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The nonleptonic weak decay of $\Lambda^+_c \to \bar{K}^0 \eta p$ is analyzedfrom the viewpoint of probing the $N^*(1535)$ resonance, which has a big decaybranching ratio to $\eta N$. Up to an arbitrary normalization, the invariantmass distribution of $\eta p$ is calculated with both the chiral unitaryapproach and an effective Lagrangian model. Within the chiral unitary approach,the $N^*(1535)$ resonance is dynamically generated from the final stateinteraction of mesons and baryons in the strangeness zero sector. For theeffective Lagrangian model, we take a Breit-Wigner formula to describe thedistribution of the $N^*(1535)$ resonance. It is found that the behavior of the$N^*(1535)$ resonance in the $\Lambda^+_c \to \bar{K}^0 N^*(1535) \to \bar{K}^0\eta p$ decay within the two approaches is different. The proposed$\Lambda^+_c$ decay mechanism can provide valuable information on theproperties of the $N^*(1535)$ and can in principle be tested by facilities suchas BEPC II and SuperKEKB.

Role of the $N^*(1535)$ in the $\Lambda^+_c \to \bar{K}^0 \eta p$ decay