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In this paper the size-dependence of energy relaxation, which is induced by the electron-phonon (e-ph) interactions and the electron-surface (e-s) interactions in noble metal nanoparticles, is investigated. Then based on the analysis and the derivation of the e-s coupling constant in metal nanospheres, the formula of the effective electron-phonon coupling constant Geff of hollow gold nanospheres (HGNs) is deduced. Moreover, the correctness of the formulae gets proved by contrast analyses of the calculated Geff values and experimental values obtained from literature.

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