Theoretical Analysis of the EPR Spectrum Saturation Effect with Account for Spectral Diffusion in a System with a Gaussian Distribution of Spin Resonance Frequencies
Tóm tắt
We have analyzed the effect of saturation of the EPR spectrum for the model situation when a set of resonance frequencies of spin packets is described by a Gaussian distribution and spectral diffusion, which is a random process without correlation, exists. We have obtained the form of the spectrum for arbitrary values of magnetic–resonant parameters: relaxation times for the longitudinal and transverse components of the magnetization vector of the system, the spectral diffusion rate, the dispersion of the Gaussian distribution of resonance frequency, and the magnetic induction of the microwave field. We have derived an analytic expression for the saturation curve of the EPR spectrum. Detailed analysis of the dependence of the spectrum saturation curve on the spin system parameters is performed for the optimal case when the microwave field frequency coincides with the average frequency of the Gaussian distribution for resonance frequencies. The value of the microwave field induction at which the peak of the saturation curve is attained has been determined for arbitrary values of the paramagnetic relaxation time, spectral diffusion rate, and dispersion of the Gaussian spin frequency distribution. We have formulated the algorithm for determining the spin–lattice relaxation time using the experimentally determined microwave field induction for which the saturation curve passes through the peak. It should be noted that numerical calculations have been performed for parameters typical of EPR spectroscopy. The general analytic expression derived for the shape of the spectrum in the saturation conditions and qualitative conclusions concerning the effect of spectral diffusion on the saturation of stationary spectra obtained in this study can also be used in other fields of spectroscopy.
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