Theory of line widths and shifts in Electron spin resonance arising from spin exchange interactions

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Abstract
Equations are derived which describe the E.S.R. spectra of free radicals in solution when the spin exchange interaction J S 1. S 2 provides the dominant relaxation mechanism. It is shown that modified Bloch equations provide an adequate description if J is much greater than any frequency differences in the spectrum and the hyperfine interactions can be neglected during spin exchange collisions, but that in general the exchange rate depends on the frequency differences and spin de-phasing effects can occur even in the absence of spin exchange. Also, small shifts in resonance frequencies are shown to arise because of electron spin polarization in the applied field; but these are usually much smaller than the line widths.