  A Landau-Zener multi-crossing method has been used to investigate the tunnel
splittings in high quality Mn$_{12}$-acetate single crystals in the pure
quantum relaxation regime and for fields applied parallel to the magnetic easy
axis. With this method several individual tunneling resonances have been
studied over a broad range of time scales. The relaxation is found to be
non-exponential and a distribution of tunnel splittings is inferred from the
data. The distributions suggest that the inhomogeneity in the tunneling rates
is due to disorder that produces a non-zero mean value of the average
transverse anisotropy, such as in a solvent disorder model. Further, the effect
of intermolecular dipolar interaction on the magnetic relaxation has been
studied.
