  $^{57}$Fe and $^1$H relaxation measurements have been performed in single
crystal and oriented powder of enriched $^{57}$Fe8 molecular cluster in the
temperature range 0.05--1.7 K in zero external field and with small perturbing
longitudinal field ($< 1$ T). On the basis of the experimental results it is
argued that in zero external field the nuclear spin-lattice relaxation
($1/T_1$) mechanism is driven by a strong collision mechanism whereby $1/T_1$
is a direct measure of the incoherent tunneling probability in the low lying
magnetic energy states of the molecular nanomagnet. The approximate value of
the effective tunneling rate vs $T$ and $H$ derived directly from $1/T_1$ is
shown to be consistent with theoretical estimates based on known parameters of
the Hamiltonian.
