Hyperfine splitting spin Hamiltonian

In the Breit Hamiltonian in (3.2) we have omitted all terms which depend on spin variables of the heavy particle. As a result the corrections to the energy levels in (3.4) do not depend on the relative orientation of the spins of the heavy and light particles (in other words they do not describe hyperfine splitting). Moreover, almost all contributions in (3.4) are independent not only of the mutual orientation of spins of the heavy and light particles but also of the magnitude of the spin of the heavy particle. The only exception is the small contribution proportional to the term Sio, called the Darwin-Foldy contribution. This term arises in the matrix element of the Breit Hamiltonian only for the spin one-half nucleus and should be omitted for spinless or spin one nuclei. This contribution combines naturally with the nuclear size correction, and we postpone its discussion to Subsect. 6.1.2 dealing with the nuclear size contribution. 

The nuclear Zeeman term describes the interaction of the nuclear spins with the external magnetic field. Just as the hyperfine splitting, this term is not incorporated in the original purely electronic Breit-Pauli Hamiltonian as presented in Eqs. (59) and (60) but becomes relevant for ESR spectroscopy. 

The EPR spectra have always been interpreted2994 using an effective S = 2 spin Hamiltonian including the Zeeman term, /iBB g-S, and the hyperfine term, ICa-A-S, which describes the interaction of the unpaired electrons with the copper nucleus (7Cu = I). The spectra are very sensitive to the ratio between the isotropic coupling constant J and the local zero field splitting of nickel(II), Z)Ni.2982 In the limit J DNi it can easily be shown that the following relations hold ... 

The resolution of the molecular beam experiments is high enough to observe even rather small nuclear hyperfine interactions such as the spin-spin and spin-rotation interactions as well as the larger quadrupole coupling interactions. The largest terms in the Hamiltonian for the hyperfine splittings are given below 66) ... 

In the general case, both isotropic and anisotropic hyperfine interachons contribute to the experimental spectrum. The whole interaction is therefore dependent once again on orientation and must be expressed by a tensor. The effechve spin Hamiltonian for this more reahstic descriphon of a paramagnehc species in the solid state was given earher in Equahon 1.28. Nevertheless the A tensor may be split into its component isotropic and anisotropic parts as follows ... 

In zero magnetic field the two-pulse photon-echo decay exhibits a beat which is shown in Fig. 32. Such beat patterns may be expected for radicals where the hyperfine splitting in the ground and excited state is different, in other words, the spin Hamiltonians in these states do not commute. The spectrum was not further analyzed but it was concluded that the beat was... 

Figure 8 Mossbauer spectrum of a frozen aqueous solution of [ Fe +]-ferrioxamine B (12mM) employing BSA (lOOmM) as a dilutant to minimize spin-spin relaxation. The solid line represents a simulation based on a spin Hamiltonian line width = 0.35 mm s zero-field splitting, D = 1.2 cm E rhombicity parameter, E/D = 0.33 8 = 0.52mms A q = —0.84mms asymmetry parameter, rj = and isotropic hyperfine coupling tensor Axx/gN/XN = Ayy/gNMN = Azz/gx/XN = —22.1 T. The simulation does not completely fit the experimental data. This discrepancy is caused by relaxation effects that are not dealt with in the spin Hamiltonian simulation...

Paramagnetic species trapped in solid materials usually possess anisotropic g- and hyperfine couplings. Zero-field splittings occur when 5 > V2. The spin Hamiltonian formalism described in Appendix A3.1 is a convenient means to summarise the different interactions. The following spin-Hamiltonian is adequate to illustrate most aspects of the analysis. 

A more general spin Hamiltonian of the form (3.9) is applied when zero-field splittings (S > V2), anisotropic hyperfine interactions (/ 0), and nuclear quadrupole couplings (/ > 1) occur. 

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