We performed high resolution diffraction and inelastic neutron scattering measurements of Mn_{12}-acetate. Using a very high energy resolution, we could separate the energy levels corresponding to the splitting of the lowest S multiplet. Data were analyzed within a single spin model (S=10 ground state), using a spin Hamiltonian with parameters up to 4^{th} order. The non regular spacing of the transition energies unambiguously shows the presence of high order terms in the anisotropy (D= -0.457(2) cm^{-1}, B_4^0 = -2.33(4) 10^{-5}cm^{-1}). The relative intensity of the lowest energy peaks is very sensitive to the small transverse term, supposed to be mainly responsible for quantum tunneling. This allows an accurate determination of this term in zero magnetic field (B_4^4 = pm 3.0(5) 10^{-5} cm^{-1}). The neutron results are discussed in view of recent experiments and theories.
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