  We present pump-probe measurements on the single-molecule magnet Fe_8 with
microwave pulses having a length of several nanoseconds. The microwave
radiation in the experiments is located in the frequency range between 104 GHz
and 118 GHz. The dynamics of the magnetization of the single Fe_8 crystal is
measured using micrometer-sized Hall sensors. This technique allows us to
determine the level lifetimes of excited spin states, that are found to be in
good agreement with theoretical calculations. The theory, to which we compare
our experimental results, is based on a general spin-phonon coupling formalism,
which involves spin transitions between nearest and next-nearest energy levels.
We show that good agreement between theory and experiments is only obtained
when using both the Delta m_S = +-1 transition as well as Delta m_S = +-2,
where Delta m_S designates a change in the spin quantum number m_S. Temperature
dependent studies of the level lifetimes of several spin states allow us
finally to determine experimentally the spin-phonon coupling constants.
