Quantum size effect on optical absorption in a small spherical shell

To investigate the quantum size effect on optical absorption spectra in a small metallic particle of a spherical-shell shape, first-principles calculations are performed based on Kubo's formula. The resonant frequency of collective modes and their linewidths are studied systematically by changing the thickness of the shell, using the Hartree-Fock and random-phase approximations, which are free from self-interaction. The system-size dependence of the resonant frequency of the modes is in good agreement with the classical theory, while that of their linewidth reflects the quantum size effect, which cannot be explained classically. The origin of the line broadening should be attributed to the Landau-damping mechanism.