We have considered the excitation spectra of neutral rare-gas atoms physisorbed on metal surfaces. The adsorbed atom and its image interact through the dipole-dipole interaction and radiate to each other as well. The charge of the image atom is screened by the dielectric function of the surface plasmons. Due to the common radiation field between the atom and its image, the excitation spectra consist of the symmetric and antisymmetric modes, respectively. Each of them splits into two excitations: the atomic-like and the surface plasmon-like excitations, which arise because of the presence of the surface plasmons. The surface plasmon-like excitations appear near the surface plasmon frequencies and consist of broad spectral lines, which have large radiative widths and small relative intensities in comparison with those of the atomic like excitations, that emerge near the atomic frequencies. The spectral functions describing the symmetric and antisymmetric modes have been calculated in the presence of the plasmon damping and consist of asymmetric Lorentzian lines, where the extent of the asymmetry depends on the strength of the surface plasmons. Competition between the cooperative radiative and non-radiative processes takes place. In the absence of plasmon damping or when the effective radiative damping is greater than the damping of the surface plasmons, the largest enhancement of the relative intensities per atom occurs for the spectra of the symmetric modes of the excited Xe, Kr and Ar when they are physisorbed on Mg with K and Li holding the second and third place, respectively. The relative intensities per atom for the spectra of Xe, Kr and Ar on the surfaces of A1, Cu, Ag and Au are much less than the corresponding ones for the single free atoms in question, respectively. The enhancement or the decrease of the maximum relative intensity per atom is due to the dynamic effect arising from the presence of the surface plasmons. In the opposite limit, when the nonradiative process due to the damping of the surface plasmons dominates, the relative intensities per atom for the peaks of the symmetric and anti-symmetric modes take positive and negative values describing the physical processes of absorption and stimulated emission, respectively. Hence, a cancellation is expected to occur between the peaks of the symmetric and anti-symmetric modes, which arise from two nearby excited states of the physisorbed atom on the metal surface, provided that an overlap exists between the frequency profiles of the two peaks in question. The red (blue) shifted peak of the symmetric mode of the higher (lower) excited state and the blue (red) shifted peak of the antisymmetric mode of the lower (higher) excited state of the atom cancel each other out provided that the frequency profiles of their lineshapes nearly coincide. This may be a possible explanation of the persistence-extinction phenomenon that has been observed for a number of rare-gas metal substrate systems in the low coverage limit, where it has been proposed that a charge-transfer instability exists. The computed spectra of the symmetric and antisymmetric modes for excited Xe, Kr and Ar physisorbed on the metal surfaces of K, Li, Mg, Al, Cu, Ag, Au and Ti are presented graphically and discussed. Results of numerical calculations indicate that at low coverage the peaks of excited Xe on Al, Ti and Au and excited Kr on Au, vanish; this is compatible with the experimental observations. At low coverage, the height of the peaks of the spectral lines is shown to be proportional to the number of atoms at the surface of the metal N and, hence, the total spectral function describing the exctiation spectra varies as N2; this is compatible with the observed data.
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