipole transitions are... 

Since the Mossbauer transition in Fe is of the magnetic dipole type (M ). there are only transitions between nuclear sublevels with A/nj = 0, 1 and A/= +1. This selection rule yields only six transitions between the two ground state sublevels (/= 1/2) and the four excited state sublevels (7=3/2). Figure 9 illustrates the splitting of the nuclear levels, the allowed transitions, and the resulting Fe Mossbauer spectrum, a sextet due to the magnetic hyperfine interaction. 

Since the splitting of the spectral lines is directly proportional to the magnetic field experienced by the nucleus, Mossbauer spectroscopy provides a very effective means by which this field may be measured. The transition probabilities between the nuclear substates affect the intensities of the lines in the Mossbauer spectrum which can therefore give information on the relative orientation of the magnetic field at the nucleus and the direction of propagation of the gamma-ray beam. 

A typical Mossbauer experiment thus involves an oscillating radioactive source that contains a parent isotope (e.g., "Co for Fe), a stationary absorber that is usually the sample, and a detector. The Mossbauer spectrum consists of a plot of y-ray counts (relative absorption) as a function of the velocity of the source. In the source the radioactive isotope feeds the excited state of the Mossbauer isotope, which decays to the ground state. The energy of the recoil-free emitted radiation is Doppler modulated. Resonant absorption occurs when the energy of the y-ray just matches the nuclear transition energy for a Mossbauer atom in the absorber. This is detected by the decreased... 

Time-dependent phenomena can influence the Mossbauer spectrum whenever they make the position of the Mossbauer nucleus or the properties of the nuclear environment and, hence, the hyperfine interactions change with time. Time-dependent effects can influence both the spectral lineshapes and the values of the Mossbauer hyperfine parameters. The nuclear transitions and the hyperfine interactions have characteristic times, and each type of relaxation phenomenon must be considered in the context of the appropriate time scale. In case of super-paramagnetic relaxation, the magnetic hyperfine interaction fluctuates with time. The magnetic hyperfine field acting at a given Mossbauer... 

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