Spin-Hamiltonian parameters Zeeman term

The stated aim of this review is to demonstrate that elassical analyses of physieal organie ehemistry are feasible with respect to complex systems such as supported metal catalysts through the application of advanced EMR spectroscopic techniques and determining the relevant spin Hamiltonian parameters via the Zeeman-dependent hyperfine spectrum. The principles of analysis were outlined in the preceding section and entail replicate collection of ESEEM or ENDOR spectra by incremental steps and mapping the trajectory of peak positions. Deconvolution of peaks may be made either by traditional tau-suppression in the stimulated echo pulse sequence or via advanced pulse sequences such as HYSCORE (2-D ESEEM, Hofer, 1994). Mapping of spectral peak position as it varies depending on the Zeeman field is very important to the accurate determination of hyperfine terms. 

The first three terms are usually the ones of relevance for the ESR analysis, where D and A are the zero-field (or fine structure) and hyperfine coupling tensors. They are represented by 3-3 symmetric matrices and specified by three principal values and three principal directions as for the -tensor. The remaining nuclear Zeeman and quadrupole (/ > Vi) terms do not affect the ESR spectra, unless they are of comparable magnitude to the hyperfine coupling, but must be taken into account in the analysis of ENDOR and ESEEM spectra. The spin Hamiltonian formalism introduced by M.H.L. Pryce and A. Abragam [79] is used explicitly or implicitly in the ESR literature as a convenient way to summarise resonance parameters. 

The spin Hamiltonian of the Er + and Dy ions in the LiRp4 crystals is given by formula (118) with the Zeeman term in the form of eq. (119) and with The constants of spin-phonon interaction, calculated with the parameters of electron-deformation interaction from table 10, are given in table 25 (some of these constants were measured in EPR experiments on the uniaxially stressed LiTmF4 crystals activated by the Er and Dy + ions). In this case parameters of the magnetostriction Bx T, h) in eq. (235) can be written as follows... 

Advanced EMR methods may be used to conduct quantitative measurements of nuclear hyperfine interaction energies, and these data, in turn, may be used as a tool in molecular design because of their direct relation to the frontier orbitals. The Zeeman field dependence of hyperfine spectra enables one to greatly improve the quantitative analysis of hyperfine interaction and assign numeric values to the parametric terms of the spin Hamiltonian. Graphical methods of analysis have been demonstrated that reduce the associated error that comes from a multi-parameter fit of simulations based on an assumed model. The narrow lines inherent to ENDOR and ESEEM enable precise measures of peak position and high-resolution hyperfine analyses on even powder sample materials. In particular, ESEEM can be used to obtain very narrow lines that are distributed at very nearly the zero-field NQI transition frequencies because of a quantum beating process that is associated with... 

Abstract. Following a suggestion of Kostelecky et al. we have evaluated a test of CPT and Lorentz invariance from the microwave spectrosopy of muonium. Precise measurements have been reported for the transition frequencies U12 and 1/34 for ground state muonium in a magnetic field H of 1.7 T, both of which involve principally muon spin flip. These frequencies depend on both the hyperfine interaction and Zeeman effect. Hamiltonian terms beyond the standard model which violate CPT and Lorentz invariance would contribute shifts <5 12 and <5 34. The nonstandard theory indicates that P12 and 34 should oscillate with the earth s sidereal frequency and that 5v 2 and <5 34 would be anticorrelated. We find no time dependence in m2 — vza at the level of 20 Hz, which is used to set an upper limit on the size of CPT and Lorentz violating parameters. 

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