  We consider in detail how the quantum-mechanical tunneling phenomenon occurs
in a well-behaved octic potential. Our main tool will be the euclidean
propagator just evaluated between two minima of the potential at issue. For
such a purpose we resort to the standard semiclassical approximation which
takes into account the fluctuations over the instantons, i.e. the finite-action
solutions of the euclidean equation of motion. As regards the one-instanton
approach, the functional determinant associated with the so-called stability
equation is analyzed in terms of the asymptotic behaviour of the zero-mode. The
conventional ratio of determinants takes as reference the harmonic oscillator
whose frequency is the average of the two different frequencies derived from
the minima of the potential involved in the computation. The second instanton
of the model is studied in a similar way. The physical effects of the
multi-instanton configurations are included in this context by means of the
alternate dilute-gas approximation where the two instantons participate to
provide us with the final expression of the propagator.
