  The work is devoted to the problem of multiple signals of nuclear spin echoes
in magnets, excited by a series of radio-frequency (RF) arbitrary duration
pulses exceeding the free induction decay time. The quantum-statistical
approach based on the Liouville equation solution for the statistical operator
of system is developed for the investigation of echo-processes. The obtained
theoretical results for the number of echo signals, time moments of their
formation and their intensities are in good agreement with experiments carried
out on magnets (ferrites, ferrometals, half metals, manganites). The pointed
approach is general and could be applied to EPR and NQR, which is interesting
also for its application for remote detection of explosives and narcotics. The
application of wide RF pulses and their sequences makes it possible to
accumulate weak signals, enriches the echo-response spectrum with clearly
separated intensive lines, i.e. essentially increases the sensitivity of
apparatus and, correspondingly, the possibilities to explore the fine details
of dynamical and relaxation processes taking place in nuclear spin-systems with
sufficiently long relaxation times. The work contains also results of new
experiments on study of relaxation processes in these systems.
