The synchrotron radiation has openened many research fields because it’s a very precise source of radiation. For example the 14.4 keV in 57Fe is 5 neV wide, according to the uncertainty principle that’s a lifetime of 140 ns.
So with a very high precision of radiation and fast detectors, the nuclear resonance proceses can be separated from the instantaneous proceses.
When the nucleus is excited it de-excites again emitting radiation, the incoming and outgoing radiation interfere giving oscillations (quantum beats), if the energy of the radiation coincides with the energy of the nuclear levels it excites the nuclei and is re-emitted forward with a time delay determined by the lifetime of the nuclear excited state. So the periods and amplitudes of the oscillations can be studied to deduce the magnetic and electronic properties of the nucleus.