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Tunneling between the two lowest energy levels of single molecule magnetswith Ising type anisotropy, accompanied by the emission or absorption ofphonons, is considered. Quantitatively accurate calculations of the rates forsuch tunneling are performed for a model Hamiltonian especially relevant to thebest studied example, \Fe8. Two different methods are used: high-orderperturbation theory in the spin-phonon interaction and the non-Ising-symmetricparts of the spin Hamiltonian, and a novel semiclassical approach based onspin-coherent-state-path-integral instantons. The methods are found to be ingood quantitative agreement with other, and consistent with previous approachesto the problem. The implications of these results for magnetization ofmolecular solids of these molecules are discussed briefly.

Low-Temperature Phonoemissive Tunneling Rates in Single Molecule Magnets