The decay rate of an excited atom in the dipole approximation is described by using Fermi's golden rule which is related to the imaginary part of the vector potential Green's function by applying the fluctuation dissipation theorem and Kubo's formula. In this paper, we examined the radiative properties of an excited atom in front of a real metal and it can be seen that the decay rate of an excited atom in the presence of surface plasmons increases as the distance between atom and the surface vanishes.

Keywords: decay rate, surface plasmons, vector potential Green\'s function, Fermi\'s golden rule

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