  The perfect quenching of spin tunneling first predicted for a model with
biaxial symmetry, and recently observed in the magnetic molecule Fe_8, is
further studied using the discrete phase integral (or
Wentzel-Kramers-Brillouin) method. The analysis of the previous paper is
extended to the case where the magnetic field has both hard and easy
components, so that the Hamiltonian has no obvious symmetry. Herring's formula
is now inapplicable, so the problem is solved by finding the wavefunction and
using connection formulas at every turning point. A general formula for the
energy surface in the vicinity of the diabolo is obtained in this way. This
formula gives the tunneling apmplitude between two wells unrelated by symmetry
in terms of a small number of action integrals, and appears to be generally
valid, even for problems where the recursion contains more than five terms.
Explicit results are obtained for the diabolical points in the model for Fe_8.
These results exactly parallel the experimental observations. It is found that
the leading semiclassical results for the diabolical points appear to be exact,
and the points themselves lie on a perfect centered rectangular lattice in the
magnetic field space. A variety of evidence in favor of this perfect lattice
hypothesis is presented.
