Enhancement of quantum tunneling for excited states in ferromagnetic particles

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 Lehmann-Symanzik-Zimmermann 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 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.