Based on the experimental work by Boscaino et al on the EPR transient nutations (TNs) and free induction decay (FID) in solids, we propose the modified Bloch equations (MBEs). In addition to the Tomita expression for power-dependent parameter T2u, we give an original phenomenological expression for power-dependent parameter T2v and tuning Δ. Both analytical (in the form of a Torrey solution with these parameters) and numerical solutions of MBE are obtained for TN and for different FID regimes with very good agreement between theory and experiment. We also discuss the meaning and role of the instantaneous diffusion mechanism in the transient pulse experiments.

On the grounds of Bloch equations modified by taking into account the power dependence of the dispersion and damping parameters, we give general expressions for hole shapes burnt in the absorption and polarization spectra of the two-level systems. The general expressions are used for detailed numerical calculations of the hole shapes and hole widths in a concrete paramagnetic system (quartz with [AlO4]0 centres). This system earlier was studied experimentally and theoretically through the transient nutation and free induction decay methods. The results on the hole width in our modified-Bloch-equations model are in good qualitative agreement with the FID data.

We propose modified Bloch equations (MBEs) with specific power-dependent relaxation and dispersion parameters characteristic for two-pulse excitation and when the magnetic dipole–dipole interactions in the electron spin system control the dephasing. We discriminate between the ‘active’ (excited by both pulses) and ‘passive’ (excited by the second pulse only) spins: it is shown that the ‘active’ spins participate in a new effect, an active spin frequency modulation effect giving rise to the power-dependent dispersion and multiple electron spin echoes (ESEs); the ‘passive’ spins contribute to the power-dependent relaxation. The MBEs are solved and a general expression for the two-pulse ESEs is obtained. Detailed numerical analysis of this expression gives results in good quantitative agreement with the recent experiments on the two-pulse ESEs at conventional low applied fields. The developed theory is applied also to high field ESEs, which are promising for future investigations. On the basis of published results it is deduced that the instantaneous diffusion mechanism is ineffective.

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