  It is known that the decay process \eta\rightarrow\pi^0\pi^+\pi^- in free
space is possible due to the isospin-symmetry breaking in Quantum
Chromodynamics (QCD), i.e., the small mass difference between u and d quarks:
The small width is intimately related with the mixing property between \eta and
\pi^0 mesons for which the chiral anomaly play a role. In asymmetric nuclear
matter such as heavy nuclei, isospin-symmetry breaking is large and it is
expected that the mixing property of the mesons changes significantly and the
above-mentioned decay width of the \eta created in such a medium may be
enhanced. This is an intriguing possibility to revealing a medium effect on a
hadron in nuclei. We apply the in-medium chiral perturbation theory to estimate
the modification of the \eta -\pi^0 mixing angle and the partial width of
\eta\pi^0\pi^+\pi^- in asymmetric nuclear matter as a function of the isospin
asymmetry. We find that these quantities can be greatly enhanced in
neutron-rich matter, which should be deteactable in experiment.
