Inhomogeneous hyperfine broadening

In many cases, the actual width of a Mossbauer line has strong contributions from inhomogeneous broadening due to the distribution of unresolved hyperfine splitting in the source or absorber. Often a Gaussian distribution of Lorentzians,... 

If inhomogeneous broadening of the EPR linewidth is primarily due to unresolved hyperfine couplings (hfc), at higher frequencies the g-an iso (ropy will dominate over the hyperfine interactions, i.e., the condition (Ag/gIS0H0) > AHhk must be fulfilled. 

An alternative model (Venable 1967) proposes that the main cause of inhomogeneous broadening is unresolved superhyperfine interactions and, therefore, that the linewidth expression should be equivalent to the Equation 5.12 for the angular dependence of first-order hyperfine splitting ... 

Recently, an ESR spectrum from Aujj at 4.4 K, with g= 1.9204 and linewidth 67 mT, has been reported [54]. The intensity of the signal followed the Curie-Weiss law, and the g-value and linewidth were independent of temperature. If the linewidth were determined by the electronic spin-spin relaxation time Tj, it would be expected to increase with temperature, so its temperature-independence suggests inhomogeneous broadening by unresolved hyperfine coupling to P and Au nuclei. Similar behaviour has been found in rhodium carbonyl clusters [18]. 

The EPR lines encountered in photosynthetic material often consist of the envelope of many hyperfine lines (they are inhomogeneously broadened Gaussians) and contain little structural information. From their ENDOR spectrum, however, several hyperfine coupling constants could be determined. 

Even for a single radieal the speetial resolution can be enhanced for disordered solid samples if the inhomogeneous linewidth is dominated by unresolved hyperfine interactions. Whereas the h5 erfine line broadening is not field dependent, the anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

Fig. 1. Rhombic EPR absorption envelope illustrating spin packets from individual centers that add together to give the inhomogeneously broadened powder EPR pattern. In particular, a pair of packets representing a hyperfine splitting of A for an / = i nucleus is depicted. [Adapted from W. B. Mims and J. Peisach, Biol. Magn. Reson. 3, 213 (1981).]...

The most precise measurements of the fine-structure parameters D and E have in fact been carried out using zero-field resonance. Figure 7.6 shows the three zero-field transitions in the Ti state of naphthalene molecules in a biphenyl crystal at T = 83 K. In these experiments, the absorption of the microwaves was detected as a function of their frequency [5]. The lines are inhomogeneously broadened and nevertheless only about 1 MHz wide. Owing to the small hnewidth of the zero-field resonances, the fine-structure constants can be determined with a high precision. This small inhomogeneous broadening is due to the hyperfine interaction with the nuclear spins of the protons (see e.g. [M2] and [M5]). For triplet states in zero field, the hyperfine structure vanishes to first order in perturbation theory, since the expectation value of the electronic spins vanishes in all three zero-field components (cf Sect. 7.2). The hyperfine structure of the zero-field resonances is therefore a second-order effect [5]. 

Fig. 18, there are three types of ions having a tripod-type scheme [21], since the Pr ions have three excited-state hyperfine levels and the optical transition is inhomogeneously broadened. 

The principal advantage of ENDOR spectroscopy is the much finer energy scale upon which the state-to-state transitions are recorded. As discussed in 3, conventional cw-EMR spectroseopy detects the weak hyperfine interactions of the spin Hamiltonian as a perturbation of the electronic Zeeman effect in many practical situations, inhomogeneous broadening will wash out the hyperfine structure of the speetrum. In such cases of inhomogeneously broadened EMR spectra, interaction can only be deconvoluted for practical analysis via simulations (Hyde Fron-cisz, 1982). The ENDOR method, however, records a spectram that represents the... 

Spectroscopy conducted on ions which have been trapped by an appropriate configuration of fields leads to results void of inhomogeneous broadening sources and allows measurements with high spectral resolution. In a recent laser-microwave double resonance experiment conducted on Yb trapped ions, Blatt and co-workers (1983) resolved the ground state hyperfine splitting of the 171 isotope with a Q-factor, i.e., Avlv, of 10 . 

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