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It is known that the decay process \eta\rightarrow\pi^0\pi^+\pi^- in freespace is possible due to the isospin-symmetry breaking in QuantumChromodynamics (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 nuclearmatter such as heavy nuclei, isospin-symmetry breaking is large and it isexpected that the mixing property of the mesons changes significantly and theabove-mentioned decay width of the \eta created in such a medium may beenhanced. This is an intriguing possibility to revealing a medium effect on ahadron in nuclei. We apply the in-medium chiral perturbation theory to estimatethe 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 isospinasymmetry. We find that these quantities can be greatly enhanced inneutron-rich matter, which should be deteactable in experiment.

Possible medium effects on \eta-\pi^0 mixing and \eta \rightarrow \pi^0 \pi^+ \pi^- decay in the asymmetric nuclear matter