Mossbauer excited states

Nuclear decay processes that are often used to populate Mossbauer isotope excited states are (30) electron capture (electron + proton neutron), / decay (neutron - proton + electron), and isomeric transition (a long half-life nuclear excited state decays to the Mossbauer excited state). In addition, several of the parent nuclides of the heavy isotopes can be populated by a-particle emission. 

Parent nuclides produced by the processes mentioned above can all be used for several half-lives. In contrast, one can also populate the Mossbauer excited state directly via Coulomb excitation (84). In this technique, a beam of high-energy ( 10 MeV) charged particles (e.g., O4+, Cl7 +) is directed onto the Mossbauer isotope and the electromagnetic field generated by these particles induces nuclear transitions, which can include transitions to the Mossbauer excited state. Subsequent decay to the nuclear ground state then provides the appropriate y radiation. The half-life of a source created in this manner is the half-life of the Mossbauer excited state (e.g., several nanoseconds), and thus Coulomb excitation is necessarily an in situ technique, i.e., the Mossbauer effect experiment must be performed at the location of the charged particle beam. 

An important dilference between these complexes and the examples of crossover already discussed is that the Mossbauer spectra only show evidence for one distinct iron environment in each case. The implication is that the lifetimes of the two spin configurations are small in comparison to the Mossbauer excited-state lifetime of 10 s. In other words the spectrum is time-averaged. In a ligand field of perfect cubic symmetry there is no interaction between the two states and a superposition of the spectra of each of these is predicted. For lower symmetries the spin-orbit coupling causes state mixing of the and via the Ti state, which causes a rapid exchange. 

The nucleus in a Mossbauer experiment is part of a many-body system consisting of the surrounding electrons and the quasiparticles corresponding to the various other degrees of freedom of the solid. Relaxation effects result from the various time-dependent processes in the vicinity of the nucleus. The nucleus thus acts as a local microscopic probe, which does not participate directly in the relaxation processes in its environment, but which senses these processes via the hyperfine interactions. Now, in interpreting the relaxation behaviour it is necessary to consider the nature and interrelationship of the important timescales of the problem. Some of these timescales are determined by the nature of the Mossbauer isotope and the interaction being studied, i.e., the mean lifetime of the Mossbauer excited state and the Larmor precession time t,. The other timescales relate to, and are characterised by, the nature of the fluctuations in the nuclear environment. These latter timescales are the inverse of the various relaxation rates and, as mentioned earlier, these can be controlled in the laboratory in various ways. The character of the relaxation spectra obtained obviously depends crucially on the interplay of the various timescales as discussed below. 

The important characteristic times of the problem are the inverse of characteristic angular frequencies, which are related to characteristic energies via expressions of the type E = ho). These characteristic times are (i) the mean life time of the Mossbauer excited state, which determines the minimum width of the energy levels, = Tj, expressed in angular frequency (ii) the time where is the angular... 

Mosshauer effect The resonance fluorescence by y-radiation of an atomic nucleus, returning from an excited state to the ground state. The resonance energy is characteristic of the chemical environment of the nucleus and Mossbauer spectroscopy may be used to yield information about this chemical environment. Used particularly in the study of Fe. Sn and Sb compounds. 

A major discrepancy that remains unresolved in the excited-state properties of the [Fe384]° cluster in D. gigas Fdll concerns the existence of a low-lying, fully valence-delocalized state that becomes populated at temperatures above 25 K. 8uch a state is clearly apparent in the temperature-dependent Mossbauer studies of reduced D. gigas Fdll (29) and P. furiosus 3Fe Fd (198) and is represented by one quad-rupole doublet with AEq 0.9 mm/s and S = 0.45 mm/s. 8uch a... 

Mossbauer spectroscopy of AvF clearly demonstrated the presence of P clusters (174). The EPR spectra of dithionite-reduced VFe proteins are complex, indicating the presence of several paramagnetic species. Avl exhibits broad EPR signals, with g values of 5.8 and 5.4 integrating to 0.9 spins per V atom, which have been assigned to transitions from the ground and first excited state of a spin S = system (175). EPR data for AcF are more complex, with g values at 5.6, 4.3, and 3.77 that appear to arise from a mixture of S = species (176). The signals were associated with a midpoint potential of... 

