Quenched spin tunneling and diabolical points in magnetic molecules. 1. Symmetric configurations - art. no. 094413

The perfect quenching of spin tunneling that has previously been discussed in terms of interfering instantons, and has recently been observed in the m agnetic molecule Fe-8, is treated using a discrete phase integral (or Wentz el-Kramers-Brillouin) method. The simplest model Hamiltonian for the phenom enon leads to a Schrodinger equation that is a five-term recursion relation . This recursion relation is reflection symmetric when the magnetic field a pplied to the molecule is along the hard magnetic axis. A completely genera l Herring formula for the tunnel splittings for all reflection-symmetric fi ve-term recursion relations is obtained. Using connection formulas for a no nclassical turning point that may be described as lying "under the barrier, " and which underlies the oscillations in the splitting as a function of ma gnetic field. this Herring formula is transformed into two other formulas t hat express the splittings in terms of a small number of action and action like integrals. These latter formulas appear to be generally valid, even fo r problems where the recursion contains more than five terms. The results f or the model Hamiltonian are compared with experiment, numerics, previous i nstanton based approaches, and the limiting case of no magnetic field.