Ultraslow motions and asymptotic lineshapes in ESR

The characteristic shape of the ESR spectra under ultraslow motion conditions, that is, when the rate of the rotational motion is much smaller than the magnetic anisotropies, is analyzed starting from the axial g-tensor problem with the diffusion model. By means of an effective relaxation frequency which takes into account both the intrinsic linewidth and the contribution of the dynamical processes, the asymptotic profiles and the corresponding scaling procedures of the spectrum are derived. By resorting to the adiabatic approximation the treatment is extended to radicals having axial hyperfine interactions, with the same asymptotic profiles predicting the shape of individual peaks in ultraslow motion spectra. The approximate spectrum calculated from the asymptotic lineshapes is compared with the numerical solution of the stochastic Liouville equation for a typical nitroxide radical. The early convergence of the outer peaks supports the use of their widths as probes of the correlation time and a simple procedure, which takes into account the correct scaling laws, is proposed for the analysis of experimental spectra. The model de[endence of the ultraslow motion spectra is also considered, with a comparison between the diffusion equation and the strong collision operator.