The one-- and two-- particle densities of up to four interacting electrons with spin, confined within a quasi one--dimensional ``quantum dot are calculated by numerical diagonalization. The transition from a dense homogeneous charge distribution to a dilute localized Wigner--type electron arrangement is investigated. The influence of the long range part of the Coulomb interaction is studied. When the interaction is exponentially cut off the ``crystallized Wigner molecule is destroyed in favor of an inhomogeneous charge distribution similar to a charge density wave .
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