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Electron Temperature Dependence of the Optical Properties of Small Sodium Nanoparticles

We report a novel behavior of the surface plasmon linewidth in sodium nanospheres Na$_{1760}$ changing with the electron temperature, which monotonically decreases and bears a discontinuous sudden drop at high electron temperatures. Our calculation is based on the model constructed by splitting the total Hamiltonian of all valence electrons of a metallic nanoparticle into two sub-Hamiltonians and their coupling, and obtained results can be verified by the pump-probe femtosecond spectroscopy experiments. In addition, we propose that it is the size uncertainty of small nanoparticles that yields the intrinsic linewidth of the surface plasmon resonance, which is supported by the available data of clusters Na$_{8}$ and Na$_{20}$.