Retarded electromagnetic response of a spherical quantum dot: A self-consistent field calculation

Starting from a self-consistent solution of the Maxwell equations, we present a theoretical investigation of the retarded electromagnetic response of a single-electron quantum dot with an isotropic parabolic confinement potential. It is shown that the correct expressions for the spontaneous decay rate and the Lamb shift are obtained from a general resonance condition. We derive an expression for the absorption cross section and compare the result to the expressions obtained within the Born approximation and dipole approximation. A numerical comparison of the cross sections is presented, and, in particular, the size dependence of the deviations is studied.