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We report a novel behavior of the surface plasmon linewidth in sodiumnanospheres Na$_{1760}$ changing with the electron temperature, whichmonotonically decreases and bears a discontinuous sudden drop at high electrontemperatures. Our calculation is based on the model constructed by splittingthe total Hamiltonian of all valence electrons of a metallic nanoparticle intotwo sub-Hamiltonians and their coupling, and obtained results can be verifiedby the pump-probe femtosecond spectroscopy experiments. In addition, we proposethat it is the size uncertainty of small nanoparticles that yields theintrinsic linewidth of the surface plasmon resonance, which is supported by theavailable data of clusters Na$_{8}$ and Na$_{20}$.

Electron Temperature Dependence of the Optical Properties of Small Sodium Nanoparticles