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Excitation spectrum of a two-electron `metal cluster'

We study a system of two electrons moving in the Coulomb field generated by a uniform positive charge distribution and interacting with each other. This system, while allowing for an exact calculation of its excitation spectrum, contains several features of a jellium model description of metal clusters. In particular, the interaction is a realistic one. Special attention is devoted to the dipole collective mode and to its multiple excitations. It is shown that, in addition to a quasi-vibrational band based on the ground state, other bands exist whose vibrational character is much less pronounced.