  In response to recent nuclear-magnetic-resonance (NMR) measurements on the
molecular cluster Mn_{12}O_{12} acetate, we study the nuclear spin-lattice
relaxation rate 1/T_1 developing a modified spin-wave theory. Our microscopic
new approach, which is distinct from previous macroscopic treatments of the
cluster as a rigid spin of S=10, not only excellently interprets the observed
temperature and applied-field dependences of 1/T_1 for ^{55}Mn nuclei but also
strongly supports the ^{13}C NMR evidence for spin delocalization over the
entire molecule.
