  The transverse and longitudinal relaxation rates 1/$T_2$ and 1/$T_1$ of
$^{55}$Mn in molecular cluster magnet Mn$_{12}$Ac have been measured al low
temperatures down to 200mK and in the fields upto 9T. Both of 1/$T_2$ and
1/$T_1$ exhibit remarkable decreases with decreasing temperature and with
increasing field, with the relative relation $T_1/T_2 \approx 200$. In the
analysis, we adopt a simple model that the thermal fluctuation of the cluster
spin $S$=10 associated with the spin-phonon interactionis, is only due to the
excitation to the first excited state from the ground state with the average
life-times $\tau_ 1$ and $\tau_0$ ($\tau_ 0$$\gg$$\tau_1$). We show that
1/$T_2$ is interpreted in terms of the strong collision regime as given by
1/$\tau_ 0$, and that 1/$T_1$ is understood by the high-frequency limit based
on standard perturbation treatment for the step-wise fluctuating field, thus
being proportional to 1/$\tau_0\omega_N^2$.