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 effect spectroscopy, MES, Is based on the ability of certain nuclei to undergo recoilless emission and absorption ofY rays (16). The energy and multiplicity of the ground and excited states of a given nucleus are modified by the chemical environment. It Is thus most often necessary to compensate for the differences In... 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

Fig. 2.1 Nuclear resonance absorption of y-rays (Mossbauer effect) for nuclei with Z protons and N neutrons. The top left part shows the population of the excited state of the emitter by the radioactive decay of a mother isotope (Z, N ) via a- or P-emission, or K-capture (depending on the isotope). The right part shows the de-excitation of the absorber by re-emission of a y-photon or by radiationless emission of a conversion electron (thin arrows labeled y and e , respectively)...

Resonant y-ray absorption is directly connected with nuclear resonance fluorescence. This is the re-emission of a (second) y-ray from the excited state of the absorber nucleus after resonance absorption. The transition back to the ground state occurs with the same mean lifetime t by the emission of a y-ray in an arbitrary direction, or by energy transfer from the nucleus to the K-shell via internal conversion and the ejection of conversion electrons (see footnote 1). Nuclear resonance fluorescence was the basis for the experiments that finally led to R. L. Mossbauer s discovery of nuclear y-resonance in ir ([1-3] in Chap. 1) and is the basis of Mossbauer experiments with synchrotron radiation which can be used instead of y-radiation from classical sources (see Chap. 9). 

For nuclear y-resonance absorption to occur, the y-radiation must be emitted by source nuclei of the same isotope as those to be explored in the absorber. This is usually a stable isotope. To obtain such nuclei in the desired excited meta-stable state for y-emission in the source, a long-living radioactive parent isotope is used, the decay of which passes through the Mossbauer level. Figure 3.6a shows such a transition cascade for Co, the y-source for Fe spectroscopy. The isotope has a half-life time //2 of 270 days and decays by K-capmre, yielding Fe in the 136 keV excited state ( Co nuclei capmre an electron from the K-shell which reduces the... 

Scattered radiation. In a transmission experiment, the Mossbauer sample emits a substantial amount of scattered radiation, originating from XRF and Compton scattering, but also y-radiation emitted by the Mossbauer nuclei upon de-excitation of the excited state after resonant absorption. Since scattering occurs in 4ti solid angle, the y-detector should not be positioned too close to the absorber so as not to collect too much of this unwanted scattered radiation. The corresponding pulses may not only uimecessarily overload the detector and increase the counting dead time, but they may also affect the y-discrimination in the SCA and increase the nonresonant background noise. 

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

Table 4.1 Quadrupole moments for the ground state (g) and the excited state (e) of some Mossbauer nuclei quoted in millibam (1 mb = 10 m )...

Fig. 4.6 Quadrupole splitting of the excited state of Fe with I = 3/2 and the resulting Mossbauer spectrum. Quadrupole interaction splits the spin quartet into two degenerate sublevels 7, OT/) with energy separation A q = 2 q. The ground state with I = 1/2 remains unsplit. The nuclear states are additionally shifted by electric monopole interaction giving rise to the isomer shift 8...

In a conventional Fe Mossbauer experiment with a powder sample, one would observe a so-called quadrupole doublet with two resonance lines of equal intensities. The separation of the lines, as given by (4.36), represents the quadrupole splitting The parameter Afg is of immense importance for chemical applications of the Mossbauer effect. It provides information about bond properties and local symmetry of the iron site. Since the quadrupole interaction does not alter the mean energy of the nuclear ground and excited states, the isomer shift S can also be derived from the spectrum it is given by the shift of the center of the quadrupole spectrum from zero velocity. 

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

To calculate Mossbauer spectra, which consist of a finite number of discrete lines, the nuclear Hamiltonian, and thus also Hsu, has to be set up and solved independently for the nuclear ground and excited states. The electric monopole interaction, that is, the isomer shift, can be omitted here since it is additive and independent of Mj. It can subsequently be added as an increment 5 to the transition energies of each of the obtained Mossbauer lines. 

Quotations of the hyperfine coupling in terms of energy (or frequency) are not unique for Mossbauer spectra, unless the values are explicitly referenced to the nuclear ground or the excited state. Therefore, it is common to introduce the... 

Because of the different properties of the nuclear ground and excited states, the hyperfine coupling constants (A-values) for Mossbauer nuclei are often quoted in units of the internal field, where /I represents an energy and is the... 

The nuclear y-resonance effect in ° Ni was first observed in 1960 by Obenshain and Wegener [2]. However, the practical application to the study of nickel compounds was hampered for several years by (1) the lack of a suitable single-line source, (2) the poor resolution of the overlapping broad hyperfine lines due to the short excited state lifetime, and (3) the difficulties in producing and handling the short-lived Mossbauer sources containing the Co and Cu parent nuclides, respectively. 

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