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Based on $(27.12\pm 0.14)\times 10^{8}$ $\psi(2S)$ events collected with theBESIII detector, we search for the decay $\eta_c (2S) \rightarrow \pi^{+}\pi^{-} \eta_c$ with $\eta_c\rightarrow K_S^0 K^{\pm}\pi^{\mp}$ and$\eta_c\rightarrow K^{+}K^{-}\pi^{0}$. No significant signal is observed, andthe upper limit on the product branching fraction$\mathcal{B}(\psi(2S)\rightarrow \gamma \eta_{c}(2S))\times\mathcal{B}$($\eta_c(2S) \rightarrow \pi^{+} \pi^{-} \eta_c$) is determined to be$2.21\times10^{-5}$ at the 90\% confidence level. In addition, the analysis ofthe process $\psi(2S)\to\gamma \eta_{c}(2S), \eta_{c}(2S)\rightarrow\pi^{+}\pi^{-}K^{0}_{S}K^{\pm}\pi^{\mp}$ gives a clear $\eta_c(2S)$ signal witha statistical significance of $10\sigma$ for the first time, %The productbranching fraction $\mathcal{B}(\psi(2S)\rightarrow \gamma\eta_{c}(2S))\times\mathcal{B}(\eta_{c}(2S)\rightarrow\pi^{+}\pi^{-}K^{0}_{S}K\pi) $ is measured to be $(9.31 \pm 0.72 \pm2.77)\times 10^{-6}$, and and the branching fraction$\mathcal{B}(\eta_{c}(2S)\rightarrow \pi^{+}\pi^{-}K^{0}_{S}K^{\pm}\pi^{\mp})$is determined to be ($1.33 \pm 0.11 \pm 0.4 \pm 0.95 $)$\times 10^{-2}$, wherethe first uncertainty is statistical, the second is systematic, and the thirduncertainty is due to the quoted $\mathcal{B}(\psi(2S)\rightarrow \gamma\eta_{c}(2S))$.

Search for $\eta_c (2S)\to\pi^{+}\pi^{-}\eta_{c}$ and $\eta_c (2S)\to\pi^{+}\pi^{-}K^0_S K^{\pm}\pi^{\mp}$ decays