  A formula suitable for a quantitative evaluation of the tunneling effect in a
ferromagnetic particle is derived with the help of the instanton method. The
tunneling between n-th degenerate states of neighboring wells is dominated by a
periodic pseudoparticle configuration. The low-lying level-splitting previously
obtained with the LSZ method in field theory in which the tunneling is viewed
as the transition of n bosons induced by the usual (vacuum) instanton is
recovered. The observation made with our new result is that the tunneling
effect increases at excited states. The results should be useful in analyzing
results of experimental tests of macroscopic quantum coherence in ferromagnetic
particles.
