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Assuming a hadronic molecular nature for the vector charmonium-like states $\\psi(4360)$ and $\\psi(4415)$, we evaluate the radiative decay widths of $\\psi(4360)\\to\\gamma\\eta_{c1}$ and $\\psi(4415)\\to\\gamma\\eta_{c1}^{\\prime}$. 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Assuming a hadronic molecular nature for the vector charmonium-like states $\\psi(4360)$ and $\\psi(4415)$, we evaluate the radiative decay widths of $\\psi(4360)\\to\\gamma\\eta_{c1}$ and $\\psi(4415)\\to\\gamma\\eta_{c1}^{\\prime}$. 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