Semiclassical quantization and resonance in spin tunnelling

We derive a semiclassical quantization for a spin, study it for not too small a spin quantum number (S>5), and compute the 2S+1 eigenvalues of a Hamiltonian exhibiting resonant tunnelling as the magnetic field parallel to the anisotropy axis is increased. Special attention is paid to the resonance condition. As a corollary we prove that semiclassical quantization and quantum-mechanical perturbation theory agree there where they should.