Tunneling of a large spin via hyperfine interactions

We consider a large spin S in the magnetic field parallel to the uniaxial crystal field, interacting with N much greater than 1 nuclear spins Ii via Hamiltonian H=-DSz2+HzSz+AS .Sigma(i=1)(N)I(i) with A much less than D, at temperature T. Tunneling splittings and the selection rules for the resonant values of H-z are obtained perturbatively. The quantum coherence exists at T much less than ASI while at T greater than or similar to ASI the coherence is destroyed and the relaxation of S is described by a stretched dependence which can be close to log t under certain conditions. Relevance to Mn-12 acetate is discussed.